Ecological safety evaluation method for plateau characteristic agribusinesses based on knowledge granularity

Abstract

The ecological safety of plateau-characteristic agribusinesses (PCABs) encompasses not only environmental protection during production but also enhancing output without harming the ecosystem. Objectively evaluating PCABs’ ecological safety levels is crucial for making management decisions and promoting local sustainable development. However, existing evaluation methods fail to incorporate expert knowledge structures, leading to limitations in both scientific validity and practical applicability. To address this gap, we propose an ecological safety evaluation method based on knowledge granularity, tailored to PCABs. The evaluation process involves the following steps: first, numerous knowledge points across macro-, meso-, and micro-levels are organized, and a hierarchical knowledge structure is designed for experts to freely select. Second, using belief distribution functions, experts provide evaluation information at varying levels of knowledge granularity. Third, expert weights and reliability parameters are determined through entropy and similarity calculations. Subsequently, the generalized combination rule is applied to progressively integrate multilevel knowledge-granularity evaluation information, from bottom to top and from individual to group, producing high-quality group evaluations. Finally, the method is applied to a typical plateau specialty agribusiness; the results indicate that its ecological safety status is “good.” On that basis, we make targeted management recommendations.

Introduction

As a cornerstone of human survival, agriculture forms the lifeblood of social prosperity and stability. “Characteristic agriculture,” a new trend in agricultural development, refers to agriculture based on the market and on characteristics related to location, resources, and technology. According to function, characteristic agriculture can be further classified into modern agriculture with plateau characteristics¹organic agriculture², and urban agriculture³, among other forms. Compared with other types of specialty agriculture, plateau-characteristic agriculture plays an important role in producing regionally distinctive agricultural goods, improving regional ecological conservation capacity, and promoting sustainable development in plateau regions⁴.

Plateau-characteristic agribusinesses (PCABs) refer to enterprises engaged in production and processing for agriculture in plateau areas, with research and development, cultivation, breeding, processing, and the sale of locally distinctive agricultural products as their main business. However, the development of PCABs faces various ecological security problems. These include a more pronounced contradiction between humans and land, decreases in the area of arable land, the degradation of arable land, and threats to food security⁵. The plundering of arable land for cultivation has also led to surface pollution and excessive pesticide residue, threatening the quality and safety of agricultural products⁶. Moreover, the agricultural infrastructure remains imperfect, constraining food quality and production efficiency⁷. Such problems not only threaten local sustainable development but also pose challenges to global ecological security and development. As a result, ecological security and sustainable agricultural development have become important research topics.

Ecological security serves as a fundamental cornerstone for building resilient and sustainable social and economic systems. As a multidimensional concept, it encompasses three interconnected components: natural ecological security, social ecological security, and economic ecological security. Together, these components form an integrated and complex artificial ecological security system. In recent years, scholarly research on ecological security has witnessed significant advancement across multiple dimensions. Moreover, the academic research on ecological security has made significant progress in a number of dimensions. The scope of the research field has expanded considerably and the development of indicator systems has become increasingly complex. Additionally, researchers have adapted and applied a variety of assessment methods to effectively measure and analyze the state of ecological security.

Regarding research areas, studies have assessed ecological security levels in areas such as agriculture⁸, tourism⁹, land¹⁰, cities¹¹, watersheds¹², oceans¹³, grasslands¹⁴, and forests¹⁵. In terms of indicator systems, commonly used frameworks include the pressure-state-response model¹⁶ and its derivatives, such as the driving force-pressure-state-impact-response^17,18 and driving force-pressure-state-impact-response-management (DPSIRM)¹⁹ models. Researchers have also proposed models tailored to specific contexts, such as the technology-environment-resources-economy (TERE) model²⁰ and the production-operation-service (POS) model²¹. The methods used in the ecological safety evaluation process can be broadly divided into two main categories: numerical modeling methods and ecological modeling methods. Table 1 demonstrates the most commonly used methods in existing studies on ecological safety evaluation types.

Table 1 Commonly used ecological safety evaluation methods.

The 17 Sustainable Development Goals of the 2030 Agenda for Sustainable Development—especially Goal 2: “ending hunger, achieving food security, improving nutrition, and promoting sustainable agriculture”—offer guidance for research on sustainable agricultural development³⁴. Agricultural research has therefore shifted its focus from traditional objectives, such as enhancing production efficiency³⁵ and fostering technological innovation³⁶, to emphasizing rational resource utilization³⁷ensuring food security, maintaining agroecological safety³⁸, and achieving the broader goals of sustainable agricultural development³⁹.

Regarding agroecological security evaluation, the research focus has expanded from the environmental effects of agricultural production⁴⁰ to aspects such as resource utilization and socioeconomic dimensions^41,42,43. Methods have been designed based on multi-indicator decision analysis and complex evaluation models. Examples include the hierarchical DEMATEL approach for complex systems^44,45, generalized combinatorial rules for evidential reasoning⁴⁶, the agricultural resilience assessment tool⁴⁷, user-driven agricultural system models⁴⁸, the sustainable agriculture coordination multiobjective optimization model³³, and the deep learning agricultural system model⁴⁹. Regarding future development strategies, studies have proposed various programs based on science and technology application and innovative agricultural practices. Examples include the following: increasing agricultural science and technology innovation, improving the R&D and application capacity of agricultural machinery and equipment, accelerating the digital transformation of agriculture, improving production efficiency⁵⁰, promoting biotech and cleantech, developing climate-smart agriculture to promote green transformation^51,52, using big data and blockchain to share management experience and technology related to sustainable agriculture⁵³, constructing an agroecological security risk monitoring and early-warning mechanism, and strengthening the supervision of ecological protection and restoration^54,55.

In summary, some important results have emerged from research on ecological security and sustainable agricultural development. Nonetheless, there is still room for improvement in the research, both in terms of the specific research object (PCABs) and evaluation methods.

First, the evaluation indicators are not specific to PCABs. Although studies have constructed a number of ecological security evaluation index systems, they involve a variety of fields and are oriented toward macro-level ecological security from a holistic perspective. There is a lack of indicators closely related to the production and operation behaviors and results of enterprises. In addition, the ecological security of PCABs is affected by many unique local factors (e.g., climatic conditions, geographic environment, species resources, natural disaster occurrence, and slow economic development). It is debatable, then, whether existing evaluation indicators are suitable for evaluating the ecological security of PCABs.

Second, the choice of information processing and evaluation methods affects the accuracy of the results⁵⁶. Existing studies tend to focus on applied research, paying more attention to the evaluation results at the expense of the design of the evaluation method. Such negligence could affect the efficiency and effectiveness of evaluation, as current evaluation methods cannot effectively reflect the differences in expert knowledge structures in decision-making processes. Experts involved in evaluation and decision-making mainly come from government departments, higher education institutions, and research institutes, representing different professional fields or interest groups, and their knowledge structures might differ considerably. Government experts focus on macro-level policy and system-level considerations, academics excel at exploring mechanisms and theoretical frameworks, and research institute professionals specialize in micro-level technical research and data analysis. As a result, experts may vary in their familiarity with different aspects of ecological security. Requiring them to make overly specific judgments beyond their primary areas of expertise may inadvertently introduce bias or increase uncertainty in the evaluation results⁵⁷. Such differences in knowledge structures underscore the importance of the design of evaluation methods.

To address the lack of relevance in evaluation indicators, this study considers data accessibility, existing research results, and the actual situation of PCABs to identify 41 ecological security evaluation indicators for PCABs from macro-, meso-, and micro-level perspectives. Focusing on the problem of large differences in the knowledge structures of experts, we construct an ecological security evaluation method for PCABs based on the idea of knowledge granularity. First, we integrate the 41 indicators based on different logics to form three knowledge structures with a hierarchical nature to adapt to expert decision-making needs. Second, we use belief distribution functions to extract experts’ evaluation information and transform each expert’s qualitative judgment into quantitative probability values, overcoming the problem of differences in different experts’ understanding of the indicators. Third, we use the generalized combination (GC) rule^46,58 to integrate multilevel knowledge-granularity evaluation information from bottom to top and from individuals to groups, finally obtaining high-quality group evaluation information.

Next, “Preliminaries” introduces the prerequisites. Then, “The proposed method” introduces our ecological safety evaluation method for PCABs based on knowledge granularity. In “Case study simulation”, we apply our designed approach to a real case study to evaluate the ecological security level of a typical PCAB. “Conclusion” concludes and notes some directions for future research.

Preliminaries

This section introduces concepts related to knowledge granularity, the core concepts of the GC rule, and methods for automatically calculating weights and reliability.

Knowledge granularity

Knowledge points (KPs), which form the foundational units of any knowledge structure, represent the smallest independently comprehensible elements. A knowledge structure (KS) is the result of logically or systematically integrating these KPs into a hierarchical model, leading to a hierarchical decomposition of complex problems and an organized representation of knowledge. Knowledge granularity describes the precision level, hierarchical depth, or abstraction of different KPs within a KS. Specifically, fine-grained KPs have a higher degree of recognizability, provide more specific and detailed information, and are suitable for in-depth deconstruction and precise analysis. By contrast, coarse-grained KPs present a comprehensive character, can provide broader and more generalized information, and are more suitable for comprehensive understanding and decision-making from a holistic, macro-level perspective.

In multicriteria decision-making, KPs can be equated to evaluation criteria. The KS can be understood as a hierarchical structural model (evaluation indicator system) that is formed by integrating these KPs according to a specific logical rule or framework. Knowledge granularity, in turn, corresponds to the stratification of these metrics (e.g., Level 1, Level 2, and Level 3 metrics), with different levels of indicators reflecting different levels of precision, abstraction, and recognizability. The logic or rules for integrating KPs vary, leading to different KS. As shown in Fig. 1, both KS 1 and 2 consist of the same underlying elements (six KPs: f₁–f₆), but the logic of each KP in the integration process is different. In KS 1, KPs f₁–f₃ are synthesized to become Level 2 indicator $C_{{1 \supset 1}}^{1}$, KPs f₅ and f₆ are synthesized to become Level 2 indicator $C_{{2 \supset 1}}^{1}$, and KP f₄ is directly adopted as a Level 2 indicator $C_{{1 \supset 2}}^{1}$ due to its conceptual independence.

Fig. 1

The formation of KSs.

Subsequently, these two Level 2 indicators, $C_{{1 \supset 1}}^{1}$ and $C_{{1 \supset 2}}^{1}$ are synthesized to become Level 1 indicator $C_{1}^{1}$. The Level 2 indicator $C_{{2 \supset 1}}^{1}$ is directly adopted as the Level 1 indicator $C_{2}^{1}$. KS 2 employs a different logic, which results in a different hierarchy.

It is worth noting that knowledge granularity is the same across KPs within the same levels. At different levels, KPs at higher levels (e.g., Level 1 indicators) reflect coarser granularity and provide more general but less detailed insights. By contrast, KPs at lower levels (e.g., Level 3 indicators) reflect finer granularity and contain richer detail. For example, in Fig. 1, the Level 2 indicators $C_{{1 \supset 1}}^{1}$, $C_{{1 \supset 2}}^{1}$, and $C_{{2 \supset 1}}^{1}$ have the same knowledge granularity, while Level 1 indicator $C_{1}^{1}$ has coarser knowledge granularity than the three Level 2 indicators.

GC rule

The first generation of Dempster–Shafer (DS) evidence theory⁵⁹ and the second generation of evidential reasoning (ER)⁶⁰ have been widely used to analyze multicriteria decision-making scenarios in uncertain environments. However, DS is unable to distinguish between the weight and reliability of evidence, and ER involves three infeasible aspects: reliability dependence, unreliability effectiveness, and intergeneration inconsistency. Therefore, Du et al.⁴⁶ established a GC rule that incorporated both weight and confidence for DS and ER, effectively overcoming the abovementioned problems. The GC rule, as a generalized form of the evidence combination rule, is more versatile and flexible in dealing with uncertain scenarios, and ER and DS can be regarded as its two special cases.

Definition 1

⁵⁹. Suppose $\Theta =\left\{ {{\theta _j}|j=1,2, \ldots ,J} \right\}$ is a finite complete set composed of J mutually exclusive hypotheses; it is called a frame of discernment, and ${\theta _j}$ is the ${j^{th}}$ hypothesis. The power set $P(\Theta )$ or ${2^\Theta }$ of $\Theta$ that is composed of 2^J elements is usually expressed as follows:

$${2^\Theta }=P(\Theta )=\left\{ {\emptyset ,{\theta _1}, \cdots ,{\theta _J},\left\{ {{\theta _1},{\theta _2}} \right\}, \cdots ,\left\{ {{\theta _1},{\theta _J}} \right\}, \cdots ,\left\{ {{\theta _1},{\theta _{J - 1}}} \right\},\Theta } \right\}$$

(1)

Definition 2

⁶⁰. Suppose $\left[ {\theta ,{p_i}(\theta )} \right]$ represents evidence ${e_i}(i=1,2 \ldots ,I)$ showing that proposition $\theta$ occurs with probability ${p_i}(\theta )$. Then, the belief distribution (BD) functions of evidence e_i can be denoted by a profiled expression, given by

$$bi=\left\{ {\left[ {\theta ,{p_i}(\theta )} \right]|\forall \theta \subseteq \Theta ,0 \leq {p_i}(\theta ) \leqslant 1,\sum\nolimits_{{\theta \subseteq \Theta }} {{p_i}(\theta )} =1} \right\}$$

(2)

where $\theta$ is an arbitrary subset of $\Theta$.

Definition 3

⁶⁰. Suppose a mapping function $m:{2^\Theta } \to ~\left[ {0,1} \right]$ on the frame of discernment $\Theta =\left\{ {{\theta _j}|j=1,2, \ldots ,J} \right\}$ satisfies

$$\left\{ \begin{gathered} m(\theta )=0{\text{ }}\theta {\text{=}}\emptyset \hfill \\ m(\theta ) \geq 0,\sum\nolimits_{{\theta \subseteq {\text{ }}\Theta }} {m(\theta )=1{\text{ }}\theta \ne \emptyset } \hfill \\ \end{gathered} \right.$$

(3)

Then, $m(\theta )$ is called the basic probability assignment (BPA) function of $\theta$. If $m(\theta )>0$, $\theta$ is called the focal element of the BPA function.

In GC rules, the BPA function refers to the result obtained by the generalized discounting of BD functions. The generalized discounting method is described below.

Definition 4

⁴⁶. Suppose ${p_i}(\theta )$ indicates the belief degree that evidence e_i supports proposition $\theta$, and the weight and reliability of e_i are w_i and r_i, respectively, where $0 \leq {w_i} \leq 1,\sum\nolimits_{{i=1}}^{I} {{w_i}} =1,0 \leq {r_i} \leq 1,{\hbox{max} _{1 \leq i \leq I}}{r_i}=1$. Then, the weighted BD with reliability for evidence e_i can be calculated by the generalized discounting method:

$${m_i}(\theta )=\left\{ \begin{gathered} 0{\text{ }}\theta =\emptyset \hfill \\ {w_i} \cdot {r_i} \cdot {p_i}{\text{(}}\theta {\text{) }}\theta \subset \Theta \hfill \\ {w_i} \cdot {r_i} \cdot {p_i}(\theta )+{w_i}(1 - {r_i}){\text{ }}\theta =\Theta \hfill \\ 1 - {w_i}{\text{ }}\theta =P(\Theta ) \hfill \\ \end{gathered} \right.$$

(4)

When different pieces of evidence are in extreme conflict, the fusion result might be counterintuitive. This can be avoided when evidence with weight and reliability is discounted using a generalized discounting method.

Next, the BPA functions ${m_i}(\theta )$ need to be fused. The fusion of multiple independent evidences can be achieved using the analytical algorithm in the analytical GC rule.

Definition 5

⁵⁸. Suppose I pieces of independent evidence are ${e_1}, \ldots ,{e_I}$; their BPA functions discounted by generalized discounting are ${m_1}(\theta ), \ldots ,{m_I}(\theta )$. Then, the fusion result ${\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{m} _{e(i)}}(\theta )$ of these evidences can be obtained as follows:

$${\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{m} _{e(I)}}(\theta )=\left\{ \begin{gathered} \Pi _{{i=1}}^{I}\sum\nolimits_{{\theta \subseteq {X_i}}} {{m_i}({X_i})} - \sum\nolimits_{{\theta \subset {X_i}}} {{m_i}({X_i})} +\sum\nolimits_{{ \cap _{{i=1}}^{I}{X_i}=\theta ,\forall {X_i} \ne \theta }} {\Pi _{{i=1}}^{I}{m_i}({X_i}),\theta \subseteq \Theta } \hfill \\ \Pi _{{i=1}}^{I}{m_i}\left[ {P\left( \Theta \right)} \right],\theta =P\left( \Theta \right) \hfill \\ \end{gathered} \right.$$

(5)

After obtaining the fusion results, we also need to perform normalization.

Definition 6

⁵⁸. Suppose the result of the fusion of ${e_1}, \cdots ,{e_I}$ is ${\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{m} _{e(I)}}(\theta )$, as in Eq. (5). The final combined degree of belief to which I pieces of independent evidence jointly support proposition $\theta$ for $\forall \theta \subseteq \Theta$ is given by

$$p(\theta )=\frac{{{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{m} }_{e(I)}}(\theta )}}{{\sum\nolimits_{{\theta \subseteq \Theta }} {{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{m} }_{e(I)}}(\theta )} }}{\text{,}}\theta \subseteq \Theta $$

(6)

where $0 \leqslant {p_{e(I)}}(\theta ) \leq 1$, $\forall \theta \subseteq \Theta$, and $\sum\nolimits_{{\theta \subseteq \Theta }} {{p_{e(I)}}(\theta )} =1$.

Finally, we perform “pignistic” probability transformation to obtain the probability of each proposition.

Definition 7

⁶¹. Suppose $\Theta =\left\{ {{\theta _j}|j=1,2, \ldots ,J} \right\}$ is the frame of discernment, and the arbitrary nonempty subset of $\Theta$ is $\theta$, whose BPA function is denoted by $m(\theta )$. Then, the pignistic probability $BetP({\theta _j})$ of ${\theta _j}$ can be defined as follows:

$$BetP({\theta _j})=\sum\nolimits_{{\theta \subseteq \Theta ,{\theta _j} \in \theta }} {\frac{{m(\theta )}}{{\left| \theta \right|}}} ,j=1,2, \ldots ,J$$

(7)

where j refers to the ordinal number of proposition $\theta$, $\left| \theta \right|$ is the cardinality of $\theta$, and $BetP({\theta _j})$ represents the probability that proposition ${\theta _j}$ occurs.

Method for calculating reliability and weights

The weight of evidence reflects the relative importance of that evidence, which can be determined by calculating the Deng entropy value of the evidence. Specifically, the lower the Deng entropy value of the evidence, the lower its uncertainty and the more favorable it is for experts to make decisions. We can then assume that the more important the evidence is, the greater the weight.

Definition 8

⁶². Suppose $\Theta =\left\{ {{\theta _j}|j=1,2, \ldots ,J} \right\}$ is the frame of discernment, the arbitrary nonempty subset of $\Theta$ is $\theta$, and $m(\theta )$ is a BPA function defined on $\Theta$; then, Deng entropy is defined as follows:

$$E= - \sum\nolimits_{{\theta \subseteq \Theta }} {m(\theta ){{\log }_2}} \frac{{m(\theta )}}{{{2^{\left| \theta \right|}} - 1}}$$

(8)

where $\left| \theta \right|$ refers to the cardinality of $\theta$.

Definition 9

⁶³. Suppose the Deng entropy of evidence ${e_i}$$(i=1,2, \ldots ,I)$ is ${E^i}$; then, the weight ${w_i}$ of evidence ${e_i}$ can be calculated using the following equation:

$${w_i}=\frac{{{E^i}}}{{\sum\nolimits_{{i=1}}^{I} {{E^i}} }}$$

(9)

.

The reliability of the evidence reflects the accuracy of the expert’s opinion and can be determined by calculating the degree of similarity between the pieces of evidence. Group decision-making generally assumes that the truth is in the hands of the majority and that the majority opinion is always correct. Therefore, if the evidence provided by a particular expert is highly similar to the evidence provided by the majority of experts, then that expert’s opinion can be considered more accurate and reliable. Conversely, if the evidence provided by an expert significantly differs from the evidence provided by other experts, the expert’s opinion might be considered inconsistent with the majority opinion and less reliable.

Definition 10

⁶⁴. Suppose ${m_1}(\theta )$ and ${m_2}(\theta )$ are two BPA functions with the same frame of discernment $\Theta$, ${\theta _n}$ is the n_th element in the power set $P(\Theta )$, and $\left| {P(\Theta )} \right|$ is the cardinality of $P(\Theta )$. Then, the Euclidean distance $D({m_1},{m_2})$ and similarity $S({m_1},{m_2})$ between the two BPA functions can be defined as follows:

$$D({m_1},{m_2})=\frac{1}{{\sqrt 2 }}\sqrt {\sum\nolimits_{{n=1}}^{{\left| {P(\Theta )} \right|}} {{{\left[ {{m_1}\left( {{\theta _n}} \right) - {m_2}\left( {{\theta _n}} \right)} \right]}^2}} } $$

(10a)

$$S({m_1},{m_2})=1 - D({m_1},{m_2})$$

(10b)

Definition 11

⁶⁵. Suppose ${\bar {S}_i}$ denotes the average similarity of expert ${e_i}$. Then, the reliability of the evidence provided by expert ${e_i}$ can be calculated using the following equation:

$${r_i}=\frac{{{{\bar {S}}_i}}}{{\hbox{max} ({{\bar {S}}_1},{{\bar {S}}_2}, \ldots {{\bar {S}}_I})}}$$

(11)

where ${\bar {S}_i}=\sum\nolimits_{{i^{\prime}=1}}^{I} {S({m_i},{m_{i^{\prime}}})} /I$, $S({m_i},{m_{i^{\prime}}})$ is the similarity between ${m_i}(\theta )$ and ${m_{i^{\prime}}}(\theta )$, and ${m_i}(\theta )$ and ${m_{i^{\prime}}}(\theta )$ (with the same frame of discernment $\Theta$) are BPA functions provided by experts ${e_i}$ and ${e_{i^{\prime}}}$$(i,i^{\prime}=1,2, \ldots ,I)$, respectively.

The proposed method

In this section, we will construct the ecological security evaluation method of PCABs based on the perspective of knowledge granularity. First, we sorted the evaluation indices of PCABs from three perspectives, namely, macro, meso and micro, and then combined these evaluation indices according to different logics to form three KSs with a hierarchical nature. Then, examples are given to illustrate how to use BD functions to extract evaluation information with knowledge granularity, how to determine the weights of experts, the reliability parameter and how to fuse these evaluation information. Finally, the process of determining the evaluation level is described.

Design of evaluation indicators

The selection of evaluation indicators is crucial for ensuring both scientific rigor and practical applicability of assessment outcomes. Based on literature review and considering data availability and the actual situation of PCABs, we identified 41 indicators across the macro, meso and micro levels as detailed in Table 2⁶⁶.

Macro-level indicators provide insights into the overarching trends and conditions of plateau regions, with data typically sourced from local government agencies. These factors include core indicators such as the ecological quality index, biodiversity, per capita water resources, and soil and water conservation rates. The plateau regions’ natural conditions, including abundant sunlight, deep soil, and clean water sources, provide a foundational advantage for PCAB raw material production. However, the ecosystems in this region are relatively fragile and have weak resistance to environmental changes. The above macro indicators reflect the regional resource and environmental characteristics upon which PCAB’s plateau farms and pastures (i.e., the production side) depend, as well as the overall pressures they face, providing an important basis for policymakers to regulate regional resources and protect the ecological environment.

Mesoscale indicators focus on depicting the development trends and common characteristics of the plateau-characteristic agriculture industry chain or cluster. These include the overall output of plateau-characteristic agriculture, the average sewage treatment rate across the industry, the extent of its contribution to local farmer employment, and the number of enterprises recognised as leaders in agricultural industrialisation. The production methods of PCABs emphasise green and sustainable practices. Meso-level indicators highlight the importance of balancing ecological sustainability with industrial development and economic goals, reflecting the common environmental carrying capacity and operational constraints faced by PCAB industrial clusters in the process of applying modern technology to optimise productivity.

Micro-level indicators focus on the production and operational activities of individual enterprises, directly determining their ecological safety performance. Examples include the fertiliser utilisation rate of crops on enterprise-owned farms, the resource utilisation rate of livestock manure, the number of “ three products and one standard ” certifications obtained by the enterprise, and the intensity of R&D investment. While the highland environment provides high-quality raw materials, enterprises must invest in scientific and technological personnel to optimise cultivation techniques and develop stress-resistant crop varieties that an adapt to climate fluctuations, thereby transforming natural advantages into product competitiveness. The core value of micro-level indicators lies in revealing how individual companies respond to macro-level constraints and meso-level industry trends, achieving sustainable production through specific management practices and technological applications (such as clean energy equipment).

Table 2 Indicators for evaluating the ecological security of PCABs.

Design of KSs

To support flexible evaluation and reflect differences in expert knowledge, we adopt a hierarchical structure for constructing the knowledge models. In this structure, higher-level indicators represent more abstract or aggregated concepts (coarse granularity), while lower-level indicators represent specific, detailed knowledge units (fine granularity). This design not only aligns with the principle of knowledge granularity, but it also enables the integration of evaluation inputs from decision-makers at different levels—such as policymakers, domain experts, and technical staff—according to their cognitive capabilities and professional knowledge. Such layered structures are commonly used in multi-criteria decision analysis and enhance both clarity and practical applicability.

To implement this idea, we integrated the 41 indicators in Table 2 based on different logic frameworks (specifically using DPSIRM, TERE, and POS as the guiding models) and constructed three different hierarchical KSs, denoted as: $KS=\left\{ {k{s_n}|n=1,2,3} \right\}=\left\{ {k{s_1},k{s_2},k{s_3}} \right\}$.

These KSs differ in their logical integration of KPs, resulting in variations in the first- and second-level indicators, even though the evaluation object and the third-level indicators (lowest-level indicators) remain consistent across all structures. The “framing effect”⁸⁰ suggests that the manner in which information is presented can alter people’s perceptions and choices. Specifically, variations in presentation styles, context settings, or descriptions can significantly influence decision-makers’ perceptions and behaviors, subsequently shaping their judgments. This underscores the importance of presenting knowledge in multiple forms. By designing multiple KS, we enable the analysis of problems from diverse, multidimensional perspectives. This flexibility is particularly advantageous in decision-making, where considering alternative frameworks often leads to more informed and balanced outcomes.

We use the notation $\supset$ to describe the hierarchical nesting relationship between the indicators in each layer within the KS. All KSs constructed in this study are three-layer nested structures. Thus, in the $k{s_n}$$(n=1,2,3)$, the k_th indicator in the h_th layer can be denoted as $C_{{{k_1} \supset \cdots \supset {k_h}}}^{n}$, where ${k_h}=1,2, \ldots ,{K_{{k_1} \supset \cdots \supset {k_{h - 1}}}}$; the internal framework of the h_th layer can be denoted as $C_{h}^{n}=\left\{ {C_{{{k_1} \supset \cdots \supset {k_h}}}^{n}|{k_1}=1,2, \ldots ,{K_{{k_0}}},{k_2}=1,2, \ldots ,{K_{{k_1}}},{k_3}=1,2, \ldots ,{K_{{k_1} \supset {k_2}}}} \right\}$; and the framework of the $k{s_n}$ can be denoted as ${C^n}=\left\{ {C_{h}^{n}|h=1,2,3} \right\}=\left\{ {C_{1}^{n},C_{2}^{n},C_{3}^{n}} \right\}$.

DPSIRM KS

We hierarchically integrate the 41 evaluation indicators in Table 2 based on DPSIRM¹⁹ to form the $k{s_1}$. The model organizes and analyzes the mechanisms of action of six interrelated factors—drive (D), pressure (P), state (S), impact (I), response (R), and management (M)—providing a comprehensive evaluation framework from the perspective of sustainable development.

• The $k{s_1}$ follows a three-layered hierarchy. It consists of layer 1 indicators, ${C_1},{C_2}, \ldots ,{C_6}$, at the guideline level; layer 2 indicators, ${C_{1 \supset 1}},{C_{1 \supset 2}}, \ldots ,{C_{6 \supset 2}}$, at the subguideline level; and layer 3 indicators, ${C_{1 \supset 1 \supset 1}},{C_{1 \supset 1 \supset 2}}, \ldots ,{C_{6 \supset 2 \supset 3}}$, at the knowledge unit level. The layer 2 indicators can be seen as the result of integrating the layer 3 indicators (KPs). For example, in Fig. 2, by integrating “natural population growth rate” ${C_{1 \supset 1 \supset 1}}$ and “urbanization rate” ${C_{1 \supset 1 \supset 2}}$, we obtain the layer 2 indicator “social driver” ${C_{1 \supset 1}}$. Similarly, the layer 1 indicators can be seen as the result of integrating the layer 2 indicators. In Fig. 2, by integrating the two layer 2 indicators “social driver” and “economic driver,” we obtain the layer 1 indicator “driver”. Subsequent hierarchies of $k{s_2}$ and $k{s_3}$ are also the same.

Fig. 2

The hierarchical diagram of ks₁.

TERE KS

We hierarchically integrate the 41 evaluation indicators in Table 2 based on the TERE model²⁰ to form the $k{s_2}$. The structure reflects the dynamics of the carrying capacity of local ecosystems through the mechanism of the interaction of four elements: technology (T), economy (E), resources (R), and environment (E). The $k{s_2}$ follows a three-layer hierarchy, as shown in Fig. 3. It consists of layer 1 indicators, ${C_1},{C_2}, \ldots ,{C_4}$, at the guideline level; layer 2 indicators, ${C_{1 \supset 1}},{C_{1 \supset 2}}, \ldots ,{C_{4 \supset 3}}$, at the subguideline level; and layer 3 indicators, ${C_{1 \supset 1 \supset 1}},{C_{1 \supset 1 \supset 2}}, \ldots ,{C_{4 \supset 3 \supset 3}}$, at the knowledge unit level.

Fig. 3

The hierarchical diagram of ks₂.

POS KS

We hierarchically integrate the 41 evaluation indicators in Table 2 based on the POS model²¹ to form the $k{s_3}$. This structure organizes ecological security evaluation indicators around production (P), operation (O), and service (S), focusing on agricultural modernization and efficiency. The $k{s_3}$ follows a three-layer hierarchy, as shown in Fig. 4. It consists of layer 1 indicators, ${C_1},{C_2},{C_3}$, at the guideline level; layer 2 indicators, ${C_{1 \supset 1}},{C_{1 \supset 2}}, \ldots ,{C_{3 \supset 4}}$, at the subguideline level; and layer 3 indicators, ${C_{1 \supset 1 \supset 1}},{C_{1 \supset 1 \supset 2}}, \ldots ,{C_{3 \supset 4 \supset 3}}$, at the knowledge unit level.

Fig. 4

The hierarchical diagram of ks₃.

Individual evaluation information extraction with knowledge granularity

Assume the main body of evaluation is the expert e_i $(i=1,2, \ldots ,I)$, the object of evaluation is PCAB, the evaluation problem is the ecological safety level of the enterprise, and the evaluation index system is $k{s_1},k{s_2},k{s_3}$ constructed in “Design of KS”. Each expert can choose one of the three KSs and make a direct evaluation of any KP at any level of granularity. It might be appropriate to set expert e_i $(i=1,2, \ldots ,I)$ to use $k{s_n}$$(n=1,2,3)$ to make a direct evaluation of KP $C_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}$$({k_h}=1,2, \ldots ,{K_{{k_1} \supset \cdots \supset {k_{h - 1}}}},h=1,2,3)$.

Although the above process can ensure that the expert’s KS is accurately reflected in the evaluation, it cannot reflect the expert’s uncertainty and overall judgment characteristics in the evaluation process. According to definition 2, the BD functions represent an individual expert assigning his/her beliefs (probabilities) for any outcome $\theta$ in the discrimination framework $\Theta$. To improve the efficiency and effectiveness of evaluation, experts are here asked to use the BD functions to provide judgment information.

Specifically, first, assume the discrimination framework describing all evaluation outcomes of the subject of the evaluation is $\Theta =\left\{ {{\theta _j}|j=1,2, \ldots ,J} \right\}$, where ${\theta _j}$ denotes a possible evaluation result; for instance, $\Theta =\left\{ {{\theta _1},{\theta _2},{\theta _3}} \right\}=\left\{ {{\text{Worst,Average}},{\text{Excellent}}} \right\}$. Second, expert e_i selects the KPs $C_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}$ of any granularity in the $k{s_n}$ and uses the BD functions to provide direct judgment information. This is the process of assigning probability $p_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}(\theta )$ (the probability of judgment $\theta$ occurring) to one or more outcomes $\theta$ that are most likely to occur in $\Theta$. At this point, the BD functions can be expressed as

$$b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}=\left\{ {\left[ {\theta ,p_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}(\theta )} \right]|0 \leq p_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}(\theta ) \leq 1,\forall \theta \subseteq \Theta ,\sum\nolimits_{{\theta \subseteq \Theta }} {p_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}(\theta )} =1} \right\}$$

(12)

where $n=1,2, \ldots ,N$, $i=1,2, \ldots ,I$, ${k_h}=1,2, \ldots ,{K_{{k_1} \supset \cdots \supset {k_{h - 1}}}}$, and $h=1,2, \ldots ,H$.

Finally, when experts is unable to make a judgment on certain KPs due to a lack of information, insufficient knowledge, or another limitation  (which we call empty KPs), we assign a default BD function $b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}=\left\{ {(\Theta ,1.000)} \right\}$. This BD function indicates that the expert assigns full probability to the entire discrimination framework $\Theta$; that is, the expert does not express a preference for any particular outcome.

The above mechanism has three advantages. First, as shown in Fig. 5, the expert can freely choose one of $k{s_1},k{s_2},k{s_3}$ to make a judgment to suit his/her decision-making needs. Second, the mechanism can reflect the overall judgment information of the expert. As shown in Fig. 5, the expert can evaluate the KPs of all layers (layers 1–3) to provide his/her direct evaluation information.

Third, the mechanism can effectively reflect uncertainty in the evaluation process. As shown in Fig. 5, the expert e_i chose to evaluate the three KPs in layer 3: $C_{{1 \supset 2 \supset 1}}^{{1\sim i}}=\{ {f_3}\}$, $C_{{1 \supset 2 \supset 2}}^{{1\sim i}}=\left\{ {{f_4}} \right\}$, and $C_{{1 \supset 2 \supset 3}}^{{1\sim i}}=\left\{ {{f_5}} \right\}$. At this time, the expert only needs to use the BD functions to provide incomplete information. Assume that the expert’s immediate judgment is as follows: (1) 80% probability of “average” $({\theta _2})$ and 20% probability of “excellent” $({\theta _3})$; (2) 30% probability of “worst” $({\theta _1})$ and 70% probability of either “average” or “excellent” $({\theta _2},{\theta _3})$; (3) no specific judgment can be made, so the entire discrimination framework is assigned full probability (100%). As a result, we can obtain three BD functions: $b_{{1 \supset 2 \supset 1}}^{{1\sim i}}=\left\{ {({\theta _2},0.800),({\theta _3},0.200)} \right\}$, $b_{{1 \supset 2 \supset 2}}^{{1\sim i}}=\left\{ {({\theta _1},0.300),\left[ {\left( {{\theta _2},{\theta _3}} \right),0.700} \right]} \right\}$, and $b_{{1 \supset 2 \supset 3}}^{{1\sim i}}=\left\{ {(\Theta ,1.000)} \right\}$. The above mechanism is sufficient to significantly reduce the interference of uncertainty factors in the evaluation process.

It is important to note that the expert can assign probabilities not only to a single outcome but also to multiple outcomes. For example, in the BD function $b_{{1 \supset 2 \supset 2}}^{{1\sim i}}=\left\{ {({\theta _1},0.300),\left[ {\left( {{\theta _2},{\theta _3}} \right),0.700} \right]} \right\}$, $\left[ {\left( {{\theta _2},{\theta _3}} \right),0.700} \right]$ means the expert is not sure whether the KP should be rated as  “average” or “excellent,” but is confident that one of these two outcomes has a 70% probability of being true.

Fig. 5

Expert e_i’s evaluation information extraction process.

Evaluation of information fusion mechanisms, processes and models

After experts use BD functions to provide direct judgment information with different knowledge granularities, they need to integrate a large amount of information. The GC rule is designed to deal with multicriteria decision-making problems in uncertain environments. It overcomes the limitations of the first-generation DS theory of evidence and the second-generation theory of ER and can integrate the weight and reliability of the evidence. The method deals with a large amount of uncertain information in the decision-making process by means of evidence fusion and is very suitable for dealing with the fusion of BD functions in this study.

Based on the idea of the GC rule, the fusion mechanism of evaluation information can be summarized as discount–fusion–redistribution (DFR). The fusion process can be divided into two parts: fusion of individual evaluation information and fusion of group evaluation information. The fusion idea generally follows an order from bottom to top (low layer→high layer) and from individual (one expert) to group (all experts).

DFR fusion process

For any two adjacent layers, the evaluation information of the bottom layer is subjected to DFR fusion calculation, and the information of the top layer is obtained. The process of DFR fusion calculation is as follows:

As shown in Fig. 6, each expert selects a KS for judgment, and expert e_i selects ks_n. Ks_n can be decomposed into h layers, and in layer h-1, KP $C_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{n}$ can be decomposed into a number of KPs ($C_{{{k_1} \supset \cdots \supset 1}}^{n}, \cdots ,C_{{{k_1} \supset \cdots \supset {k_h}}}^{n}$) in layer h. The BD functions of KPs $C_{{{k_1} \supset \cdots \supset 1}}^{n}, \cdots ,C_{{{k_1} \supset \cdots \supset {k_h}}}^{n}$ can be expressed as $b_{{{k_1} \supset \cdots \supset 1}}^{{n\sim i}}, \cdots ,b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}$, respectively.

Fig. 6

The DFR process for GC rules.

Step 1 Discounting.

We substitute $b_{{{k_1} \supset \cdots \supset 1}}^{{n\sim i}}, \cdots ,b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}$ into Eq. (4) and discount them using the generalized discounting method, and the result obtained is called the BPA function, where the BPA function $m_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}$ of BD function $b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}$ can be expressed as

$$m_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}=\left\{ \begin{gathered} 0{\text{ }}\theta =\emptyset \hfill \\ w\left( {b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}} \right) \cdot r\left( {b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}} \right) \cdot p_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}{\text{(}}\theta {\text{) }}\theta \subset \Theta \hfill \\ w\left( {b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}} \right) \cdot r\left( {b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}} \right) \cdot p_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}(\Theta )+w\left( {b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}} \right) \cdot \left[ {1 - r\left( {b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}} \right)} \right]{\text{ }}\theta =\Theta \hfill \\ 1 - w\left( {b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}} \right){\text{ }}\theta =P(\Theta ) \hfill \\ \end{gathered} \right.$$

(13)

where $n=1,2,3$, $i=1,2, \ldots ,I$, ${k_h}=1,2, \ldots ,{K_{{k_1} \supset \cdots \supset {k_h}}}$, and $h=1,2,3$.

Step 2 Fusing.

Then, substituting the above BPA function into Eq. (5) for fusion yields $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{m} _{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$, which we call the synthesized BPA (S-BPA) function, as follows:

The above BPA function is fused by substituting it into Eq. (5) to obtain X, which we call

$$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{m} _{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}=\left\{ {\left[ {\theta ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{m} _{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}\left( \theta \right)} \right]|0 \leqslant \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{m} _{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}\left( \theta \right) \leqslant 1,\forall \theta \in P\left( \Theta \right),\sum\nolimits_{{\theta \in P\left( \Theta \right)}} {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{m} _{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}\left( \theta \right)=1} } \right\}$$

(14)

where $n=1,2,3$, $i=1,2, \ldots ,I$, ${k_h}=1,2, \ldots ,{K_{{k_1} \supset \cdots \supset {k_{h - 1}}}}$, and $h=1,2,3$.

Step 3 Redistributing.

Substituting the above S-BPA function $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{m} _{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$ into Eq. (6) redistributes the probability of $P(\Theta )$ to the other focal elements. The obtained result $f_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$ we call the redistributed synthesized BPA (RS-BPA) function, which can be expressed as follows:

$$f_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}=\left\{ {\left[ {\theta ,f_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}\left( \theta \right)} \right]|0 \leqslant f_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}\left( \theta \right) \leqslant 1,\forall \theta \subseteq \Theta ,\sum\nolimits_{{\theta \subseteq \Theta }} {f_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}\left( \theta \right)=1} } \right\}$$

(15)

where $f_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}\left( \theta \right)=\frac{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{m} _{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}\left( \theta \right)}}{{\sum\nolimits_{{\theta \subseteq \Theta }} {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{m} _{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}\left( \theta \right)} }}$, $n=1,2,3$, $i=1,2, \ldots ,I$, ${k_h}=1,2, \ldots ,{K_{{k_1} \supset \cdots \supset {k_{h - 1}}}}$, and $h=1,2,3$.

The DFR fusion calculation ends here, at which point the RS-BPA function $f_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$ contains information about the evaluation of KP $C_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{n}$ by expert e_i.

Process of individual evaluation information fusion

The fusion of individual evaluation information: Within the given KS, the BD functions are calculated by fusing the DFR from a low layer to a high layer. The final fusion result we call the (individual) comprehensive evaluation information.

In this study, evaluation information can be divided into two categories. The first is direct evaluation information: information obtained by an expert who uses BD functions to make judgments about the status of particular KPs based on existing knowledge and conditions. As shown in Fig. 6, expert e_i had evaluated the KP $C_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{n}$ in layer h-1 using the BD function $b_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$. $b_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$ then represented the direct evaluation information of expert e_i on KP $C_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{n}$.

The second category is indirect inference information. The information does not come from the direct judgment of a particular KP but is the inferential result obtained from the DFR fusion calculation of the evaluation information of its subordinate KPs. As shown in Fig. 6, KP $C_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{n}$ in layer h-1 can be decomposed into a number of KPs $C_{{{k_1} \supset \cdots \supset 1}}^{n}, \ldots ,C_{{{k_1} \supset \cdots \supset {k_h}}}^{n}$ in layer h, and their direct evaluation information is denoted as $b_{{{k_1} \supset \cdots \supset 1}}^{{n\sim i}}, \ldots ,b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}$, respectively. We perform DFR fusion computation on the direct evaluation information to obtain the RS-BPA function $f_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$. $f_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$ then represents the indirect inference information of expert e_i on KP $C_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{n}$.

In this study, individual evaluation information is mainly divided into two stages. First, direct evaluation information from the same layer is merged, and then it is used as indirect inference information and merged with direct evaluation information from the upper layer across layers. This process is repeated according to the hierarchical structure until the top layer is reached.

• (1) Basic nested structure.

The basic nested structure (BNS) is the smallest unit within a KS that involves nested relationships. A BNS consists of a higher-layer indicator and its corresponding lower-layer subindicators. A BNS with $C_{{{k_1} \supset \cdots \supset {k_h}}}^{n}$ as the highest layer indicator can be denoted by $\langle C_{{{k_1} \supset \cdots \supset {k_h}}}^{n}=\left\{ {C_{{{k_1} \supset \cdots \supset {k_{h+1}}}}^{n}|{k_{h+1}}=1,2, \ldots ,{K_{{k_1} \supset \cdots \supset {k_h}}}} \right\}$, where $h=1,2, \ldots H$, and ${k_{h+1}}$, and ${K_{{k_1} \supset \cdots \supset {k_h}}}$ represent the ordinal and total number of subindicators in the BNS $\langle C_{{{k_1} \supset \cdots \supset {k_h}}}^{n}$, respectively. As shown in Fig. 7, in BNS $\langle C_{{1 \supset 2}}^{1}$, indicator $C_{{1 \supset 2}}^{1}$ can be decomposed into three subindicators: $\langle C_{{1 \supset 2}}^{1}=\left\{ {C_{{1 \supset 2 \supset 1}}^{1},C_{{1 \supset 2 \supset 2}}^{1},C_{{1 \supset 2 \supset 3}}^{1}} \right\}$.

Fig. 7

Individual evaluation information fusion process.

Owing to the nested relationship, $C_{{{k_1} \supset \cdots \supset {k_h}}}^{n}$ is both the top indicator for BNS $\langle C_{{{k_1} \supset \cdots \supset {k_h}}}^{n}$ and one of the subindicators for BNS $\langle C_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{n}$. As shown in Fig. 7, indicator $C_{{1 \supset 2}}^{1}$ is both a top indicator for BNS $\langle C_{{1 \supset 2}}^{1}$ and a subindicator for BNS $\langle C_{1}^{1}$.

• (2) Indicator weight and reliability.

The entire process of fusing individual evaluation information involves only a single expert. Thus, the reliability of the evaluation information provided by this expert for all indicators can be assumed to be 1 (i.e., $r=1.000$).

However, the evaluation information provided by this expert for different indicators has different weights. The weights of the indicators are determined by the expert to reflect the goal-oriented nature of the evaluation. Within each BNS, the sum of the weights of its subindicators is 1. For example, as shown in Fig. 7, in the BNS $\langle C_{{1 \supset 2}}^{1}$, the sum of the weights of its subindicators f₃ $(C_{{1 \supset 2 \supset 1}}^{1})$, f₄$(C_{{1 \supset 2 \supset 2}}^{1})$, and f₅ $(C_{{1 \supset 2 \supset 3}}^{1})$ is 1.

• (3) Two main stages of fusion.

Based on the fusion path, we first perform the fusion of evaluation information within a single layer. Suppose the expert e_i chooses to evaluate the $k{s_n}$. Then, the BD functions of the subindicators $C_{{{k_1} \supset \cdots \supset {k_h}}}^{n}$ of BNS $\langle C_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{n}$ in $k{s_n}$ can be expressed as $b_{{{k_1} \supset \cdots \supset {k_h}}}^{{n\sim i}}$.

We perform a DFR fusion calculation of these BD functions $C_{{{k_1} \supset \cdots \supset {k_h}}}^{n}$ to obtain the RS-BPA function $f_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$, as shown in Eq. (15). $f_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$ represents the indirect inferred information about the top indicator $C_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{n}$ of the BNS $\langle C_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{n}$ by expert e_i.

Next, cross-layer fusion is performed. The expert e_i can also directly evaluate the indicator $C_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$, using the BD function $b_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$ to represent its evaluation information. It is not difficult to find that at this point, both $f_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$ and $b_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$ contain the evaluation information of the expert e_i on indicator $C_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$. We perform DFR fusion computation on them (they are equally important, with a weight of 0.5 each; i.e., $w(f_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}})=w(b_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}})=0.5$).

The process of fusing the direct evaluation information of experts on an indicator and the indirect inference information is called cross-layer fusion. The result of the fusion is denoted as $f_{{k_1} \supset \cdots \supset {k_{h - 1}}}^{\prime n\sim i}$, which represents the total evaluation information of the expert e_i on the indicator $C_{{{k_1} \supset \cdots \supset {k_{h - 1}}}}^{{n\sim i}}$ and is expressed as follows:

$$f_{{k_1} \supset \cdots \supset {k_{h - 1}}}^{\prime n\sim i} = \left\{ {\left[ {\theta ,f_{{k_1} \supset \cdots \supset {k_{h - 1}}}^{\prime n\sim i}\left( \theta \right)} \right]|0 \le f_{{k_1} \supset \cdots \supset {k_{h - 1}}}^{\prime n\sim i}\left( \theta \right) \le 1,\forall \theta \subseteq \Theta ,\sum\nolimits_{\theta \subseteq \Theta } {f_{{k_1} \supset \cdots \supset {k_{h - 1}}}^{\prime n\sim i}\left( \theta \right) = 1} } \right\}$$

(16)

where $n=1,2,3$, $i=1,2, \ldots ,I$, ${k_h}=1,2, \ldots ,{K_{{k_1} \supset \cdots \supset {k_{h - 1}}}}$, and $h=1,2,3$.

Group evaluation information fusion process

By continuously repeating the fusion process of individual evaluation information in “Process of individual evaluation information fusion”, we can obtain the comprehensive evaluation information of each individual expert on his/her chosen KS. At this point, it is necessary to perform another DFR fusion of this comprehensive evaluation information to obtain the evaluation information of the group.

• (1) Automatic determination of expert weights and reliability parameters.

Before using GC rules for group fusion, the weight and reliability parameters of each expert need to be calculated. We consider each piece of integrated evaluation information as a piece of evidence, and its two parameters, weight and reliability, can be calculated directly according to the definitions in “Method for calculating reliability and weights”. It is worth noting that the weights at this stage mainly describe the relative importance between different experts, while the weights in “Process of individual evaluation information fusion” represent the relative importance between different indicators.

First, the weights of different experts are computed using Eqs. (10a) and (10b). Assume $\theta$ is an arbitrary nonempty subset in the discrimination framework $\Theta$, and ${F^{n\sim i}}$$(n=1,2,3,i=1,2, \ldots ,I)$ is the comprehensive evaluation information of $k{s_n}$ by expert e_i. Then, the weight ${w_i}$ of expert e_i can be computed by the following steps:

Step 1: Calculate the Deng entropy (uncertainty) corresponding to ${F^{n\sim i}}(\theta )$ using the following equation:

$${E^{n\sim i}}= - \sum\nolimits_{{\theta \subseteq \Theta }} {{F^{n\sim i}}} \cdot {\log _2}\frac{{{F^{n\sim i}}}}{{{2^{\left| \theta \right|}} - 1}}$$

(18a)

where $\left| \theta \right|$ refers to the cardinality of $\theta$.

Step 2: Calculate the weight ${w_i}$ of expert ${e_i}$ using the following equation:

$${w_i}={w_{n\sim i}}=\frac{{{E^{n\sim i}}}}{{\sum\nolimits_{{n=1}}^{N} {\sum\nolimits_{{i=1}}^{I} {{E^{n\sim i}}} } }}$$

(18b)

Note that in this study, each expert will only evaluate one KS. Thus, we consider ${w_{n\sim i}}$ (the weight of the comprehensive evaluation information of expert ${e_i}$ on $k{s_n}$) as the weight of expert ${e_i}$ itself.

Next, the reliability of different experts is computed using Eq. (11). Assume that $\theta$ is an arbitrary nonempty subset in the discrimination framework $\Theta$. ${F^{n\sim i}}$ and ${F^{n^{\prime}\sim i^{\prime}}}$ denote the comprehensive evaluation information of experts ${e_i}$ and ${e_{i^{\prime}}}$ on $k{s_n}$ and $k{s_{n^{\prime}}}$, respectively. Then, the reliability ${r_i}$ of expert ${e_i}$ can be calculated using the following steps:

Step 1: Calculate the similarity between ${F^{n\sim i}}$ and ${F^{n^{\prime}\sim i^{\prime}}}$ using the following equation:

$$S({F^{n\sim i}},{F^{n^{\prime}\sim i^{\prime}}})=1 - \sqrt {\sum\nolimits_{{\theta \subseteq \Theta }} {\frac{1}{2}{{\left[ {{F^{n\sim i}} - {F^{n^{\prime}\sim i^{\prime}}}} \right]}^2}} }$$

(19a)

Note that since each expert will only evaluate one KS, this process calculates the similarity between all comprehensive evaluation information.

Step 2: Calculate the average similarity ${\bar {S}_i}$ of expert ${e_i}$ using the following equation:

$${\bar {S}_i}=\frac{{\sum\nolimits_{{i^{\prime}=1}}^{I} {S({F^{n\sim i}},{F^{n^{\prime}\sim i^{\prime}}})} }}{I}$$

(19b)

Step 3: Calculate the reliability ${r_i}$ of expert ${e_i}$ using the following equation:

$${r_i}=\frac{{{{\bar {S}}_i}}}{{\hbox{max} ({{\bar {S}}_1},{{\bar {S}}_2}, \ldots ,{{\bar {S}}_I})}}$$

(19c)

As a result, the expert weight set and reliability set are denoted, respectively, as $W=\left\{ {{w_i}|0 \leq {w_i} \leq 1,\sum\nolimits_{{i=1}}^{I} {{w_i}=1,i=1,2, \ldots ,I} } \right\}$ and $R=\left\{ {{r_i}|0 \leq {r_i} \leq 1,i=1,2, \ldots ,I} \right\}$.

• (2) Integration of group evaluation information and definition of evaluation ratings

We substitute all comprehensive evaluation information,  along with the weights and reliability of the experts, into the GC rule to perform for the DFR fusion calculation. We can obtain the group (all experts) evaluation information, denoted as F, which is expressed as follows:

$$F=\left\{ {\left[ {\theta ,F\left( \theta \right)} \right]|0 \leqslant F\left( \theta \right) \leqslant 1,\forall \theta \subseteq \Theta ,\sum\nolimits_{{\theta \in \Theta }} {F\left( \theta \right)=1} } \right\}$$

(20)

Next, by substituting the group evaluation information F into Eq. (7) and performing a pignistic probabilistic transformation, the BPA function can be obtained as follows:

$$BetP=\left\{ {\left[ {{\theta _j},BetP({\theta _j})} \right]|0 \leq BetP({\theta _j}) \leq 1,\forall {\theta _j} \subseteq \Theta ,\sum\nolimits_{{{\theta _j} \subseteq \Theta }} {BetP({\theta _j})=1} } \right\}$$

(21)

where $j=1,2, \ldots ,J$. In $BetP$, ${\theta _1}, \ldots ,{\theta _j}$ correspond to probabilities $BetP({\theta _1}), \ldots ,BetP({\theta _J})$, respectively.

Finally, choose any of the following two principles to determine the final evaluation rating:

Principle 1: Consider the hypothesis with maximum probability as the final evaluation result (maximum affiliation principle). Specifically, in the BPA function $BetP$, if there is any one hypothesis ${\theta _j} \in \Theta$, $j \leq J$, such that $BetP({\theta _j})=\hbox{max} \left[ {BetP({\theta _1}), \ldots ,BetP({\theta _J})} \right]$ holds, then the final evaluation result can be regarded as ${\theta _j}$.

Principle 2: Consider the hypothesis with the greatest expected value as the final evaluation result (principle of maximum mathematical expectation). Specifically, in the BPA function $BetP$, if there is any one hypothesis ${\theta _j} \in \Theta$, $j \leq J$, such that $E({\theta _j})=\hbox{max} \left[ {E({\theta _1}), \ldots ,E({\theta _J})} \right]$ holds, then the final evaluation result can be regarded as ${\theta _j}$. In this study, the expectation value is calculated as follows:$E({\theta _j})=j \times BetP({\theta _j})$, where j is the value of the subscript of proposition ${\theta _j}$.

Evaluation steps

Figure 8 depicts the flowchart of the evaluation method designed in this study. Its evaluation steps are summarized as follows:

Step 1: KP organization, KS design, and information extraction. This involves the targeted sorting of KPs, combing them according to different logics, forming multiple hierarchical KS, and using BD functions to extract evaluation information provided by individual experts.

Step 2: Individual evaluation information fusion. According to the fusion path, all evaluation information is subjected to DFR fusion calculation (from low level to high level), and the comprehensive evaluation information of each expert can be obtained, as shown in Eq. (17).

Step 3: Calculate expert weights and reliability. Considering each individual composite evaluation information as a piece of evidence information, the weights of the experts are calculated using Eqs. (18a) and (18b), and the reliability of the experts is calculated using Eqs. (19a)–(19c).

Step 4: Group evaluation information fusion. DFR fusion is calculated for all individual comprehensive evaluation information to obtain the group comprehensive evaluation information, as shown in Eq. (20).

Step 5: Obtaining the evaluation results. The group composite evaluation information is transformed into pignistic probabilities, and the specified principles are followed to determine the final evaluation results.

Fig. 8

The flowchart of the proposed method.

Case study simulation

We take a typical PCAB as the evaluation object and use the method constructed in “The proposed method” to evaluate its ecological security level. Additionally, we present a detailed demonstration of conducting DFR fusion calculations.

Case background

The NK Group LLC is ranked among the top 100 leading enterprises in China’s agricultural industrialisation. The company channels its efforts into three domains: green food, agriculture and forestry resources, and agricultural services. Its expansive portfolio encompasses highland specialties such as natural rubber, grains and oils, sugar, tea, coffee, fruits, vegetables, flowers, walnuts, and potatoes. Beyond production, NK Group ventures into agricultural machinery manufacturing, cutting-edge scientific research, and e-commerce platforms for trading agricultural products. It has operations across Yunnan Province and extends to major cities such as Beijing, Shanghai, and Hong Kong. It also has international operations in Laos, Myanmar, and Singapore.

To facilitate expert evaluation of the enterprise, we collected data on 41 indicators (Table 3). The micro-level indicator data came from enterprise interviews and questionnaires. The macro- and meso-level indicators, meanwhile, came from different databases: CEIC database, China Statistical Yearbook, Yunnan Provincial Statistical Yearbook, and Yunnan Agricultural Yearbook, as well as publications such as “Yunnan Provincial Statistical Bulletin of National Economic and Social Development,” “Yunnan Provincial 14th Five-Year Plan,” “Modern Agriculture Development Plan with Plateau Characteristics of Yunnan Province,” and “Yunnan Environmental Status Bulletin.”

Table 3 The data for each indicator.

We invited five experts, $E=\left\{ {{e_1},{e_2},{e_3},{e_4},{e_5}} \right\}$, from related fields, each of whom could choose any one of $k{s_1},k{s_2},k{s_3}$ to evaluate. In addition, the ecological security level of PCABs could be divided into four grades: poor $({\theta _1})$, average $({\theta _2})$, good $({\theta _3})$, and excellent $({\theta _4})$. Thus, the discriminant framework was set as $\Theta =\left\{ {{\theta _1},{\theta _2},{\theta _3},{\theta _4}} \right\}=\left\{ {{\text{Poor, Average,Good,Excellent}}} \right\}$.

Evaluation process

Extraction and integration of individual evaluation information

Fig. 9

Fusion paths for individual evaluation information for expert ${e_1}$.

Within a specified period of time, five experts selected a KS for evaluation based on the data and information collected for the 41 indicators. Among them, experts ${e_1},{e_2}$ chose $k{s_1}$, experts ${e_3},{e_4}$ chose $k{s_2}$, and expert ${e_5}$ chose $k{s_3}$. The weight of each KP in each KS was subjectively determined by the experts. Subsequently, we asked each expert to provide evaluation information using the BD functions, as shown in Appendix Tables A. 1–5. To facilitate differentiation, we used gray to mark empty KPs.

Subsequently, we follow the fusion path of expert ${e_1}$ (Fig. 9) and keep repeating the DFR process from the low level (layer 3) to the high level (layer 1). We can then obtain the individual comprehensive evaluation information ${F^{1\sim 1}}$ (which represents information on the comprehensive evaluation of $k{s_1}$ by expert ${e_1}$).

Similarly, we fused a large number of BD functions provided by the other four experts $({e_2},{e_3},{e_4},{e_5})$ according to their own fusion paths for DFR fusion, and we could obtain four instances of individual comprehensive evaluation information: ${F^{1\sim 2}},{F^{2\sim 3}},{F^{2\sim 4}},{F^{3\sim 5}}$. Table 4 shows all of the individual comprehensive evaluation information.

Table 4 Comprehensive evaluation information from each individual expert.

Integration of group evaluation information and definition of evaluation ratings

We take the data in Table 4 and substitute them into Eqs. (18a)–(19c) to calculate the two parameters of weight and reliability for each expert, as shown in columns 1 and 2 of Table 5. For example, the first two columns in the third row of Table 5 are the weight of the first expert, 0.199, and the reliability, 0.998.

Then, we take the comprehensive evaluation information of the individual experts, together with the corresponding weights and reliability values, and perform a DFR calculation. The group evaluation information F can be obtained as shown in row 7 of Table 5.

Table 5 Expert weights, reliabilities and DFR process.

Finally, we substitute F into Eq. (7) and perform pignistic probability transformation, which yields the following result:

$$BetP=\left\{ {({\theta _1},0.093),({\theta _2},0.326),({\theta _3},0.432),({\theta _4},0.148)} \right\}$$

The results show that the probabilities of the enterprise’s ecological security level are 9.30% for poor, 32.60% for medium, 43.20% for good, and 14.80% for excellent. It is obvious that ${\theta _3}$ is the hypothesis with the highest pignistic probability and the highest expected value. The level of ecological security of the agribusiness can be regarded as “good,” regardless of whether principle 1 or principle 2 is followed.

Analysis and discussion of case simulation results

The simulation results show that the ecological safety level of the NK Group LLC is rated as “good,” with a corresponding probability of 43.2%. While this indicates a generally favorable performance, this result also suggests that the enterprise falls short of achieving a higher ecological safety classification. The probability value reflects a balance between certain areas of strength and others in which further improvement is necessary. A closer examination of the evaluation indicators reveals that the enterprise benefits significantly from the region’s strong ecological foundation and policy environment but exhibits weaknesses in economic efficiency, innovation input, and value chain development, which collectively constrain its comprehensive ecological performance.

The favorable ecological evaluation of the NK Group is largely attributable to the enterprise’s location in a region with excellent natural endowments. Yunnan Province ranks first in China in terms of biodiversity, and indicators such as the ecological quality index (73.46), proportion of good water bodies (94.1%), and extensive soil conservation measures provide a stable resource base for ecological agriculture. Additionally, local authorities have issued nearly 300 policy documents promoting ecological protection and green development, further supporting the external conditions under which the enterprise operates. These factors enable NK Group to adopt eco-friendly production modes such as organic farming, multi-variety cropping, and resource-conserving irrigation, which contribute to reduced agricultural pollution and a high rate of ecological certification.

Nevertheless, the enterprise’s internal capacity to convert ecological advantages into economic value remains limited. Its profit margin is extremely low at 0.44%, indicating weak financial performance. Despite having 6,257 certified green and organic products, the enterprise still relies heavily on the sale of raw agricultural commodities with insufficient downstream processing. The agro-processing development ratio is only 2.1:1, reflecting its limited industrial transformation capability. Moreover, the enterprise’s investment in agricultural R&D (¥125 million) and mechanization rate (53%) are relatively low, suggesting a lack of technological innovation and modernized production systems. These constraints hinder the transformation of ecological quality into a sustained competitive advantage and increase the enterprise’s vulnerability to both market and environmental shocks.

Overall, the ecological safety status of the NK Group is shaped by a paradox; while the surrounding natural environment is highly favorable and institutional support is strong, the enterprise lacks the internal drivers necessary to achieve ecological–economic synergy. This finding highlights the dual logic of ecological safety, i.e., ensuring environmental protection while also building the internal capacity for sustainable growth. Without a robust economic foundation and technological support, ecological goals are difficult to sustain in the long term.

To overcome the current development dilemma, NK Group LLC need to build a multidimensional upgrade path. On the one hand, they should strive to extend the agricultural industry chain, focus on cultivating the deep-processing capacity of advantageous agricultural products, obtain international quality certification through the construction of standardized production systems, and shape the brand matrix of agricultural products with regional characteristics. On the other hand, they need to accelerate the integration and application of intelligent technologies and deploy precision agriculture-management systems and whole-process digital traceability platforms to enhance both production efficiency and quality control. In the dimension of industrial integration, it would be useful to explore the synergistic development mode of agriculture and cultural tourism and develop special ecological experience projects to expand the value-creation space. At the policy level, we need to focus on measures such as subsidies for technological transformation and export tax rebates. This could help achieve both environmental protection and economic benefits through the construction of a transmission mechanism of “technological innovation–value added–brand premium.”

Conclusion

The ecological security of PCABs encompasses not only environmental protection during agricultural production but also the pursuit of enhanced agricultural output. Striving for economic gains at the expense of resource depletion and environmental degradation is akin to draining a pond to catch fish. Moreover, prioritizing environmental protection to the detriment of growth resembles the futility of climbing a tree to catch fish. PCABs must therefore strike a balance between economic growth and ecological preservation.

By adopting a knowledge-granularity perspective, we design a novel method for evaluating the ecological safety level of PCABs and propose a set of systematic evaluation processes: (1) Index selection. By combining data accessibility and the actual situation of the evaluation object, we sort out the relevant indicators (KPs) at the macro, meso, and micro levels. (2) Building KSs. These KPs are combined from different perspectives to form a hierarchical KS; an expert can select a KS and evaluate all of its layers (layers 1–3) using BD functions to provide evaluation information. (3) Calculate the weight and reliability of each expert. The importance and quality of the information provided by each expert are quantified by calculating entropy and similarity to determine the two parameters of weight and reliability. (4) Information fusion. Using GC rules to fuse information from different knowledge granularities from bottom to top and from individual to group, group evaluation information is finally obtained and the hypothesis with the highest “pignistic” probability or the largest expected value is taken as the evaluation result. Our designed evaluation method can be used to evaluate ecological security levels in other regions by simply redesigning the evaluation indicators. In addition, we select a typical PCAB as the evaluation object and evaluate its ecological safety level using our method. We show that the ecological safety status of the enterprise is “good,” and we put forward management suggestions.

In the practical application of our method, human–computer collaboration needs to be strengthened to ensure the scientific and operational nature of the evaluation process. The main task of experts is to provide evaluation information, while the calculation process can be automatically completed by the decision-support system. Knowledge granularity–based ecological safety evaluation involves complex data processing and information fusion processes, which are prone to errors and can significantly increase the time cost if relying on manual calculation. Therefore, using intelligent computing tools, such as AI-based decision-support systems or big data analysis, can improve the method’s application efficiency while reducing uncertainty caused by human intervention.

Our method nevertheless has some limitations. It does not account for psychological factors that might influence expert decision-making. Experts involved in decision-making can be influenced by factors such as the “primacy effect,” the “halo effect,” or their own emotions, resulting in cognitive biases that lead to distorted judgments. Additionally, experts might represent different interest groups and might therefore deliberately conceal or misrepresent information or manipulate the opinions of others. Future research can further explore how to quantify the psychological factors of experts, combining them with knowledge granularity to further enhance the method’s applicability as a comprehensive tool for ecological safety assessment. Further, more experts should be involved in the assessment, and consensus decision-making groups (where experts need to reach consensus) as well as nonconsensus decision-making groups, should be set up to ensure that the assessment results are more realistic and credible.