Neutrosophic Decision-Making Techniques in Complex Systems

Neutrosophic decision-making extends classical and fuzzy frameworks by explicitly incorporating three independent degrees—membership, non-membership and indeterminacy—to represent uncertain, inconsistent or incomplete information. In complex systems spanning environmental management, supply chains, healthcare and network analysis, decision makers face multifaceted data ambiguity that defies binary or probabilistic modelling alone. Neutrosophic approaches employ numerical constructs such as single-valued, interval-valued and cubic neutrosophic sets to capture both crisp and interval information within a single unified structure. Aggregation operators, distance and similarity measures and de-neutrosophication techniques then enable the synthesis of multi-criteria and group preferences. Recent advances have introduced higher-order partitioning of indeterminacy, robust statistical estimators and flexible parametric operations, enhancing adaptability to nonlinear interactions and large-scale data. By generating interval-valued outcomes, these methods provide decision makers with ranges that reflect the true extent of uncertainty, supporting risk analysis, policy formulation and dynamic optimisation in real-world scenarios.

Research from Nature Portfolio

A study on robust neutrosophic statistical estimation has advanced decision-making by leveraging accurate measurements of auxiliary variables to derive interval estimates for population medians under deep uncertainty. Unlike classical point estimators, the proposed neutrosophic estimator yields a range within which the true median is likely to lie, accounting for vagueness in data. Through a first-order approximation, the authors derive bias and mean square error expressions, demonstrating superior efficiency compared with traditional estimators in both simulated and empirical datasets. This methodological innovation emphasises the role of neutrosophic statistics in delivering more informative inference for complex decision problems where data ambiguity and vagueness are intrinsic.

Research from all publishers

Enhanced performance evaluation in operational research has employed pentagonal neutrosophic numbers within a data envelopment analysis framework, enabling more nuanced discrimination among efficient and inefficient units. By modelling efficiency scores as five-point structures that reflect varying degrees of membership, indeterminacy and non-membership, the approach captures subtle performance differences under uncertain evaluations. In environmental decision-making, a pentapartitioned neutrosophic cubic set has been introduced to manage air pollution assessment across urban areas. This model partitions indeterminacy into contradiction, ignorance and unknown subcomponents and combines interval and crisp values to yield a comprehensive aggregation operator. Applied to major city air quality indices, it guides policymakers in revising emission controls under multi-source uncertainties. Foundational work on Dombi aggregation operators for neutrosophic cubic sets has provided a flexible family of parametric operators for multiple attribute decision-making. By adjusting an operational parameter, decision analysts can calibrate the balance between optimism and pessimism when fusing single-valued and interval information, with illustrative examples demonstrating application to investment and supplier selection problems.

Neutrosophic Decision-Making Techniques in Complex Systems publication trend

The graph below shows the total number of articles in neutrosophic decision-making techniques in complex systems across all publications each year (not limited to Nature Index journals).

Technical terms

Neutrosophic set: A generalisation of fuzzy sets characterised by independent membership, non-membership and indeterminacy degrees for each element.

Neutrosophic number: A numerical triple representing the membership, indeterminacy and non-membership values of an element.

Neutrosophic cubic set: A hybrid structure that simultaneously incorporates single-valued and interval-valued neutrosophic numbers for richer uncertainty representation.

Pentagonal neutrosophic number: An extension of neutrosophic numbers using five parameters to describe varying degrees of truth, indeterminacy and falsity.

Pentapartitioned neutrosophic set: A decomposition of indeterminacy into sub-components such as contradiction, ignorance and unknown, enhancing granularity in uncertainty modelling.

Aggregation operator: A mathematical function that combines multiple neutrosophic values into a single neutrosophic outcome for decision analysis.

References

1. Enhanced Performance Evaluation Through Neutrosophic Data Envelopment Analysis Leveraging Pentagonal Neutrosophic Numbers. Journal of Operational and Strategic Analytics (2023).
2. Designing pentapartitioned neutrosophic cubic set aggregation operator-based air pollution decision-making model. Complex & Intelligent Systems (2023).
3. Estimating neutrosophic finite median employing robust measures of the auxiliary variable. Scientific Reports (2024).
4. Dombi Aggregation Operators of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making. Algorithms (2018).