Fuzzy Preference Relations in Group Decision-Making

Fuzzy preference relations are a class of pairwise comparison tools that allow decision makers to express degrees of preference between alternatives as values in a continuum between indifference and strict preference. Within a group setting, members may harbour uncertain or subjective judgements which can be captured by extending classical fuzzy sets to richer frameworks such as intuitionistic or interval-valued intuitionistic fuzzy sets. These frameworks accommodate both membership and non-membership degrees, as well as hesitancy, enabling a more nuanced representation of expert opinions. Key challenges include ensuring consistency across pairwise matrices, accommodating incomplete or missing entries, quantifying consensus among participants and aggregating individual preferences into a collective ranking. Recent advances have focused on developing consistency correction mechanisms, consensus-reaching processes and direct ranking methods that preserve the original preference information while yielding robust group decisions. Practical applications span supplier selection, disaster risk assessment, cloud computing vendor evaluation and other multi-attribute scenarios where stakeholders hold diverse risk attitudes and information levels.

Research from Nature Portfolio

An improved multi-attribute group decision-making framework has been developed to incorporate interval-valued intuitionistic fuzzy preferences while explicitly accounting for the decision makers’ risk attitudes. The method determines individual weights by combining similarity and proximity metrics and introduces a risk aversion coefficient to adjust the fuzzy decision matrix. An interval-valued intuitionistic fuzzy entropy measure is then used to extract attribute weights, and a modified TODIM (an interactive multi-criteria decision-making approach) assesses the relative superiority of each alternative. The framework effectively handles unknown attribute weights and asymptotic behaviour in fuzzy matrices, leading to enhanced decision robustness. A mechanical assembly supplier selection case study demonstrates the method’s rationality and practical effectiveness.

Research from all publishers

One direct approach maps pairwise fuzzy preferences into transition probabilities, constructing a stochastic matrix whose stationary distribution yields a collective ranking. This Rank Centrality method aligns with a statistical interpretation of the Bradley-Terry-Luce model and offers theoretical sensitivity analysis alongside empirical validation on numerical examples.

An intuitionistic multiplicative preference set environment employs a possibility degree measure and novel aggregation operators to handle asymmetrically distributed pairwise information. Connection-number based intuitionistic multiplicative sets capture identity, contradiction and discrepancy degrees, enabling a complete ranking process illustrated through multiple decision-making examples.

A group consensus framework for hesitant fuzzy linguistic preference relations introduces distance measures and automatic as well as interactive consensus-reaching mechanisms. Two algorithms guide the convergence towards a common preference matrix, exemplified by a green supplier selection problem and compared favourably with existing approaches.

Fuzzy Preference Relations in Group Decision-Making publication trend

The graph below shows the total number of articles in fuzzy preference relations in group decision-making across all publications each year (not limited to Nature Index journals).

Technical terms

Fuzzy preference relation: A representation of pairwise comparisons in which each preference is expressed as a membership degree between 0 and 1, indicating intensity of favour.

Interval-valued intuitionistic fuzzy number: A fuzzy number defined by an interval for membership and an interval for non-membership, allowing a range for hesitancy.

Multiplicative consistency: A property ensuring that the product of pairwise comparisons along any cycle approximates unity, thus maintaining logical coherence.

Hesitant fuzzy preference relation: A structure capturing a set of possible membership degrees for a single preference, reflecting uncertainty or indecision.

Rank centrality: A method converting aggregated pairwise preferences into transition probabilities of a Markov chain, whose stationary distribution yields a ranking.

Aggregation operator: A mathematical function that combines individual preference matrices into a collective matrix, preserving key consistency and consensus properties.

References

1. Interval-valued intuitionistic fuzzy multi-attribute group decision-making method considering risk preference of decision-makers and its application. Scientific Reports (2022).
2. A new decision making model based on Rank Centrality for GDM with fuzzy preference relations. European Journal of Operational Research (2022).
3. Multi-attribute group decision-making process based on possibility degree and operators for intuitionistic multiplicative set. Complex & Intelligent Systems (2021).
4. Decision framework of group consensus with hesitant fuzzy linguistic preference relations. CAAI Transactions on Intelligence Technology (2020).
5. Nature Disaster Risk Evaluation with a Group Decision Making Method Based on Incomplete Hesitant Fuzzy Linguistic Preference Relations. International Journal of Environmental Research and Public Health (2018).
6. A Group Decision Making Method with Interval-Valued Intuitionistic Fuzzy Preference Relations and Its Application in the Selection of Cloud Computing Vendors for SMEs. Informatica (2020).