Hesitant Fuzzy Decision-Making Techniques

Hesitant fuzzy decision-making techniques address situations in which experts or stakeholders hesitate among several possible values when assessing the membership of an alternative to a given set. By allowing a set of candidate membership degrees rather than a single crisp value, this approach captures ambiguity and diversity of opinion in environments as varied as resource allocation, supplier selection, risk assessment and healthcare planning. Core components include distance and similarity measures to compare hesitant profiles, aggregation operators to fuse multiple hesitant evaluations, and ranking methods—often based on extensions of TOPSIS or other multi-criteria decision-making frameworks. Over the past decade, numerous generalisations have enriched the original model, introducing non-membership hesitation, probability or proportional weights, temporal sequencing and hierarchical ranking of evaluations. These methods collectively enhance the flexibility and descriptive power of fuzzy decision support when precise quantification is infeasible or when group consensus must reflect a spectrum of expert judgments.

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Building on the seminal formulation of hesitant fuzzy sets, the concept of dual hesitant fuzzy sets was introduced to integrate simultaneous hesitation in both membership and non-membership degrees. This model offers richer expressiveness when experts express concurrent favourable and unfavourable assessments and has been applied to clustering, correlation analysis and multi-attribute group decision-making, demonstrating improved discrimination among alternatives without resorting to ad hoc data extension.

More recently, ranked hesitant fuzzy sets have emerged as an intuitive extension that orders multiple evaluations by their plausibility or credibility without requiring explicit probability or proportional weights. By assigning a strict ranking among candidate values, this method simplifies aggregation and scoring in multi-agent contexts, yielding robust decision rules and facilitating implementation via computational tools.

Another advance is the time-sequential hesitant fuzzy set, designed to capture how expert hesitation evolves over successive time points. This formulation introduces operators and score functions that reflect temporal fluctuations in confidence, enabling more dynamic decision models in settings such as project management and real-time monitoring where assessments change as information accrues.

Hesitant Fuzzy Decision-Making Techniques publication trend

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

Technical terms

Hesitant fuzzy set: A fuzzy set in which each element is associated with a finite set of possible membership degrees, reflecting expert hesitation.

Dual hesitant fuzzy set: An extension of hesitant fuzzy sets that allows separate sets of possible values for both membership and non-membership degrees.

Ranked hesitant fuzzy set: A hesitant fuzzy set in which candidate membership values are arranged in a strict order according to plausibility or importance.

Time-sequential hesitant fuzzy set: A model in which hesitant evaluations are indexed by time, capturing how membership hesitation evolves across successive assessments.

References

1. Dual Hesitant Fuzzy Sets. Journal of Applied Mathematics (2012).
2. Multiple‐Attribute Decision‐Making Problem Using TOPSIS and Choquet Integral with Hesitant Fuzzy Number Information. Mathematical Problems in Engineering (2020).
3. Correlation Measures of Dual Hesitant Fuzzy Sets. Journal of Applied Mathematics (2013).
4. Multi-Attribute Decision-Making Approach Based on Dual Hesitant Fuzzy Information Measures and Their Applications. Mathematics (2019).
5. Ranked hesitant fuzzy sets for multi-criteria multi-agent decisions. Expert Systems with Applications (2022).
6. Time-sequential hesitant fuzzy set and its application to multi-attribute decision making. Complex & Intelligent Systems (2022).
7. A Novel Multi-Attribute Group Decision-Making Approach in the Framework of Proportional Dual Hesitant Fuzzy Sets. Applied Sciences (2019).
8. Interval-Valued Probabilistic Dual Hesitant Fuzzy Sets for Multi-Criteria Group Decision-Making. International Journal of Computational Intelligence Systems (2019).