Probabilistic Hesitant Fuzzy Decision-Making Methods

Probabilistic hesitant fuzzy decision-making methods extend classical fuzzy frameworks by allowing decision makers to express multiple membership values for each criterion together with associated probabilities. This dual representation captures both hesitation and occurrence likelihood, enriching the modelling of uncertainty and preference strength. At the core lies the probabilistic hesitant fuzzy set (PHFS), which associates a probability distribution with a finite set of possible membership degrees. A range of aggregation operators, distance measures and ranking indices have been developed to fuse, compare and prioritise alternatives under PHFS information. These methods support group and individual decision contexts across domains such as supplier selection, cloud-service evaluation, investment appraisal and strategic planning. By integrating probabilistic information, PHFS-based approaches improve reliability, accommodate partial knowledge and reduce the loss of nuance inherent in single-value fuzzy or interval-valued fuzzy methods. Recent efforts have focused on enhancing consensus processes, devising novel operators based on Archimedean norms and developing optimisation routines to determine criteria weights under incomplete probability distributions. Together, these advances provide a versatile toolkit for multi-criteria decision-making (MCDM) under complex and uncertain environments, with demonstrable benefits in both theoretical rigour and practical applicability.

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Probabilistic Hesitant Fuzzy Decision-Making Methods publication trend

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

Technical terms

Probabilistic hesitant fuzzy set (PHFS): A fuzzy set in which each possible membership degree is coupled with an occurrence probability, modelling both hesitancy and likelihood.

Aggregation operators: Mathematical functions (for example, weighted averaging, ordered weighted averaging) used to combine multiple PHFS evaluations into a single collective assessment.

COPRAS method: A multi-criteria decision-making procedure that ranks alternatives by combining relative significance and utility measures, adapted here to probabilistic hesitant fuzzy information.

Distance measures: Quantitative metrics defining how dissimilar two PHFSs are, underpinning ranking, clustering and weight-determination algorithms.

Regret theory: A behavioural decision framework that quantifies decision makers’ sensitivity to feeling of regret and rejoicing, employed to refine preference aggregation under uncertainty.

References

1. Probability-hesitant fuzzy sets and the representation of preference relations. Technological and Economic Development of Economy (2018).
2. Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators With New Distance Measures. Mathematics (2018).
3. An integrated decision-making COPRAS approach to probabilistic hesitant fuzzy set information. Complex & Intelligent Systems (2021).
4. Multi-Attribute Decision-Making Method Based Distance and COPRAS Method with Probabilistic Hesitant Fuzzy Environment. International Journal of Computational Intelligence Systems (2021).
5. Probabilistic hesitant fuzzy multiple attribute decision-making based on regret theory for the evaluation of venture capital projects. Economic Research-Ekonomska Istraživanja (2020).