Ranked hesitant fuzzy sets for multi-criteria multi-agent decisions

Abstract

This paper introduces and investigates ranked hesitant fuzzy sets, a novel extension of hesitant fuzzy sets that is less demanding than both probabilistic and proportional hesitant fuzzy sets. This new extension incorporates hierarchical knowledge about the various evaluations submitted for each alternative. These evaluations are ranked (for example by their plausibility, acceptability, or credibility), but their position does not necessarily derive from supplementary numerical information (as in probabilistic and proportional hesitant fuzzy sets). In particular, strictly ranked hesitant fuzzy sets arise when no ties exist, i.e., when for any fixed alternative, each submitted evaluation is either strictly more plausible or strictly less plausible than any other submitted evaluation. A detailed comparison with similar models from the literature is performed. Then in order to produce a natural strategy for multi-criteria multi-agent decisions with ranked hesitant fuzzy sets, canonical representations, scores and aggregation operators are designed in the framework of ranked hesitant fuzzy sets. In order to help implementation of this model, Mathematica code is provided for the computation of both scores and aggregators. The decision-making technique that is prescribed is tested with a comparative analysis with four methodologies based on probabilistic hesitant fuzzy information. A conclusion of this numerical exercise is that this methodology is reliable, applicable and robust. All these evidences show that ranked hesitant fuzzy sets are an intuitive extension of the hesitant fuzzy set model designed by V. Torra, that can be implemented in practice with the aid of computationally assisted algorithms.