A modification of probabilistic hesitant fuzzy sets and its application to multiple criteria decision making

Document Type: Research Paper


1 Department of Mathematics, Quchan University of Technology, Iran.

2 Andalusian Research Institute in Data Science and Computational Intelligence, University of Granada, Granada 18071, Spain



Probabilistic hesitant fuzzy set (PHFS) is a fruitful concept that adds to hesitant fuzzy set (HFS) the term of probability which is able to retain more information than the usual HFS. Here, we demonstrate that the existing definitions of PHFS are not still reasonable, and therefore, we first improve the PHFS definition. By endowing the set and algebraic operations with a new re-definition of PHFS, we propose a class of T-norm-based and S-norm-based operations for PHFSs together with a number of aggregation operators. Eventually, on the basis of the new operators, the effectiveness and practicality of re-defined PHFS will be tested using {three} multiple criteria decision making (MCDM) problems concerning the automotive industry safety evaluation, the evaluation of Chines hospitals and
the evaluation of alternatives in an investment company.