(1909-5491) A Modification of Probabilistic Hesitant Fuzzy Sets and its Application to Multiple Criteria Decision Making

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 defifnitionsof PHFS are not still reasonable, and therefore, we fifrst improve the PHFS deffinition. By endowing the set and algebraic operations with a new re-defifnition of PHFS, we propose a class of T-norm-based and S-norm-based operationsfor PHFSs together with a number of aggregation operators. Eventually, on the basis of the new operators, the effectiveness and practicality of re-defifned 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.