Bipolar valued probabilistic hesitant fuzzy sets based on Generalized Hybrid Operators in multi-criteria decision making problems based TOPSIS

Abstract This paper aims to present some novel ordering methods to obtained Bipolar valued probabilistic hesitant fuzzy sets (BVPHFS) by extending probabilistic hesitant fuzzy sets (PHFS). PHFS is a strong version of hesitant fuzzy sets (HFS) in terms of evaluated as probabilistic of each element in HFS. Thus, this case proposes flexibility about selection of an element and aids to overcome with noise channels. Then, some properties of BVPHFS are surveyed. Further, some new aggregation operators are discussed called bipolar valued probabilistic hesitant fuzzy weighted average operator (BVPHFWA), Generalized bipolar valued probabilistic hesitant fuzzy weighted average operator (GBVPHFWA), bipolar valued probabilistic hesitant fuzzy weighted geometric operator (BVPHFWG), Generalized bipolar valued probabilistic hesitant fuzzy weighted geometric operator (GBVPHFWG), bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric operator (BVPHFHWAG) and Generalized bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric (GBVPHFHWAG) and some basic properties are presented. Moreover, two different algorithms are put forward with helping to TOPSIS method and by using aggregation operators over BVPHFSs. The validity of proposed operators are analyzed by proposing an example and results are compared in their own.