Fuzzy Parameterized Hesitant F uzzy Linguistic Term Soft Sets FPHFLTSSs i n Multi Criteria Decision Making

Abstract

In this research, we suggest the theory of FPHFLTSSs. This theory is combination of hesitant fuzzy linguistic term soft sets (HFLTSSs) and weights of criteria in the set namely fuzzy parameterized where all the information are given in a single set. Then, we address several related concepts and the fundamental operations of this theory, namely the addition, union and intersection. In addition, we introduce the concept of scores in FPHFLTSSs based on arithmetic mean, geometry mean, and fractional of FPHFLTSSs. Next, we introduce the concept of distance between two FPHFLTSSs based on these scores which can be used in TOPSIS approach. Three algorithms are introduced to cater some problems in algorithm discovered in previous study. The first algorithm is an easy and simple step without transforming hesitant linguistic fuzzy elements into hesitant fuzzy elements. This second approach is the extended version of Liu et al. in which they suggested their positive ideal solution (PIS) distance algorithm. For the third algorithm, we suggest FPHFLTSS's arithmetic mean distances, geometry mean, and fractional distances in TOPSIS approach. Lastly, these algorithms are used for the issue of decision making in FPHFLTSSs environment to show the feasibility and efficiency of our methods.