Abstract
In this paper, by combining hesitant fuzzy soft sets (HFSSs) and fuzzy parameterized, we introduce the idea of a new hybrid model, fuzzy parameterized hesitant fuzzy soft sets (FPHFSSs). The benefit of this theory is that the degree of importance of parameters is being provided to HFSSs directly from decision makers. In addition, all the information is represented in a single set in the decision making process. Then, we likewise ponder its basic operations such as AND, OR, complement, union and intersection. The basic properties such as associative, distributive and de Morgan's law of FPHFSSs are proven. Next, in order to resolve the multi-criteria decision making problem (MCDM), we present arithmetic mean score and geometry mean score incorporated with hesitant degree of FPHFSSs in TOPSIS. This algorithm can cater some existing approach that suggested to add such elements to a shorter hesitant fuzzy element, rendering it equivalent to another hesitant fuzzy element, or to duplicate its elements to obtain two sequence of the same length. Such approaches would break the original data structure and modify the data. Finally, to demonstrate the efficacy and viability of our process, we equate our algorithm with existing methods.
Highlights
The concept of fuzzy sets presented by Zadeh [1] has conquered an enormous achievement in numerous fields
Characteristics of this work are as follows: 1. We extend the definitions of hesitant fuzzy soft sets (HFSSs) [41], [42] to the fuzzy parameterized, allowing this theory to be enhanced by weighting each parameter, namely
We consider the parameterized hesitant fuzzy soft set which includes the combination of the hesitant fuzzy set and fuzzy soft sets where an important degree is given for each element in the set of parameters
Summary
The concept of fuzzy sets presented by Zadeh [1] has conquered an enormous achievement in numerous fields. Babitha and John [41] first studied the hesitant fuzzy soft sets (HFSSs) which are the hybrid structure between HFSs and fuzzy soft set They proposed the basic operation of HFSSs such as union, intersection, complement and proved the De Morgan’s law. Beg and Rashid [43] presented the idea of an HFSSs where adaptation to manage the conditions in which experts assess an alternative giving to finite criteria in all possible values They proposed the distance measure between any two elements of the HFSSs. Rezaei andRezaei [44] proposed distance and similarity measures for HFSSs by using well-known Hamming, Euclidean, and Minkowski distance measures while Li et al [45] extended the concept of HFSS to generalized HFSSs. Among the significant milestones in the development of hesitant fuzzy soft sets and their generalizations is the introduction of the fuzzy parameterized aspect. We give the conclusion of our study and recommendation for further research
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