Abstract
The purpose of this work is to present a new theory namely fuzzy parameterized dual hesitant fuzzy soft sets (FPDHFSSs). This theory is an extension of the existing dual hesitant fuzzy soft set whereby the set of parameters have been assigned with respective weightage accordingly. We also introduced the basic operation functions for instance intersection, union, addition and product operations of FPDHFSSs. Then, we proposed the concept of score function of FPDHFSSs of which these scores function were determined based on average mean, geometry mean and fractional score. The said scores function then were divided into the membership and non-membership elements where the distance of FPDHFSSs was introduced. The proposed distance of FPDHFSSs has been applied in TOPSIS which will be able to solve the problem of fuzzy dual hesitant fuzzy soft set environment.
Highlights
Zadeh [1] presented a well-known idea namely fuzzy set
Zhu et al [4] extended the theory of HFS to dual hesitant fuzzy sets (DHFS) which has taken more information than other extensions of fuzzy sets because of the assignment of membership and non-membership values
Zhang and Shu [18] presented the ideas of dual hesitant fuzzy soft sets (DHFSSs) where the integration was done based on the concept of dual hesitant fuzzy set and fuzzy soft sets
Summary
Zadeh [1] presented a well-known idea namely fuzzy set. In a fuzzy set theory, it is easier to determine the membership degree of an element as compared to classical set. Zhu et al [4] extended the theory of HFS to dual hesitant fuzzy sets (DHFS) which has taken more information than other extensions of fuzzy sets because of the assignment of membership and non-membership values. They believed that the more information obtained, the more efficient the decision making can be made. While Zhang and Shu [18] stated that DHFSSs theory In which h(x) and g(x) are two set of some values in was proposed to cater for the problem of FDHFSs related to inheritance of inadequate information to the parameterization tools.
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