Abstract
The hesitant fuzzy set (HFS) concept as an extension of fuzzy set (FS) in which the membership degree of a given element, called the hesitant fuzzy element (HFE), is defined as a set of possible values. A large number of studies are concentrating on HFE and HFS measurements. It is not just because of their crucial importance in theoretical studies, but also because they are required for almost any application field. The score function of HFE is a useful method for converting data into a single value. Moreover, the scoring function provides a much easier way to determine each alternative's ranking order for multi-criteria decision-making (MCDM). This study introduces a new hesitant degree of HFE and the z-score function of HFE, which consists of z-arithmetic mean, z-geometric mean, and z-harmonic mean. The z-score function is developed with four main bases: a hesitant degree of HFE, deviation value of HFE, the importance of the hesitant degree of HFE, α, and importance of the deviation value of HFE, β. These three proposed scores are compared with the existing scores functions to identify the proposed z-score function's flexibility. An algorithm based on the z-score function was developed to create an algorithm solution to MCDM. Example of secondary data on supplier selection for automated companies is used to prove the algorithms' capability in ranking order for MCDM.
Highlights
In several fields, the fuzzy set (FS) [1] theory is commonly and successfully used to model some kinds of uncertainty
What if the hesitant fuzzy element (HFE) cannot be distinguished by these score functions of various lengths and deviation? What if the various HFEs have the same score? The goal of this study is to suggest a score function incorporated with HFE's hesitant degree and deviation value that is both flexible and efficient and addresses certain limitations of the current score functions
The following functions can be considered as the score index for HFEs:
Summary
The fuzzy set (FS) [1] theory is commonly and successfully used to model some kinds of uncertainty. The hesitant fuzzy set (HFS) was initially implemented by Torra [6], [7] They expanded FS to HFS since they discovered that an element's membership to a set is difficult to decide under a group setting due to doubts between a few different values. The measurements for HFEs and HFSs are the subject of an increasing number of studies This is due to their basic significance in scientific research, and because they are invaluable in most fields of use [25]. Considering Xia's score function and the variance value of the memberships. The goal of this study is to suggest a score function incorporated with HFE's hesitant degree and deviation value that is both flexible and efficient and addresses certain limitations of the current score functions.
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