Power Aggregation Operators and Similarity Measures Based on Improved Intuitionistic Hesitant Fuzzy Sets and their Applications to Multiple Attribute Decision Making

Tahir Mahmood,Ronnason Chinram,Zeeshan Ali,Wajid Ali

doi:10.32604/cmes.2021.014393

Abstract

Intuitionistic hesitant fuzzy set (IHFS) is a mixture of two separated notions called intuitionistic fuzzy set (IFS) and hesitant fuzzy set (HFS), as an important technique to cope with uncertain and awkward information in realistic decision issues. IHFS contains the grades of truth and falsity in the form of the subset of the unit interval. The notion of IHFS was defined by many scholars with different conditions, which contain several weaknesses. Here, keeping in view the problems of already defined IHFSs, we will define IHFS in another way so that it becomes compatible with other existing notions. To examine the interrelationship between any numbers of IHFSs, we combined the notions of power averaging (PA) operators and power geometric (PG) operators with IHFSs to present the idea of intuitionistic hesitant fuzzy PA (IHFPA) operators, intuitionistic hesitant fuzzy PG (IHFPG) operators, intuitionistic hesitant fuzzy power weighted average (IHFPWA) operators, intuitionistic hesitant fuzzy power ordered weighted average (IHFPOWA) operators, intuitionistic hesitant fuzzy power ordered weighted geometric (IHFPOWG) operators, intuitionistic hesitant fuzzy power hybrid average (IHFPHA) operators, intuitionistic hesitant fuzzy power hybrid geometric (IHFPHG) operators and examined as well their fundamental properties. Some special cases of the explored work are also discovered. Additionally, the similarity measures based on IHFSs are presented and their advantages are discussed along examples. Furthermore, we initiated a new approach to multiple attribute decision making (MADM) problem applying suggested operators and a mathematical model is solved to develop an approach and to establish its common sense and adequacy. Advantages, comparative analysis, and graphical representation of the presented work are elaborated to show the reliability and effectiveness of the presented works.

Highlights

In modern decision science, multi-attribute decision making (MADM) is a vital investigation area on how to choose the correct option corresponding to many prominent attributes [1–3]
We found that two different definitions of Intuitionistic hesitant fuzzy set (IHFS) which were proposed by Beg et al [44] and Geetha et al [45] are not compatible with the other existing notions
If we choose the intuitionistic hesitant fuzzy types of information’s with existing conditions that are the sum of the maximum of the truth grade and minimum of the falsity grade cannot exceed from unit interval, and the sum of the maximum of the truth grade and falsity grade exceeds the unit interval, it is very difficult to cope with such types of issues

Summary

Introduction

Multi-attribute decision making (MADM) is a vital investigation area on how to choose the correct option corresponding to many prominent attributes [1–3]. The decision-makers (DMs) utilize crisp figures to express the favorites regarding the alternative in conventional multi-attribute decision making difficulties. The model of fuzzy set is applied in many areas, mainly wherever traditional numerical methods restrict effectiveness, involving organic and social sciences, linguistics, psychology and mostly soft sciences. In these areas, variables are hard to evaluate and conditions among variables are so ill-defined. IFS is an expansion of FS to cope with doubtful and complicated data.

Methods

Results

Conclusion