Methods for Multiple Attribute Group Decision Making Based on Picture Fuzzy Dombi Hamy Mean Operator

Abstract

In this work, ambiguity and unclarity are coped with the effective tools of picture fuzzy sets (PFSs), especially where the conditions demand simulation of various dimensions for evaluation, for example, decision making. PFS requires operators to measure the coordination of two PFSs. As far as this paper is concerned, we bring new operators to PFSs with an application, validating this as the generalization of the concept of Fuzzy Sets (FSs) and Intuitionistic Fuzzy Sets (IFSs). The hybrid structure of PFSs has been incorporated with other operators to develop picture fuzzy Dombi Hamy mean (PFDHM) operator, picture fuzzy weighted Dombi Hamy mean (PFWDHM) operator, picture fuzzy Dombi dual Hamy mean (PFDDHM) operator, and PF weighted Dombi dual Hamy mean (PFWDDHM) operator. Further, the properties such as Idempotency, Monotonicity, Boundedness, and Commutativity related to each proposed operator have been discussed. By using these operators the multiple attribute group decision-making (MAGDM) methods are proposed. Moreover, we have explained the application by providing an example of a car supplier. The results are concluded by selecting the best car on the basis of attributes such as quality, production, service efficiency, and risk factors using operators defined on PFSs. A comparative study is also conducted to study the significance of the developed work.

Received: 4 April 2022 | Revised: 16 May 2022 | Accepted: 25 May 2022

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.