Pythagorean Fuzzy Hamacher Choquet integral operators and their application to multi-criteria decision making

Article type: Research Article

Authors: Abdullah, Lazim^{; *} | Mohd, Wan Rosanisah Wan

Affiliations: School of Informatics and Applied Mathematics Universiti Malaysia Terengganu, Kuala Terengganu, Malaysia

Correspondence: [*] Corresponding author. Lazim Abdullah, School of Informatics and Applied Mathematics Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Malaysia. E-mail: lazim_m@umt.edu.my

Abstract: Pythagorean fuzzy Hamacher aggregation operator is one of the aggregation operators in a Pythagorean fuzzy decision making environment. In most cases, it is assumed that all elements in Pythagorean fuzzy set (PFSs) are independent. However, in real life of decision problems, most of the criteria are interrelated. Population size in a solid waste management decision, for example, is related to human health since the two criteria are mutually dependent. This paper aims to introduce an aggregation operator that purposely dealt with the interactions between elements of PFSs. The Choquet integral operator is used to propose an innovation to the Pythagorean fuzzy Hamacher operator. Pythagorean fuzzy Hamacher Choquet integral average operators (PFHCIA) and Pythagorean fuzzy Hamacher Choquet integral geometric operators (PFHCIG) are proposed. The beauty of the proposed operators is it consider the interaction of the criteria in the decision making process. The proposed aggregation operators are the extension to the Pythagorean fuzzy Hamacher aggregation operators where Choquet integral is used to handle interactions between criteria. As the case study is considered, a water resource management problem is presented to portraythe application the proposed approach. Comparable results are also presented to check its feasibility and effectiveness. It is shown that the ranking using the proposed operators are inconsistent with the existing method. The importance of an aggregation function that can capture the problem of interdependence between the criteria is the main contribution of this paper.

Keywords: Pythagorean fuzzy set, aggregation operators, hamacher operation, decision-making, choquet integral

DOI: 10.3233/JIFS-182704

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 1, pp. 1259-1274, 2019