Complex Pythagorean Dombi fuzzy graphs for decision making

Abstract

A complex Pythagorean fuzzy set (CPFS) is the generalization of Pythagorean fuzzy set (PFS) in which the range of degrees is extended from [0, 1] to complex plane with unit disk. The averaging operators play a significant role to transform the information into a single value. The flexibility of Dombi operators with operational parameters is outstanding, and the Dombi operators are very efficient in decision-making problems. In this research article, we present a new graph called, complex Pythagorean Dombi fuzzy graph (CPDFG) as the Dombi operators are not yet applied on CPFSs. We employ graph terminology on CPFSs using Dombi operators. We define regular, totally regular, strongly regular and biregular graphs with appropriate elaboration, and their pivotal properties are discussed. Moreover, edge regularity of CPDFG is also explained with significant characteristics. We introduce two operators, namely complex Pythagorean Dombi fuzzy arithmetic averaging (CPDFAA) and complex Pythagorean Dombi fuzzy geometric averaging (CPDFGA) operators, which are capable to aggregate the complex Pythagorean fuzzy information. We utilize CPDFAA and CPDFGA operators in solving a decision-making numerical example, which is related to the selection of suitable place to build a bus terminal in a city. In order to examine the superiority of our propose operators, we provide a comparative analysis with the existing operators.