Extensions of ELECTRE-I and TOPSIS methods for group decision-making under complex Pythagorean fuzzy environment

Document Type : Research Paper


1 Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan

2 School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), P.O. Box, 32, Patiala - 147004, India



Multi-criteria group decision-making is a process in which decision makers assess the performance of alternatives on the basis of conflicting criteria to opt the most worthy alternative as solution. TOPSIS and ELECTRE are effective and commonly used methods to solve multiple criteria decision-making problems. The aim of this study is to propose two new models, namely, complex Pythagorean fuzzy TOPSIS (CPF-TOPSIS) method and complex Pythagorean fuzzy ELECTRE I (CPF-ELECTRE I) method, to tackle multiple criteria group decision-making problems comprising complex Pythagorean fuzzy data. In these methods, we compare complex Pythagorean fuzzy numbers on the basis of their score functions. We use revised closeness index for the ranking of alternatives in CPF-TOPSIS method. {In complex Pythagorean fuzzy concordance and discordance sets, we compare the alternatives on being superior and inferior to other alternatives on the basis of score degree, accuracy degree and indeterminacy. In CPF-ELECTRE I method, we use outranking decision graph to obtain the best alternative.} We illustrate the structure of both methods with the help of flow charts. To verify the accuracy of {proposed methods}, we present an explanatory example for selection of best interior designer for a hotel renovation. {We authenticate the proposed techniques by providing a brief comparative analysis of these methods with existing methods}.