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The aim of this paper is to develop an extended linear assignment method to solve multi-criteria decision-making (MCDM) problems under the Pythagorean fuzzy environment, where the criteria values take the form of the Pythagorean fuzzy numbers (PFNs) and the information about criteria weights are correlative. In order to obtain the criteria-wise rankings of the linear assignment method, we firstly define a new likelihood for the comparison between PFNs. Then, we introduce the fuzzy measure to determine the weighted-rank frequency matrix of the linear assignment method. Unlike the existing literature of the fuzzy measure, this paper incorporates the partitioned structure of the criteria set into it and proposes a new partitioned fuzzy measure. Further, we design the extended linear assignment method by using the new likelihood of PFNs and partitioned fuzzy measure for Pythagorean fuzzy multi-criteria decision-making (PFMCDM). Finally, a practical example is used to illustrate and verify our proposed method. [ABSTRACT FROM AUTHOR]

Abstract With the rapid development of Internet banking technology in Ghana, the website quality evaluation is the essential core of the customer, which is regarded as a multi-criteria decision making (MCDM) problem. Due to the uncertainty of Internet banking, the evaluation of criteria may be measured by Pythagorean fuzzy numbers (PFNs). In addition, the customer usually does not exhibit complete rationality in the decision procedure. Based on the traditional VIKOR (Vise Kriterijumska Optimizacija I Kompromisno Resenje) method of MCDM, this paper provides a new perspective of a compromised solution, which can handle the decision maker's psychological behavior by inducing TODIM (a Portuguese acronym meaning Interactive Multi-Criteria Decision Making). By defining Pythagorean fuzzy entropy and cross-entropy measures, we study the determination of the weights of the criteria in advance. Then, considering the psychological behavior of the customer, we design two types of strategies for the combination between TODIM and VIKOR. Meanwhile, the corresponding methods have been developed, i.e., Approaches I and II. After that, a simulated example of ranking Internet banking websites in the Ghanaian banking industry is given to illustrate the validity and applicability of our proposed approaches. Finally, we utilize the Wilcoxon signed-rank test and then discuss the differences among VIKOR, TODIM and our proposed methods. Highlights • This paper extends VIKOR to the Pythagorean fuzzy environment. • The Pythagorean fuzzy entropy and cross-entropy is developed for the weight. • By combining TODIM and VIKOR, we design two novel decision-making approaches. [ABSTRACT FROM AUTHOR]