Pythagorean fuzzy VIKOR approaches based on TODIM for evaluating internet banking website quality of Ghanaian banking industry

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.