A novel entropy and divergence measures with multi-criteria service quality assessment using interval-valued intuitionistic fuzzy TODIM method

Abstract

Interval-valued intuitionistic fuzzy sets (IVIFSs) are proven to be the fastest growing research area and are more flexible way to handle the uncertainty. Information measures play vital role in the study of uncertain information; therefore, number of new interval-valued intuitionistic fuzzy divergence and entropy measures have been proposed in the literature and applied for different purposes. Recently, multi-criteria decision-making (MCDM) methods with IVIFSs have broadly studied by researchers and practitioners in various fields. In this paper, firstly surveys of IVIF-divergence and entropy measures are conducted and then demonstrated some counter-intuitive cases. Then, novel divergence and entropy measures are originated for IVIFSs to avoid the shortcomings of previous measures. Later on, systematic reviews of Portuguese for Interactive Multi-criteria Decision Making (TODIM) method are presented with recent fuzzy developments. Based on classical TODIM method, a new approach for MCDM is introduced under IVIF environment which considers the bounded rationality of decision makers. In the present method, the proposed entropy measure is utilized to compute the weight vector of the criteria, and the proposed divergence measure is applied in the calculation of dominance degrees. To illustrate the effectiveness of the present approach, a decision-making problem of vehicle insurance companies is presented where the evaluation values of the alternatives are given in terms of IVIF numbers. Comparison with some existing methods shows the applicability and consistency of the present method.