Novel fuzzy knowledge and accuracy measures with its applications in multi-criteria decision-making

Entropy is regarded as a numerical representation of the degree of uncertainty concerning a random variable. However, the knowledge associated with any fuzzy set is quantified by a knowledge measure. A fuzzy Knowledge measure is viewed as dual of fuzzy information measure. The solution of a multi-criteria decision- making (MCDM) issue obtained using traditional fuzzy VIKOR approach is not closest to the best ideal solution. This is due to the fact that the defining function in traditional fuzzy VIKOR approach does not follow the axioms of a dissimilarity measure. Consequently, the existing idea of using dissimilarity measures in fuzzy VIKOR approach is controversial. The main aim of this study is to provide a novel fuzzy knowledge measure and modify the traditional fuzzy VIKOR approach. In the present study, a novel Knowledge measure in fuzzy settings is proposed. Its utility and validity are tested using numerical examples. We examine its benefits from a number of angles, including the computation of attribute weights, the computation of ambiguity, and the proper handling of the structured linguistic variables. In addition, from proposed knowledge measure, three new measures, namely, Accuracy measure, Knowledge measure and Information measure are deduced in fuzzy environment. We apply the proposed fuzzy accuracy measure in VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje) approach in place of distance measure. We give the application of proposed approach in solving the multi criteria decision-making problems. We demonstrate the practical applications and validate the proposed approach using a numerical example, especially the selection of the best teacher. Furthermore, a flowchart is given to demonstrate the proposed approach. The findings of proposed approach are then compared to those of the existing approaches to more properly reflect the capability and effectiveness of the proposed approach. The scope for further research is also mentioned at the end of the paper.