Computational Intelligence in Sustainable Reliability Engineering

11Fuzzy Information Inequalities, Triangular Discrimination and Applications in Multicriteria Decision Making

Ram Naresh Saraswat and Sapna Gahlot*

Department of Mathematics and Statistics Manipal University Jaipur, Jaipur (Rajasthan), India

Abstract

This chapter introduced few novel inequalities of fuzzy measures and established the bounds in term of triangular discrimination. We obtained some new relations between new and existing fuzzy divergence measures with the help of the properties of convex function, new f-divergence measure. Also, we showed utility of new fuzzy divergence measures in multicriteria decision-making problem.

Keywords: Fuzzy set, fuzzy new f-divergence measure, Jensen’s inequality, fuzzy triangular divergence measure, MCDM

2000 Mathematics Subject Classification: 40H05, 46A45 62B86, 03E72, 68T10

11.1 Introduction

In information theory, Shannon [4] had defined the expected value of information which is called entropy. Entropy is defined on the pair of probability distribution. Afterward, Zadeh [21] developed the nature of entropy in fuzzy set form, which is called fuzzy entropy. There are many scientists [33–36] and researchers discussed or cited fuzzy divergence measures and existing in the literatures of measures. After that De Luca and Termini [24] introduced entropy on the fuzzy set (FS), which is called Shannon’s function. Afterward, numerous researchers made additional effort during this area. Among its membership function and nearby classical sets. ...