On a knowledge measure and an unorthodox accuracy measure of an intuitionistic fuzzy set(s) with their applications

A measure of knowledge may be viewed as a dual measure of entropy in a fuzzy system; thus, it appears that the less entropy may always accompany the greater amount of knowledge. In this paper, we propose a novel measure of knowledge for an intuitionistic fuzzy set (IFS) through an axiomatic approach. We investigate the effectiveness of the proposed knowledge measure through some comparative studies with some existing entropy measures and knowledge measures of IFS. We also introduce one parametric generalized version of this knowledge measure. This paper also provides application of the proposed knowledge measures in multi-attribute decision-making (MADM). We also give two characterization results to obtain a general framework for defining new knowledge measures. Further, similarity and dissimilarity measures may also be viewed as dual concepts to deal with the problems related to pattern recognition. In this paper, we provide an accuracy measure of an intuitionistic fuzzy set relative to a given intuitionistic fuzzy set. The proposed accuracy measure seems to serve as an effective alternative to similarity and dissimilarity measures in some pattern recognition problems. We also give proof of some properties related to accuracy measure.