Dual concepts in fuzzy theory: Entropy and knowledge measure

Abstract

Entropy in a fuzzy set measures the amount of ambiguity/imprecision present in the fuzzy set. In this paper, we introduce a knowledge measure of a fuzzy set and its generalization (accuracy measure). The knowledge measure may be considered as a dual measure of fuzzy entropy. We also investigate the effectiveness and application of the proposed knowledge measure in multiple attribute decision making. Furthermore, we provide a result for obtaining a class of knowledge measure. We also prove a general method for obtaining a knowledge measure using accuracy measure. Among some suggested implications of the proposed fuzzy accuracy measure, we demonstrate the application of fuzzy accuracy measure in image thresholding.