Fuzzy Entropy Based on Fuzzy Logical Sentences

Abstract

The “Uncertainty” includes plural kinds of concepts such as randomness, vagueness, and ambiguity. Studies have been tried for defining an amount of fuzzy information and entropy. First C.E.Shannon established mathematical framework for dealing with randomness. After that, L.A.Zadeh established fuzzy theory, many studies dealing with randomness, vagueness, and ambiguity have been done. There are many studies regarding an amount of fuzzy information and entropy based on concepts randomness and vagueness. However, there is no theory dealing with ambiguity explicitly as far as the authors know. “Computing with Words(CW)” has been studied in fuzzy theory, and its usefulness is widely known. Representation of information as words can express not only human's subjectivity but also knowledge and common sense shared by many people. In this paper, we propose a new kind of an amount of fuzzy information and entropy in the case that we communicate using fuzzy logical sentences composed of words and logical connectives: NOT, AND, and OR. The proposal of the study represents an amount of ambiguity and entropy of a fuzzy logical sentence.