Consideration on New Fuzzy Information Theory based on Fuzzy Logical Sentences

Abstract

Conventional fuzzy information theory have an essential problem. A membership value 1/2 should be recognized as a meaningful value of membership function although Shannon's probabilistic value 1/2 is not. Fuzzy set theory based on fuzzy logic which is essentially 3-valued ({0, 1/2, 1}). 1/2 means "Unknown" explicitly.

In the paper, we try to define amount of fuzzy information, which is represented in ratio of cardinalities of "don't care"s. Also we define fuzzy entropy based on fuzzy logical sentences.