A Method for the Evaluation and Selection of an Appropriate Fuzzy Implication by Using Statistical Data

Abstract

In classic logic, there exists an implication of the form p=> q equiv n(p) v q (where n(p) is the negation of p and v the maximum). If we consider the fact that the propositions p and q take only the values 0 and 1, then the values of the classic implication are well-defined. In fuzzy logic, where the proposition can take any value in the closed interval [0, 1], there is an infinite number of fuzzy implications which can be used; hence, a method of selecting the most appropriate implication is required. In this paper, we propose a method of evaluation of the different fuzzy implications using available statistical data. The choice of the appropriate implication is based on the deviation of the truth value of the fuzzy implication from the real values, as described by the statistical data.