An Approximate Reasoning Method and Its Application to Fuzzy Information Systems

Abstract

The present paper focus on studying the approximate reasoning models based on fuzzy information systems. Firstly, we introduce a concept of \( \lambda \)-truth degree in Lukasiewicz propositional logic by using the probability measure on the set of all valuations, which shows that all kinds of truth degree of formulas in quantitative logic can all be brought as special cases into the unified framework of the \( \lambda \)-truth degree. It is proved that the \( \lambda \)-truth degree satisfies the Kolmogorov axioms and hence the quantitative logic and the probability logic are integrated by means of \( \lambda \)-truth degree. Secondly, by using the \( \lambda \)-truth degree we define the \( \lambda \)-similarity degree and the logic \( \lambda \)-metric among two logic formulas, and prove that there exists not isolated point under some conditions and various logic operations are continuous in the logic \( \lambda \)-metric space. Thirdly, we analyze some applications of \( \lambda \)-truth degree to approximate reasoning in fuzzy information systems, propose two diverse approximate reasoning models in the logic \( \lambda \)-metric space, and give some examples to illustrate the application of approximate reasoning models.