The Description Of Entropy Of Fuzzy Rules Under The α-Level

It is a very important task to construct and optimize a fuzzy system in fuzzy theory. So far,there are many related research results.However,there are some shortcoming and limitation.Usually,the optimization of fuzzy systems is the optimization of fuzzy rules.In this paper we proposed a new method to classify and evaluate fuzzy rules.This method is derived from the viewpoint of fuzzy rule entropy which is the measurement of uncertainty of fuzzy rule.It is a new method of building and optimizing fuzzy systems. The main contributions of the paper involve the following three aspects.1,The definition of fuzzy knowledge system is proposed.In the meanwhile,the definitions of fuzzy atomic formula and fuzzy logic formula are given.Based on the fuzzy knowledge systems,the information entropy of fuzzy rule is described which is a measurement of uncertainty of fuzzy rule.2,The definitions and some properties of the information entropy of SISO(single input single output) fuzzy rules under theα-level are discussed.A new method to classify and optimize fuzzy rules is proposed.This method classifies the fuzzy rules into three kinds:certainty rule,possibility rule,and irrational rule under theα-level.By the method of fuzzy rule information entropy,it is easy to choose the rational and valid rules that are certainty and possibility fuzzy rules;eliminate the irrational and invalid rules that are irrational rules.Therefore,it is a quantitative and effective method of constructing rational rules and optimizing the fuzzy knowledge systems.Finally,the effectiveness and feasibility of the method referred to are proved by an example.3,The results about SISO fuzzy rules are expanded into MIMO(multi-input multi-output) rules.The definitions of information entropy of MISO and SIMO fuzzy rules are proposed.The properties of the definitions and classification of MISO and SIMO fuzzy rules are discussed.