Error Evaluation Method And Robustness Analysis Of Fuzzy Reasoning

Fuzzy reasoning has become one of the most hot research directions of artificial intelligence.The property of fuzzy reasoning method is the standard for evaluating the reasoning method.There are some important properties of fuzzy inference methods such as: reduction,continuity,approximation,robustness,et al.The robustness or stability of fuzzy inference methods is a very important property of fuzzy inference method.Therefore,to study robustness of the fuzzy inference method is a necessary and meaningful work.For a fuzzy reasoning method,we not only explore its idea and applied algorithm,but also its internal structure.This paper mainly studies the robustness of several important fuzzy inference methods in the related literature.In particular,some preliminary comparing results of robustness of these fuzzy inference methods are reported.We try to provide a scientific basis for the practical applications of fuzzy inference methods.Based on the logical similarity,the robustness of several inference methods,whose are improvements of the triple I inference method,is studied.The specific robustness results of these inference methods are given under the residual implication class.As a result of the inference,the robustness results of several concrete inference method using four commonly used implications are given.The robustness results of several inference methods related to the triple I inference method are compared and analyzed.Meaningful conclusions,some interesting phenomena are obtained.In view of importance of error evaluation standards of fuzzy sets in studying of robustness,the concept of the generalized perturbation is proposed in this work,which unifies the error evaluation criteria of fuzzy sets.Generalized perturbations of several important operators and fuzzy implications are obtained.The two important fuzzy rule inference system are CRI reasoning method and BKS reasoning method.There are a lot of researches on CRI reasoning methods,but there are few researches on BKS reasoning methods.This paper studies the robustness of BKS reasoning methods based on generalized perturbation.The corresponding robustness conclusions are obtained.In fuzzy logic,some triangle norm families and fuzzy implication families contain a large number of triangle norms,implications,which have wide application value.The residual implication family derived from the Schweizer-Sklar triangle norms contains many common implications.In this paper,we study the generalized perturbation of Schweizer-Sklar triangle norm family and the corresponding fuzzy implication family,and give two types of BKS reasoning method robustness results based on the two families.