The Robustness Analysis Of Fuzzy Reasoning

Fuzzy reasoning has become an important part of fuzzy control and intelligent systems.In fuzzy reasoning,if small change of input leads to slight change of output result,the used fuzzy reasoning method is called robust.That is,the fuzzy reasoning method has better robustness.Robustness,as one of the criteria for performance of fuzzy inference,plays a very important role in design,evaluation and selection of fuzzy inference methods.Therefore,the robustness analysis of fuzzy reasoning methods is an important research topic.The main research contents of this thesis are robustness of several important fuzzy reasoning methods,some new results are obtained.As an improvement to the traditional fuzzy reasoning method,two new fuzzy reasoning methods including the symmetric inference method based on the triple I method and the fuzzy similarity inference method are proposed in the recent literatures.In this thesis,the robustness of the symmetric implication method is studied based on the normalized Minkowski distance.The robustness results of the four algorithms for different implication operators are given.The robustness analysis of the fuzzy similarity inference method is carried out.Due to compact relationship between relative perturbation and robustness of fuzzy reasoning,considering the importance of symmetry of relative perturbation,the concept of symmetric relative perturbation of fuzzy sets is proposed.Based on the new concept,the relative perturbations generated by operations of fuzzy sets are analyzed,and perturbation of the CRI reasoning method is studied.The concept of weighted logic similarity is proposed for improving the concept of average logical similarity.And the concept of weighted difference measure is proposed for remedying defects of difference measure.Based on the weighted difference measure,the perturbation of fuzzy set operations and the robustness of two important fuzzy reasoning methods are analyzed.In order to solve the confusion of concepts and notations,relationships among some concepts dealing with four properties of fuzzy reasoning methods including continuity,approximation,perturbation and robustness are clarified in this thesis.And the corresponding relation diagram of the four properties is given.In addition,relationships among some important concepts such as maximal perturbation,approximation equalities,similarity,distance,difference measure and weighted difference measure of fuzzy sets are discussed,the corresponding relation diagram is given.