The Research On The Perturbation Of Fuzzy Reasoning

After Zadeh introduced fuzzy sets, fuzzy reasoning or approximate reasoning are extensivelyused in fuzzy control and has achieved remarkable success in the field of application.In the course of fuzzy reasoning, the deviation of fuzzy input (i.e., minor premise) willundoubtedly bring about a deviation of the reasoning conclusion. We have a correspondingproblem: will a small variance (perturbation) of input cause a big variance (oscillation) of outputof fuzzy reasoning? If a slight deviation of the input results in great change to reasoning result,then such a method for fuzzy reasoning is not applicable to some uncertainy systems. Therefore,the theme of this paper is to study the perturbation of fuzzy reasoning.The major research work and results are as follows:1. Relative perturbation of fuzzy sets. We propose the concept of relative perturbation offuzzy sets, and investigate the relative perturbation with respect to some algebraic operators(union, intersection and so on). We prove that the relative perturbation is different to themaximum perturbation with respect to complement operator and power operator, and furtherdiscuss the relative perturbation of fuzzy reasoning.2. Perturbation of fuzzy reasoning based on Minkowski distance. Because the Chebyshevdistance, Hamming distance and Euclidean distance are special cases of the Minkowski distance.Therefore we give more general results about the perturbation of fuzzy reasoning based onMinkowski distance. We investigate the perturbation with respect to some algebraic operators(union, intersection and so on), t-norms and implication operators. Finally we give the resultsabout the perturbation of fuzzy reasoning based on Minkowski distance.3. Perturbation of interval-valued fuzzy reasoning. We propose the concept of perturbationsof interval-valued fuzzy sets and present various results on perturbation with respect tointerval-valued fuzzy operations. We also estimate perturbation parameters of approximatereasoning based on interval-valued fuzzy sets.4. Robustness of triple I method. The triple I method is a new kind of fuzzy reasoning withrespect to FMP and FMT models. In this paper we investigate the robustness of triple I methodand triple I sustention degree method. 5．Continuity and approximation property of fuzzy reasoning in several metrics. Weinvestigate the relation between uniform metric and Minkowski metric. It is shown that thecontinuity and approximation property of fuzzy reasoning in the uniform metric and theMinkowski metric is equivalent. And approximation property of fuzzy reasoning in the uniformmetric and the Minkowski metric is equivalent.