Research On Fuzzy Inference Methods Based On Axiomatic Fuzzy Sets

Fuzzy inference is the theoretical basis of fuzzy control,and its theory and method have been widely used in many fields including fuzzy system control,fuzzy expert system,fuzzy pattern recognition and fuzzy decision analysis.Although many methods of fuzzy inference have been put forward from different views,the theory of fuzzy inference is still far from perfect because of the lack of strict theoretical basis.The establishment of fuzzy inference method depends on fuzzy set theory.Based on axiomatic fuzzy set theory,this paper studies the theory and method of fuzzy inference,and mainly has completed the following three aspects:Under the theoretical framework of axiomatic fuzzy sets,fuzzy inference is regarded as the mapping between two fuzzy membership spaces.Firstly,based on the structural characteristics of input fuzzy sets in input fuzzy membership space,several basic expressions of fuzzy inference results are obtained for single rule,single input-single output fuzzy inference model and multi rule,single input-single output fuzzy inference model,and the related properties are studied.Secondly,for strongly negative operators,t-modular operators and t-comodule operators,the perturbation of these operators in fuzzy membership space is discussed by using Minkowski integral distance,and the continuity of fuzzy inference method proposed in this paper is analyzed on this basis.Finally,from the point of view of fuzzy logic,the fuzzy inference methods established in this paper are compared with several typical fuzzy inference methods.The results show that the fuzzy inference method established in this paper not only satisfies reducibility,but also can find reasonable theoretical support in the corresponding fuzzy logic system.