The Research On Properties And Applications Of Weighted Fuzzy Metric Spaces

Since Professor Zadeh proposed the CRI method, fuzzy control technology has been widely used in industry field and has made remarkable success. Fuzzy reasoning, as theoretical basis of fuzzy control, has naturally been concerned by the majority of scholars.At present, in the study of continuity and robustness of fuzzy reasoning, the perturbation of fuzzy reasoning will be involved. But the definition of perturbation of fuzzy reasoning is associated with fuzzy metric. In addition, since the fuzzy inference is derived from the fuzzy logic, so the measurement with logical meaning plays an important role in the study of fuzzy inference.For another, many properties of fuzzy reasoning are investigated in the fuzzy metric space. Thus the advantages and disadvantages of properties of fuzzy metric space can reflect whether the fuzzy metric is reasonable or not.The purpose of this paper is to establish a metric with logical meaning. Based on this, we will study the problems mentioned above. The main contents in this paper are as follows:(1)The weighted logic metric is proposed under the unified framework of strong regular implications with logical meaning. And the definition of perturbation between fuzzy sets is given.(2)We discussed the distribution of condensation point in the fuzzy metric space(weighted logic metric space)induced by the weighted logic metric, which proves the existence of the perturbation under the weighted logic metric.(3)Based on the weighted logic metric, the perturbation problem of fuzzy sets and robustness of Triple I method are investigated.