基于Vague集的元素间相似度量的近似推理

给出了Vague集元素间的一个相似度量方法,对于模糊概念(用Vague集表示)的隶属函数为连续的情况,将规则前件中Vague集的论域与后件中Vague集的论域作一一映射,然后给出基于Vague集的隶属函数为连续情况下的元素间相似度量的近似推理方法;对于Vague集的隶属函数为离散的情况,在作上述相同的映射后,再将规则前件中的vague集和事实中的Vague集的真/假隶属函数分别进行线性插值,使它们都成为连续函数,然后给出基于Vague集的隶属函数为离散情况下的元素间相似度量的近似推理方法.

Fuzzy Reasoning Based on Similarity Measure Between the Elements of Vague Sets

In this paper, we give a method of similarity measure between the elements of vague sets. When the membership functions (represented by vague sets) of fuzzy terms are continuous functions, we give a onetoone mapping between the universe of discourse of fuzzy terms in the antecedent of rule and that in the consequent of rule. We also give a method of approximate reasoning based on similarity measure between the elements of vague sets. When the membership functions of vague set are discrete functions, after giving onetoone mapping between the universe of discourse of fuzzy terms in the antecedent of rule and that in the consequent of rule, we present a method of linear interpolation into the true/false membership functions of the vague sets for the antecedent of rule and fact, converting them into continuous functions. Finally, we provide a method of approximate reasoning based on similarity measure between the elements of vague sets.