一种相关型模糊集合及其在模糊逻辑系统中的应用

An interrelated fuzzy set and its application to fuzzy logic systems

基于t-范数和t-余范数的模糊推理无法将模糊规则中前件集与后件集的相关性信息引入到模糊推理过程,这在某些情况下会导致模糊推理结果与实际经验不符。针对此问题,首先引入模糊集合之间相关度的概念,使模糊概念之间彼此相关。然后,在模糊集合相互关联的环境下提出相关型模糊集合的概念,包括相关type-1、相关区间型type-2以及相关一般型type-2模糊集合,并在理论上把模糊集合的基本概念和运算性质放在相关型模糊集合的环境下进行讨论,同时定义其自身特有的一些运算。最后,对相关型模糊集合在2种模糊逻辑系统(T1 FLS和IT2 FLS)中的应用进行探索,提出面向后件集的模糊推理方法。仿真实例表明:该方法比传统的模糊推理方法能捕获到规则中更多的不确定性信息。

Fuzzy inference methods based on t-norms or t-conorms are unable to bring the interrelated information between antecedents and consequents into the process of fuzzy inference, which can cause inconsistency between inference results and practical experience in some cases. To solve the problem, the concept of relation grade among fuzzy sets that can make fuzzy concepts interrelated was firstly introduced, and the concepts of interrelated fuzzy sets, such as interrelated type-l, interval type-2, and general type-2 fuzzy sets, were proposed in an environment where fuzzy sets were related with each other. Furthermore, the fundamental concepts and operations of fuzzy sets were discussed in terms of such fuzzy sets, and in particular, some of its unique operations were defined, too. Finally, some applications of such sets to fuzzy logic systems, such as type-l, interval type-2, and general type-2 fuzzy logic systems, were explored in a preliminary way, and a fuzzy reasoning method was put forward. Simulation results indicate that the proposed method can capture more information about rule uncertainties than the conventional fuzzy reasoning methods do.