基于连续三角模方幂的模糊蕴涵关于三角模与三角余模的分配方程

Distributivity of T-power Implications Over t-norms and t-conorms

模糊蕴涵关于三角模和三角余模的分配方程在近似推理,特别是在模糊推理与控制中起着重要作用,此类分配方程已得到大量研究并取得丰硕成果。最近,Massanet等基于连续三角模的方幂提出了一类新的模糊蕴涵,简称T-幂蕴涵,并且对它的基本性质做了深入研究。为拓展T-幂蕴涵以及各类模糊蕴涵关于三角模和三角余模分配方程的知识体系,通过分类讨论法,分别研究了三类T-幂蕴涵关于一般三角模与三角余模的四个分配方程,给出T-幂蕴涵关于三角模和三角余模的四个分配方程成立的充要条件。最后通过反证法推导出T-幂蕴涵不同于其他各类已知模糊蕴涵,完善了模糊蕴涵的知识框架。

Distributivity equations of fuzzy implications over triangular norms and triangular conorms play an important role in approximate reasoning,especially in fuzzy reasoning and control.A great deal of researches have been done on the distributivity equations of fuzzy implications over triangular norms and triangular conorms.Recently,Massanet et al.proposed a new kind of fuzzy implications based on powers of continuous t-norms,called T-power based implications and made an in-depth study of its properties.To extend the knowledge system of T-power implications and distributivity equations of fuzzy implications over triangular norms and triangular conorms,the paper studies four distributivity equations of T-power implications over triangular norms and triangular conorms.Necessary and sufficient conditions for the four distributivity equations of T-power implications over triangular norms and triangular conorms are given.This paper also points out that T-power implications are different from other wellknown classes of fuzzy implications,and improves finally the knowledge framework of fuzzy implications.