多重模糊蕴涵与生成模糊蕴涵的新方法

提出一种生成模糊蕴涵的新方法,即通过一个或多个选定的模糊蕴涵作多重迭代生成新的模糊蕴涵,称为多重模糊蕴涵.从选定的模糊蕴涵出发,根据不同的迭代次数,分别证明迭代结果仍为模糊蕴涵.进一步,分析当选定的模糊蕴涵具有某种性质时,所生成的多重模糊蕴涵是否仍保持这些性质.还对选定的模糊蕴涵分别为(S,N)-蕴涵和R-蕴涵这两种重要情形,进行更深入的分析.这些结果将为模糊蕴涵在控制及决策等领域的应用提供支持.

Multiple fuzzy implications and novel methods to generate fuzzy implications

This paper proposes some new methods for generating fuzzy implications. Some new fuzzy operations can be generated by using some selected fuzzy implications through multiple iterations. According to different iterative methods, all of the new fuzzy operations have been proved to be fuzzy implications. Furthermore, when the selected fuzzy implications satisfied some important properties, whether multiple fuzzy implications still keep these properties or not is also discussed. Two important cases have been investigated: the selected implications are (S, N)-implications or R-implications. This work provides some new possible selections of fuzzy implications for some applied fields such as fuzzy control and fuzzy decision making.