二型模糊蕴涵算子的一些性质  

Some Properties of Type-2 Fuzzy Implications

作　　者：赵姗[1] 李洪兴[1] 

机构地区：[1]大连理工大学电子信息与电气工程学部,辽宁大连116024

出　　处：《模糊系统与数学》2015年第4期10-18,共9页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11101066;61074044;61374118;61104038)

摘　　要：主要讨论了二型模糊蕴涵算子的模糊凸性和单调性问题。给出了扩展的模糊蕴涵算子为二型模糊蕴涵算子的一个充分条件,即模糊蕴涵算子连续。从所给反例可以看出,连续性对于扩展的模糊蕴涵算子是否保持模糊真值的模糊凸性和保持原模糊蕴涵算子的单调性有着重要的作用。如果模糊蕴涵算子不连续,则其扩展的模糊蕴涵算子不一定为二型模糊蕴涵算子。In this paper, the convexity and monotonicity of type-2 fuzzy implications are investigated. A sufficient condition under which an extended fuzzy implication is a type-2 fuzzy implication is given that fuzzy implication is continuous. The counterexamples have illustrated that the continuity acts as an important role for type-2 fuzzy implications to keep the convexity of fuzzy truth values and the monotonicity of fuzzy implications. It can be see if fuzzy implication is not continuous, its extended fuzzy implication may not be a type-2 fuzzy implication.

关 键 词：二型模糊逻辑 模糊蕴涵算子 模糊真值 

分 类 号：O159[理学—数学]