二型凸模糊集的运算  

Operations on Convex Type-2 Fuzzy Sets

作　　者：刘志强 熊清泉[1] 

机构地区：[1]四川师范大学数学与软件科学学院,成都四川610066

出　　处：《模糊系统与数学》2018年第1期88-96,共9页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11201325);四川省科技厅应用基础项目(2016JY0235);四川省教育厅重点项目(16ZA0053)

摘　　要：本文讨论了二型模糊集凸次隶属函数的运算与性质。由于二型模糊集的次隶属函数是一个一型模糊集,本文首先给出了一般模糊集的运算规律,得到了一般模糊集并与交运算的最大值性质。然后利用该性质得到了凸一型模糊集在最小t-模,最大t-余模下并与交运算的性质,最后由一般模糊集的运算规律,获得了凸、标准凸、凹凸和凹的模糊集在最小t-模,最大t-余模下的内在关系。In this paper, we discuss some properties of convex type-2 fuzzy set membership function. Because the type-2 fuzzy set membership function is a type-1 fuzzy set, we first discuss the general fuzzy set operation rule and obtained the general fuzzy sets and the maximum operation properties. Next, by the general fuzzy set operation properties we obtained join and meet operations of convex type-1 fuzzy set on minimum t-norm and maximum t-conorm. Finally, the relationships are obtained among convex, normal convex, concave and concavoconvex fuzzy set on minimum t-norm and maximum t-conorm operations relations.

关 键 词：二型模糊集 二型凸模糊集 最小t-模 最大t-余模 

分 类 号：O159[理学—数学]