不变反凸模糊集  

Anti-convex Fuzzy Set Based on Invex Set

作　　者：刘卫锋[1] 

机构地区：[1]郑州航空工业管理学院数理系,郑州450015

出　　处：《重庆师范大学学报（自然科学版）》2013年第4期46-49,共4页Journal of Chongqing Normal University:Natural Science

基　　金：河南省教育厅科学技术研究重点项目(No.12B110027);郑州航空工业管理学院青年科研基金(No.2011113003)

摘　　要：研究了不变反凸模糊集及其相关性质,推广了有关文献中反凸模糊集的概念和相关结论。首先,通过将不变凸集的思想应用到反凸模糊集,定义了一种新的广义反凸模糊集——不变反凸模糊集:设A∈F(Rn),称A为不变反凸模糊集,若存在映射η:Rn×Rn→Rn,有A(y+αη(x,y))≤A(x)∨A(y),x,y∈Rn,α∈[0,1]。然后,探讨了反凸模糊集与不变反凸模糊集的关系:当η(x,y)=x-y时,不变反凸模糊集就退化为反凸模糊集,显然,反凸模糊集成为不变反凸模糊集的特例;通过构造例子说明不变反凸模糊集不是反凸模糊集,得到不变反凸模糊集是反凸模糊集的真推广的结论。根据不变反凸模糊集的定义,研究了不变反凸模糊集的并、稠密性等性质以及模糊集成为不变反凸模糊集的条件。最后,类似于不变反凸模糊集,分别探讨了模糊集成为不变强反凸模糊集和不变严格反凸模糊集的条件。Anti-convex fuzzy set based on invex set and its related properties were researched,and anti-convex fuzzy set and some results in the related references were generalized.By applying thought of invex set to anti-convex fuzzy set,a new generalized anti-convex fuzzy set called anti-convex fuzzy set based on invex set was proposed.Let A∈F（Rn）,andA is called Anti-convex fuzzy set based on invex set,whereη：Rn×Rn→Rn,and A（y＋αη（x,y））≤A（x）∨A（y）,x,y∈Rn,α∈.Then,the relation between anti-convex fuzzy set and anti-convex fuzzy set based on invex set was discussed.If η（x,y）=x-y,then anti-convex fuzzy set based on invex set was degenerated into anti-convex fuzzy set,and obviously,anti-convex fuzzy set was made particular case of anti-convex fuzzy set based on invex set.Anti-convex fuzzy set based on invex set was not anti-convex fuzzy set by building an example,and anti-convex fuzzy set based on invex set was a true generalization of anti-convex fuzzy set.Thirdly,based on the definition of anti-convex fuzzy set based on invex set,the properties about the union and denseness of anti-convex fuzzy set based on invex set and the condition for fuzzy sets to be anti-convex fuzzy set based on invex set were studied.Lastly,similarly to ant-convex fuzzy set based on invex set,the conditions for fuzzy set to be strongly anti-convex fuzzy set based on invex set and strictly anti-convex fuzzy set based on invex set fuzzy sets were respectively studied.

关 键 词：反凸模糊集 不变反凸模糊集 不变凸集 凸模糊集 

分 类 号：O174[理学—数学]