直觉模糊BCK-代数  

Intuitionisitic Fuzzy BCK-algebras

作　　者：彭家寅[1,2] 

机构地区：[1]四川省高等学校数值仿真重点实验室 [2]内江师范学院数学与信息科学学院

出　　处：《淮阴师范学院学报（自然科学版）》2011年第4期296-303,共8页Journal of Huaiyin Teachers College;Natural Science Edition

基　　金：四川省科技厅重点资助项目(2006J13-035);四川省教育厅重点实验室专项资助项目(2006ZD050)

摘　　要：系统研究了作为Zadeh模糊理论重要扩展的Atanassov直觉模糊BCK-代数.首先,引入直觉模糊BCK-代数和它的水平代数的概念,讨论了它们相关性质.其次,研究了直觉模糊BCK-代数的同态与同构像和逆像的性质,获得了直觉模糊BCK-代数的同态像和逆像仍为直觉模糊BCK-代数.最后,给出了直觉模糊集上的直觉模糊关系、强直觉模糊关系的概念,对直觉模糊集的笛卡儿积进行了定义,揭示了直觉模糊BCK-代数与其积代数间的若干关系.The problems of intuitionistic fuzzy BCK-algebras on intuitionisitic fuzzy sets by Atanassov,which is a significant extension of fuzzy set theory by Zadeh,are systemically investigated.At first,the notions of intuitionistic fuzzy BCK-algebras and its level algebras are introduced,and their properties are discussed.The next,some properties of the homomorphic（isomorphic） image and inverse image of intuitionistic fuzzy BCK-algebras are studied,it is obtained that the homomorphic（isomorphic） image and inverse image of intuitionistic fuzzy BCK-algebras are still intuitionistic fuzzy BCK-algebras.Lastly,the notions of intuitionistic fuzzy relation,strongest intuitionistic fuzzy relation and Cartesian product of intuitionisitic fuzzy sets are given,some relations between intuitionistic fuzzy BCK-algebras and its product algebras are exposed.

关 键 词：直觉模糊集 直觉模糊BCK-代数 水平代数 直觉模糊关系 笛卡儿积 

分 类 号：O159[理学—数学]