BCK-代数的(s,t]-模糊子代数与R-模糊代数（英文）  

(s,t]-fuzzy Subalgebras and R-fuzzy Subalgebra of BCK-algebras

作　　者：彭家寅[1] 

机构地区：[1]内江师范学院数学与信息科学学院,四川内江641199

出　　处：《内江师范学院学报》2015年第6期1-10,共10页Journal of Neijiang Normal University

基　　金：国家自然科学基金(11071178);教育部数学与应用数学专业综合改革(ZG0464);四川省科技厅重点科技项目(2006J13-035);四川省数学与应用数学专业综合改革(01249)

摘　　要：建立BCK-代数的两种新的模糊子代数.首先,利用模糊点与模糊集之关系,引入了BCK-代数的(s,t]-模糊子代数之概念,由此获得了被人们认可的两类特殊而非平凡模糊子代数:(∈,∈∨q)-模糊子代数和(∈,∈∨q)-模糊子代数,进而讨论了它们的关系和性质.其次,研究了(s,t]-模糊子代数的同态象与原象的性质,给出了(s,t]-模糊子代数与其积代数之关系.最后,利用模糊逻辑之蕴涵算子,提出了BCK-代数的R-模糊子代数的和R-模糊子代数和Rλ-模糊子代数的概念,讨论了它们的性质,以及(s,t]-模糊子代数、R-模糊子代数和Rλ-模糊子代数这三者间的一系关系.Two new kinds of definiting of fuzzy subalgebras of BCK-algebras are proposed in this paper.First, by the use of the relations between fuzzy points and fuzzy subsets,the definition of a （s,t]-fuzzy subalgebras of BCK-algebras is introduced.The acceptable non-trivial concepts obtained in this manner are the （∈,∈∨q）-fuzzy subalgebras,and （∈^-,∈^-∨q）-fuzzy subalgebras.Furthermore,their relations and properties are discussed.Second, how to deal with the homomorphic image and inverse image of （s,t]-fuzzy subalgebras are studied,and the relations between a （s,t]-fuzzy subalgebra in BCK-algebras and a （s,t]-fuzzy subalgebra in the product algebra of BCK-algebras are given.Finally,by the use of the implicative operators of fuzzy logic,the concepts of R-fuzzy subalgebras and Rλ-fuzzy subalgebras of BCK-algebras are proposed and their properties are discussed, some relations among the （s,t]-fuzzy subalgebras,R-fuzzy subalgebras and Rλ-fuzzy subalgebras are studied.

关 键 词：BCK-代数 (s R-模糊子代数 (∈ ∈∨q)-模糊子代数 (∈^- ∈^-∨q)-模糊子代数 R-模糊子代数 Rλ-模糊子代数 

分 类 号：O159[理学—数学]