内江师范学院学报
內江師範學院學報
내강사범학원학보
JOURNAL OF NEIJIANG TEACHERS COLLEGE
2015年
6期
1-10
,共10页
BCK-代数,(s,t-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
BCK-代數,(s,t-模糊子代數%(∈,∈∨q)-模糊子代數%(∈-,∈-∨q)-模糊子代數%R-模糊子代數%Rλ-模糊子代數
BCK-대수,(s,t-모호자대수%(∈,∈∨q)-모호자대수%(∈-,∈-∨q)-모호자대수%R-모호자대수%Rλ-모호자대수
BCK-algebra%(s,t]-fuzzy subalgebra%(∈,∈ ∨q)-fuzzy subalgebra%(∈-,∈- ∨q)-fuzzy subalgebra%R-fuzzy subalgebra%Rλ-fuzzy subalgebra
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。
建立BCK-代數的兩種新的模糊子代數。首先,利用模糊點與模糊集之關繫,引入瞭 BCK-代數的(s,t]-模糊子代數之概唸,由此穫得瞭被人們認可的兩類特殊而非平凡模糊子代數：(∈,∈∨q)-模糊子代數和(∈-,∈-∨q)-模糊子代數,進而討論瞭它們的關繫和性質。其次,研究瞭(s,t]-模糊子代數的同態象與原象的性質,給齣瞭(s,t]-模糊子代數與其積代數之關繫。最後,利用模糊邏輯之蘊涵算子,提齣瞭BCK-代數的R-模糊子代數的和R-模糊子代數和Rλ-模糊子代數的概唸,討論瞭它們的性質,以及(s,t]-模糊子代數、R-模糊子代數和Rλ-模糊子代數這三者間的一繫關繫。
건립BCK-대수적량충신적모호자대수。수선,이용모호점여모호집지관계,인입료 BCK-대수적(s,t]-모호자대수지개념,유차획득료피인문인가적량류특수이비평범모호자대수：(∈,∈∨q)-모호자대수화(∈-,∈-∨q)-모호자대수,진이토론료타문적관계화성질。기차,연구료(s,t]-모호자대수적동태상여원상적성질,급출료(s,t]-모호자대수여기적대수지관계。최후,이용모호라집지온함산자,제출료BCK-대수적R-모호자대수적화R-모호자대수화Rλ-모호자대수적개념,토론료타문적성질,이급(s,t]-모호자대수、R-모호자대수화Rλ-모호자대수저삼자간적일계관계。
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.
