BL-代数上inf-→合成关系方程的解集  

The Solution of an inf-→ Composition Relational Equation Sets on a BL-Algebra

作　　者：杨晓文[1] 熊清泉[1] 莫艳[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2013年第3期328-333,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11201325);教育部博士点专项基金(20105134110002)资助项目

摘　　要：对满足线性序和消去律的BL-代数上模糊关系方程∧j∈J(aj→xj)=b在无限论域中的解进行了讨论.提出了可达解和不可达解的概念,讨论了极大解与它们的关系;对于不可达解部分,给出了方程的解结构特点;对于可达解部分,找出了所有的极大解,并对方程的每个可达解都找到一个相应的极大解.实际上,在有限的情况下,若满足线性序,文献中方程的所有解都是可达解,而无限时,方程也可能存在不可达解.In 2008, I. Peffilieva et al （Fuzzy Sets and Systems,2008,159：2256 -2271. ） made in-depth discussion about the so- lutions to the equation （aj→xj） = b on finite universe in a BL-algebra whieh fulfills the linear order and cancelation law. This paper, j^j - . based on the same premises, hut on an infinite universe, makes further discussion about the solutions to the equation. First, the con- cepts of attainable solution and unattainable solution are defined, the relationship between maximal solution and the two kinds of solu- tions is discussed. For the unattainable solutions, the structure characteristics of solutions of the fuzzy relation equation is given, for the attainable solution, all the maximal solutions are found and it is proved that under certain conditions each solution of the equation is less than or equal to a respective maximal one. In fact, in finite universe ease, if linear order is also satisfied, the solutions are all at- tainable, and unattainable solutions may also exist in infinite universe case.

关 键 词：BL-代数 关系方程 可达解 不可达解 极大解 

分 类 号：O159[理学—数学]