| 一类基于有界算子合成的模糊关系方程 |
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| 引用本文： | 陈伟,吴望名.一类基于有界算子合成的模糊关系方程[J].模糊系统与数学,2001,15(2):13-20. |
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| 作者姓名： | 陈伟 吴望名 |
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| 作者单位： | 1. 上海大学理学院,
2. 上海师范大学数学科学学院, |
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| 基金项目： | 国家自然科学基金资助项目 (6 98730 34 ) |
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| 摘 要： | 讨论模糊关系的有界和 -有界积合成的基本性质。对于论域 U上的一个自反和有界传递的模糊关系 R,证明它是一个预序关系。得到关于有界算子的模糊线性方程有解的充要条件及解的递归结构。在此基础上给出有限论域上的模糊关系方程 A·X=B的求解方法
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| 关 键 词： | 模糊关系 有界合成 模糊关系方程 有界算子 有界和 有界积 模糊集理论 |
| 文章编号： | 1001-7402(2001)02-0013-08 |
| 修稿时间： | 2000年4月10日 |
A Kind of Fuzzy Relational Based on Bounded Operators Composition |
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| CHENG Wei,WU Wang-ming.A Kind of Fuzzy Relational Based on Bounded Operators Composition[J].Fuzzy Systems and Mathematics,2001,15(2):13-20. |
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| Authors: | CHENG Wei WU Wang-ming |
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| Institution: | CHENG Wei 1,WU Wang ming 2 |
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| Abstract: | In this paper,we discuss the basic properties of bounded sum bounded product composition of fuzzy relations. For a reflexive and bounded transitive fuzzy relation R , we prove that R must be a preorder relation. Moreover, a sufficient and necessary condition to a fuzzy linear equation based on bounded operators has a solution and a recurrent structure of the solution set are proposed.Finally,we provide a procedure to find the solution sets of fuzzy relational equations based on bounded operators composition on finite universes. |
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| Keywords: | Bounded Sum and Bounded Product Fuzzy Relation Bounded Operators Composition Fuzzy Relational Equation |
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