摘要
讨论Ｆｕｚｚｙ向量空间和Ｆｕｚｚｙ模的有限赋值分布问题．Ｒ．Ｌｏｗｅｎ在１９８０年证明了每个Ｆｕｚｚｙ有限维向量空间仅有有限个Ｆｕｚｚｙ赋值［３］．Ｆｕｚｚｙ模是Ｆｕｚｚｙ向量空间概念的一般化，它是由Ｃ．Ｖ．Ｎｅｇｏｉｔａ和Ｄ．Ａ．Ｒａｌｅｓｃｕ于１９７５年引入的［１］．我们在１９８７年找出了一大类Ｆｕｚｚｙ模，它们具有有限Ｆｕｚｚｙ赋值分布的性质［５］．经研究，进一步得到Ｆｕｚｚｙ模具有有限Ｆｕｚｚｙ赋值的充要条件，并介绍了一种求出这些Ｆｕｚｚｙ赋值的计算方法．
We discuss fuzzy value distribution of fuzzy vector space and fuzzy module.R. Lowen proved that every fuzzy finite-dimensional vector space has only finitely fuzzy value distribution in 1980([3]). Fuzzy module is the generalization to the concept of fuzzy vector spaces and it was introduced by C. V. Negoita and D. A. Ralescu in 1975([1]). The author found a large kind of fuzzy modules equipped with the same property in 1987([5]). In this paper we obtain a sufficient and necessary condition to the fuzzy modules, which were equipped with finitely fuzzy value distribution. Moreover, a calculationg method to pick up all fuzzy values is introduced by this paper.
出处
《湖北大学学报（自然科学版）》
CAS
1995年第4期368-372,共5页
Journal of Hubei University：Natural Science
关键词
诺德模
模糊模
模糊赋值
模糊向量空间
Fuzzy vector space
Fuzzy module
Fuzzy value distribution
Noetherian module
Fuzzy quotient module
