摘要
本文指出了广义模糊数定义(Chen,Hsieh[50])的不合理性,重新定义了广义模糊数,并给出了广义模糊数的广义分解定理和广义表示定理。以此为基础,在广义模糊数集上引入了序、运算和距离,得出了它们的一些性质,初步建立了广义模糊数的基本理论。这些均以模糊数相应理论为特款,从而拓广了模糊数理论。
In this paper, it is indicated that the popular definition of generalized fuzzy numbers is unreasonable. Then generalized fuzzy numbers are redefined, generalized decomposition theorems and generalized representation theorems are given. Based on these, the orders, operations and distances are introduced on the set of generalized fuzzy numbers, and some of their properties are obtained. The basic theory of generalized fuzzy numbers is built up. All of these made the corresponding theory of fuzzy numbers as special. Consequently, the theory of fuzzy numbers is extended.
作者
张德利
郭彩梅
李晓萍
裴东河
ZHANG De-li;GUO Cai-mei;LI Xiao-ping;PEI Dong-he(College of Mathematics,Changchun Normal University,Changchun 130032,China;College of Sciences,Changchun University,Changchun 130022,China;Management College,Tianjin Normal University,Tianjin 300387,China;College of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China)
出处
《模糊系统与数学》
北大核心
2018年第4期67-81,共15页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(61374009
11271063)
吉林省自然科学基金资助项目(201215190)
关键词
模糊数
广义模糊数
运算
序
距离
Fuzzy Numbers
Generalized Fuzzy Numbers
Operations
Orders
Distances
