区间值模糊集的区间值水平截集、分解定理和表现定理  

Interval-valued Level Cut Sets, Decomposition Theorems and Representation theorems on Interval-valued Fuzzy Sets

作　　者：袁学海[1,2] 李洪兴[2] 宋晶晶[3] 

机构地区：[1]大连理工大学盘锦校区基础教学部,辽宁盘锦124221 [2]大连理工大学控制科学与工程学院,辽宁大连116024 [3]大连理工大学数学科学学院,辽宁大连116024

出　　处：《模糊系统与数学》2013年第5期1-10,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(90818025;61374118)

摘　　要：给出了区间值模糊集的区间值水平截集的新定义,建立了基于此类截集的分解定理和表现定理。首先,将区间值模糊集的区间值水平截集定义为三值模糊集,给出了区间值模糊集的四类截集的定义,指出这些截集与模糊集的截集有完全一样的性质。其次,建立了区间值模糊集的分解定理和表现定理。这些工作为研究区间值模糊集提供了新的工具。In this paper, the definitions of interval-valued level cut sets on interval-valued fuzzy sets are proposed and new decomposition theorems and representation theorems of interval-valued are given. Firstly, the interval-valued level cut sets on interval-valued fuzzy sets are considered as three-valued fuzzy sets and consequently the four kinds of cut sets of interval-valued fuzzy sets are presented. It is pointed that these cut sets have the same properties with those of fuzzy sets. Secondly, based on these cut sets, the decomposition theorems and representation theorems of interval-valued fuzzy sets are built respectively. Those works have shown that a new kind of tool for studying interval-valued fuzzy sets is acquired.

关 键 词：区间值模糊集 三值模糊集 截集 分解定理 表现定理 

分 类 号：O159[理学—数学]