Solution Sets of Interval-Valued Fuzzy Relational Equations

被引：10
|
作者：
Shunmin Wang
Shu-Cherng Fang
Henry L.W. Nuttle
机构：
[1] North Carolina State University,Operations Research Program
[2] North Carolina State University,Department of Industrial Engineering
来源：
Fuzzy Optimization and Decision Making | 2003年 / 2卷 / 1期
关键词：
fuzzy relational equations; interval-valued;
D O I：
10.1023/A:1022800330844
中图分类号：
学科分类号：
摘要：
This paper introduces the concepts of tolerable solution set, united solution set, and controllable solution set of interval-valued fuzzy relational equations. Given a continuous t-norm, it is proved that each of the three types of the solution sets of interval-valued fuzzy relational equations with a max-t-norm composition, if nonempty, is composed of one maximum solution and a finite number of minimal solutions. Necessary and sufficient conditions for the existence of solutions are given. Computational procedures based on the constructive proofs are proposed to generate the complete solution sets. Examples are given to illustrate the procedures.
引用
收藏
页码：41 / 60
页数：19
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