The alpha-embedded and A's fuzzy decomposition theorems
Fuzzy set theory becomes more popular in recent years due to its simplicity in modeling and effectiveness in control problems. Unfortunately, both fuzzy union-decomposition and fuzzy intersection-decomposition problems for fuzzy set A did not attract too much attention by the fuzzy researchers and thus not many people studied on these topics during the past 30 years. This paper gives the concepts of alpha-embedded set A(alpha) for fuzzy set A. On this basis, we propose the fuzzy union-decomposition theorems for fuzzy set A, the fuzzy intersection-decomposition theorems for fuzzy set A, the relational theorems of fuzzy union-decomposition and fuzzy intersection-decomposition for fuzzy set A. (C) 2000 Elsevier Science B.V. All rights reserved.
alpha-embedded set a(alpha) fuzzy union-decomposition theorem fuzzy intersection-decomposition theorem relational theorem