The α-embedded and A's fuzzy decomposition theorems

摘要

Fuzzy set theory becomes more poplar 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 α-embedded set A~α 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.