Some Properties Of Vague Sets Study

Vague sets and fuzzy sets are the main targets of fuzzy mathematics. Vague sets are further promotion and development of fuzzy sets. This paper analyzes a number of important definitions and properties of fuzzy sets, and defines some basic concepts of vague sets.Then we obtain a number of important properties and new results of vague sets. Main results are as follows:1. The algebraic properties of the vague sets are studied. We prove that the vague sets with the operations of join intersection and complement form a quasi-Boolean algebra. We obtain the decomposition theorem and the representation theorem of vague sets, by comparing the relationship of vague sets and fuzzy sets.2. The applications of the vague sets are studied. By comparing some of the existing calculating methods of the fuzzy entropy of vague sets, and pointing out that some of their deficiencies, we give a new calculating method of the fuzzy entropy of vague sets. And through some examples, we find that the new method is more reasonable.