Vague Set Of Algebraic Properties And Applications

The research of uncertain problem becomes a hot point that many scholars are going to discuss. The Vague theory described by this paper is also just a kind of new theory representing inexact knowledge, Gau made the definition of Vague sets the first time in 1993.The paper includes two parts. The first character and the second character introduced simply several fuzzy theories and some basic knowledge about Vague sets which will be used in this paper, this is thefirst part.The second part is the most important part in this paper, it includes three points: First, in the third character, on the basis of the concept of the four types operations of Vague sets introduced by Li Fan, on the condition that homomorphism and isomorphism between two classical groups, the extension operations of Vague sets are studied. Second, in the fourth character, we discuss Vague groups, give some interesting properties, and the most important result is the homomorphism and isomorphism between two L-Vague sets, the homomorphism and isomorphism theorems in the theory of classical groups are extended to the L-Vague groups. Third, in the fifth character, on the basis of the concept of interval valued vague sets introduced by Ma Zhifeng, we study the decision method in multiobject Vague decision system.