Vague Sets And Are Equal Based On Vague Vague Algebraic Structure Of A Number Of Conclusions

In 1965, Professor L. A. Zadeh first put forward the fuzzy sets, which represented the degree discourse elements attached to the fuzzy set by membership function, thus there is more than the classical set of expression. In 1983, Bulgarian scholars Atanassov K promoted the fuzzy set, and proposed Intuitionistic fuzzy sets,then Intuitionistic fuzzy sets was simplified and vague sets was put forward by Taiwan scholars WLGau and DJBuehrer. There are two membership degrees---positive and negative of Vague sets,which comparing to fuzzy sets is much better in the expression and the processing of uncertain information. In this paper, vague sets as the research object, mostly researched the decomposition theorem of vague sets, vague sets and vague similarity measure entropy, as well as the subgroup generated by vague and nature.This paper is divided into four parts, the structure and main contents are as follows:ChapterⅠbriefly describes the background to the issue of this study, the development of the status quo and so on, this article points out the significance of innovations and research.ChapterⅡis based on new wave of vague sets of cut sets and the decomposition theorem brought forth by Zhang Xinbo. The author extended fuzzy sets on the extension to vague sets, then proposed principles and nature of the expansion of vague sets.ChapterⅢgives two commonly used formulas of the improved optimized fuzzy measure, vague sets and vague similarity measure entropy, comparing to existing methods, illustrates its rationality and superiority by an example comparing.ChapterⅣgives the improved definition of vague subgroup which is based on the definition of vague groups and generates the vague definition of subgroups proposed by Demirci M. Some examples were given to reveal the improved definition is a generalization of the original narrative, and it gives a series of important characters to improve vague sub-groups.