Vague Set Theory And Its Application

Vague Sets Theory proposed by W.L.Gau and D.J.Buehrer, TaiWanscholars,is the development of Fuzzy Sets Theory. In the real world, thereexists quite a number of information that is fuzzy but can not be expressedand processed by Fuzzy Sets Theory, while Vague sets can express andhandle more fuzzy information. The study ofapproximate reasoning basedon Vague sets will provide a new tool to the computer simulation of fuzzythought and logical reasoning mechanism of human being.In this paper, On the basic of comparing and analyzing among presentVague Sets Theory, and preparing for Vague sets used in multiple objectivesdecision making and integration judged. Vague Matrix,Inner-product andOut-product of Vague Sets are introduced first, Then the theory of equalclustering analyze at vague set are introduced, Similarity measure is one ofimportant, effective and widely-used methods in data processing andanalysis. The paper draws comparison and analysis among presentsimilarity measure methods in the case of similarity measure between Vaguevalues, provides a new similarity measure methods.Finally Vague Sets areused in multiple objectives decision making systems, and solved the defectof index. Moreover, the method has more apply, and showed that it is moreefficient and advantageous.