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Research on Vague set transformation method to Fuzzy sets and similarity measure

Author: ZhouMeng
Tutor: YuJianKun
School: Yunnan University of Finance
Course: Applied Computer Technology
Keywords: Fuzzy sets Vague sets Transformation method Similarity measure
CLC: TP18
Type: Master's thesis
Year: 2012
Downloads: 35
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Abstract

People have long thought that the objects in the real world have precisely definedcriteria of membership to a concept when dealing with them. So, Cantor has foundedthe theory of Cantor sets in1874. In the Cantor sets, an element is either in the Cantorsets or not in it. However, the theory can only solve the problems of two classes, itappears to be helpless when dealing with ambiguous problems.Every object in the world may not precisely defined criteria of membership to aconcept. Thus, there are a lot of information and data which is ambiguous anduncertain, it is obvious that the theory of Cantor sets is unable to them. Then, Zadehproposed Fuzzy sets in1965.In the Fuzzy sets, the degree of membership that anelement belongs to the set ranges between zero to one. The theory of Fuzzy setsprovide a good method and tool for solving the ambiguous and uncertain problems.Especially in the Fuzzy decision, Fuzzy control and expert systems, the method andtool can solve the ambiguous problems well. However, the theory of Fuzzy sets hasits own deficiencies.There are some problems that have been deal with by Fuzzysets.In order to solve the probles, Gau and Bueher founded the theory of Vague sets,the theory made an extension on the basis of Fuzzy sets. In the Vague sets, the degreeof membership that an element belongs to the set is a subinterval between zero to one.It provides two minimum degrees of membership, one is that the element is in the set,the other is that the element is not in the set. Therefore, compared with the Fuzzy sets,Vague sets are better and more accurate in expressing and processing the ambiguousinformation and data.In the intelligent systems, the theory of Fuzzy sets and Vague sets is used fordealing with fuzzy information and data. So it is necessary for us to understand therelationship between Fuzzy sets and Vague sets. This paper firstly describes somebasic theory that contains concepts and operations about Fuzzy sets and Vague setswhich is used in the paper, and then discusses some methods of translating Vague setsinto Fuzzy sets and proposes a new method on the basis of them. The method is proved to be effective by some instances and used in multi-objective fuzzydecision-making.Nowadays, similarity measure is an important technology in pattern recognition,especially the similarity measure between Vague sets. Although many scholars haveproposed a lot of methods, these methods are flawed. Thus, this paper proposes a newmethod, and proves that the method satisfies some properties. In order to verify thefeasibility and effectiveness of the method, compared with some existing methods,the results show that the distinguishing ability of the method is powerful and get agood measure, and it is used in pattern recognition. In this passage, the method isused in the cluster based on Vague value.Although the application about Vague sets in many areas has obtain a better result,because the development about Vague sets is short and the contents of Vague sets stillrelatively new, some theory is not perfect, so we need to make further study in Vaguesets and its application.

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