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Ranking and Granularity Analysis of Interval-valued Fuzzy Soft Sets

Author: RenJianFeng
Tutor: FengQinRong
School: Shanxi Normal University
Course: Applied Mathematics
Keywords: Soft set Interval-valued fuzzy soft set Dominance relation RankingDecision Entropy Granularity analysis
CLC: O159
Type: Master's thesis
Year: 2014
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Interval-valued fuzzy soft set is an extension model of soft sets and it is a new concept of combining soft set and interval-valued fuzzy set. It is an important mathematical tool for dealing with uncertainties, and there have been some achievements. This paper mainly discusses two working:an algorithm of interval-valued fuzzy soft set is designed to solve ranking problems and it is applied to decision-making; entropy of covering is proposed to analyse granularity dynamic changes of covering approximation space based on interval-valued fuzzy soft set. The specific work is as follows:Ranking is an important topic of interval-valued fuzzy soft set. The text first proposes a δ-dominance relation and discusses the basic properties. Secondly, we introduce a dominance degree of two objects and a whole measure of a object, and analyse their properties. Finally, we study ranking problems of interval-valued fuzzy soft set based on these theories and design an algorithm to solve ranking problems. And the text illustrates the validity of this algorithm through the concrete example.In addition, granularity analysis is another important topic in interval-valued fuzzy soft set. The text first introduces fuzzy dominance matrix of two objects with respect to a parameter and fuzzy dominance matrix of tow objects with respect to all parameters, and disusses some prop-erties. Secondly, we propose A cut fuzzy dominance matrix and λ cut fuzzy dominance relation, and constructe covering approximation space based on λ cut fuzzy dominance relation. Finally, entropy of covering is proposed to analyse granular information dynamic changes through intro-ducing concepts of the characteristic matrix and the distribution characteristic matrix, and an illustrative example is analysed to reflect granular dynamic changes of covering approximation space.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Fuzzy Mathematics
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