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Researches About Group Decision-making Methods and Granular Analysis of Fuzzy Soft Set Information

Author: WangCuiCui
Tutor: MaoJunJun
School: Anhui University
Course: Probability Theory and Mathematical Statistics
Keywords: soft set fuzzy soft set intuitionistic fuzzy soft set aggregatingmethods group decision-making methods granularity analysis
CLC: O159
Type: Master's thesis
Year: 2013
Downloads: 32
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Abstract


In modern society, there exist uncertainty, fuzziness and complexity in many practical problems, classical uncertain theory tool (include probability theory, fuzzy set theory, rough set theory and interval numbers theory and so on) influence their inherent limitations, which are possibly the inadequacy of the parameterization method in dealing with these problems. In order to overcome these disadvantages, Molodtsov proposed a novel mathematical tool—soft set theory. In recent years, decision-making methods have attracted widely attention by many scholars based on this theory, and many theoretical results have been applied in management decision-making, economic forecasting and system engineering and so on. Under the information environment of fuzzy soft set and intuitionistic fuzzy soft set, this article has discussed problems about their aggregating methods, decision-making methods and granularity analysis and so on.At first, introduce the development process of soft set, fuzzy soft set and intuitionistic fuzzy soft set and their decision-making methods and the domestic and foreign current research situation, and give the article’s research framework.Then introduce the concepts of soft set, fuzzy soft set and intuitionistic fuzzy soft set, discuss their operations and relevant properties. Extend WA operator and WG operator into fuzzy soft sets information environment, and propose FSWA operator, FSWG operator, IFSWA operator, IFSWG operator. By define compare index, extend OWA operator and OWG operator to FSOWA operator, FSOWG operator, IFSOWA operator, IFSOWG operator.And by aggregating operator, research the multi-expert group decision making problems based on fuzzy soft set and intuitionistic fuzzy soft set. Firstly, fuzzy soft set and intuitionistic fuzzy soft set are expressed in matrix form, the constructing method of level soft set is given by threshold value vector as median and p-quintile; Secondly, define some concepts such as correlation degree, distance and so on, the expert weight is divided into completely known, partly known and unknown completely, the method of solving weight is given by using programming model, and eight different decision algorithms are put forward according to different situations; Finally, the feasibility of the decision-making methods is verified by the some practical examples.Then discuss the granularity analysis of fuzzy soft set. Concepts about the possibility degree, the weighted possibility degree, α-dominance class, α-covering, α-covering approximation space, the description set and the indistinguishability set are defined. The variable precision granularity analysis is given based on fuzzy soft matrix, and the uncertainty of approximation space has been measured by granularity capacity, and the correctness of conclusion is verified by examples.At last, the full articles are summarized and looking into the distance.

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