双极值模糊集及其应用的研究

发布时间：2018-01-29 08:41

本文关键词： 动态双极值模糊软集对数增长模型双极值模糊信息熵双极值信息系统二粒度　出处：《安徽大学》2015年硕士论文　论文类型：学位论文

【摘要】：为描述和解决实际问题中存在的不确定性和模糊性,概率论、模糊集、粗糙集、软集等理论引起了学者的广泛关注,并得到了很好的发展,且广泛应用于金融、医疗等领域,但是大部分的研究成果还是基于静态的.可是,在实际生活中,信息值是动态变化的,所以本文在模糊集和粗糙集的基础上,研究了动态双极值模糊软集以及时间权重的确定方法和优势关系下的双极值粗糙模型等问题,主要工作如下：(1)介绍了模糊集、软集、双极值模糊集的发展过程以及将时间引入直觉模糊集得到的理论成果,同时介绍了基于粗糙集模型在国内外的研究成果.(2)介绍了模糊集、软集、双极值模糊集等理论的基本概念,讨论了在实际问题中决策信息值随时间变化的情况,定义了动态双极值模糊软集,讨论了相关运算及性质.为了反映时间的作用,从两个方向出发研究动态的时间对决策问题的影响,并把这种影响转化为权重的方式引入到决策问题中.通过这两种量化时间权重的方法,然后利用集成算子将动态的双极值模糊软集集成为综合双极值模糊软集,最后根据水平软集思想确定最终决策结果,并给出实例说明.(3)在优势关系下的粗糙集和区间值信息系统理论的基础上,定义了双极值信息系统,然后将优势关系引入双极值信息系统中,依据粒计算和属性类别理论,将单粒度下的粗糙集推广到二粒度下的粗糙集,并定义了二粒度下的优势度公式,再集成得到综合优势度,最后通过比较综合优势度确定最优决策.
[Abstract]:In order to describe and solve the uncertainty and fuzziness existing in practical problems, the theories of probability theory, fuzzy set, rough set, soft set and so on have attracted wide attention of scholars, and have been well developed and widely used in finance. Medical and other fields, but most of the research results are still based on static. However, in real life, the value of information is dynamic, so this paper based on fuzzy sets and rough sets. The dynamic double extreme fuzzy soft set, the method of determining the time weight and the dual extreme rough model are studied. The main work is as follows: 1) the fuzzy set and the soft set are introduced. The development process of double extreme fuzzy sets and the theoretical results of introducing time into intuitionistic fuzzy sets are introduced. At the same time, fuzzy sets and soft sets based on rough set model are introduced. The basic concepts of the theory of double extremum fuzzy set are discussed. The change of decision information value with time in practical problems is discussed, and the dynamic double extreme fuzzy soft set is defined. In order to reflect the effect of time, the influence of dynamic time on decision making is studied from two directions. Through these two methods of quantifying the weight of time, the dynamic double extremum fuzzy soft set is transformed into a comprehensive double extreme fuzzy soft set by using the integration operator. Finally, the final decision result is determined according to the idea of level soft set, and an example is given to illustrate that based on the theory of rough set and interval value information system under advantage relationship, the double extreme value information system is defined. Then the advantage relation is introduced into the double extremum information system. According to the granular calculation and attribute category theory, the rough set under the single granularity is extended to the rough set under the two granularity, and the dominance formula under the two granularity is defined. The comprehensive dominance degree is obtained by integration, and the optimal decision is determined by comparing the comprehensive dominance degree.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O159

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