犹豫模糊集和Picture模糊集理论与应用研究

发布时间：2018-03-26 17:01

本文选题：犹豫模糊集　切入点：对偶犹豫模糊集　出处：《湖南大学》2015年博士论文

【摘要】：在纷繁芜杂的现实生活里,不确定性现象是广泛存在的.许多不确定性问题难以用现成的数学工具诸如概率论、模糊集、区间数学来处理.为了应对现实需求,Torra、Cuong以及Pawlak分别提出了犹豫模糊集、Picture模糊集和粗糙集理论,它们都是处理不确定性现象的新工具.犹豫模糊集可以视为模糊集的一种推广,它允许各个成员具有多个隶属度,从而较好地描摹了人们在思考时模棱两可与犹豫不决.Picture模糊集也可以看作是模糊集的一种推广,它的每个成员都用[0,1]上的四个数来刻画,分别对应着决策者的四种态度:赞成、中立、反对、弃权,它恰切地描绘了会议表决的场景.粗糙集则基于等价关系产生划分,然后采用上下近似算子来逼近任一给定的集合.相比模糊集而言,犹豫模糊集和Picture模糊集携带了更多的信息,因而可以更全面地刻画对象,有利于决策者做出更合理的判断.针对犹豫模糊集的研究,主要集中在相似性测量、距离、聚集算子及其在多属性决策中的应用;而Picture模糊集刚刚被提出,目前还没有展开相关的研究.尽管犹豫模糊集和粗糙集的研究已经取得了许多进展,但仍然有很多方面还需进一步发展与完善;至于Picture模糊集,其可供开垦的空间则更大.本文在现有研究成果的基础上继续讨论犹豫模糊集和Picture模糊集的理论及其应用,主要包括以下几个方面:(1)研究了一些对偶犹豫模糊聚集算子及其在多属性决策中的应用.为了有效地捕捉各个属性之间的潜藏关系,我们把Choquet积分算子引入到对偶犹豫模糊集中来,构造了对偶犹豫模糊Choquet算子(DHFCOA).我们还进一步将(DHFCOA)推广至广义对偶犹豫模糊Choquet序平均算子(GDHFCOA),研究了算子的相应性质,并讨论了这些新算子和已有算子之间的关系.基于广义对偶犹豫模糊Choquet序平均算子,我们提出了一种多属性决策方法.参数的引入,使得决策更加灵活,决策者可以因地制宜地选择合适的参数来满足不同的需求.(2)研究了一些三角犹豫模糊聚集算子及其在多属性决策中的应用.现实的决策问题中,数据之间往往并不独立,而是彼此关联,为此,我们通过结合Bonferroni算子与Choquet积分算子来构造新的三角犹豫模糊聚集算子,得到了一系列的新算子,比如三角犹豫模糊加权Bonferroni算子、三角犹豫模糊加权几何Bonferroni算子、三角犹豫模糊Choquet加权Bonferroni算子等.我们讨论了这些新算子的性质以及各算子间的关系.利用所提出的算子,我们提出了一种多属性决策方法,通过实例验证了该方法的有效性,并与已有的一些方法作了对比.(3)研究了Picture模糊集上的一些聚集算子及其性质.我们从概率角度出发,定义了Picture模糊元之间的基本运算,并据此构造了一些Picture模糊聚集算子,如Picture模糊加权平均算子、Picture模糊加权几何算子、Picture模糊混合平均算子等.接下来,我们讨论了这些算子的性质和关系,并提出了一种多属性决策方法.通过数据实例,我们说明了该方法的实用性与优越性.(4)研究了粗糙集上的增量式属性约简算法.我们考虑对象集的动态变化,建立了更新熵的递推公式,并进而给出了一种新的增量式约简算法.
[Abstract]:In the intricacies of the real life, the phenomenon of uncertainty is widespread. Many uncertainty problems are difficult to use mathematical tools available such as probability theory, fuzzy set, interval mathematics to deal with. In order to cope with the real demand, Torra, Cuong and Pawlak are respectively proposed hesitant fuzzy set, fuzzy set theory and rough set Picture and they are a new tool to deal with uncertain phenomenon. Hesitant fuzzy sets can be regarded as a generalization of fuzzy sets, which allows each member has a plurality of membership, so as to better portray people in thinking and ready to accept either course hesitant.Picture fuzzy sets can also be viewed as a generalization of fuzzy sets. Each of its members are characterized by a number of four [0,1], corresponding to four kinds of attitudes of decision makers: Aye, neutral, against and abstained, it accurately describes the meeting to vote on the scene. The rough set is based on equivalence The relationship between production division, and then using set approximation operators to approximate any given. Compared with the fuzzy sets, fuzzy sets and fuzzy sets Picture hesitate to carry more information, so it can more fully describe the object, helps decision makers to make more rational judgments. Research on hesitant fuzzy set, mainly concentrated in the similar measure distance, aggregation operator and its application in multiple attribute decision-making; fuzzy sets and Picture has just been proposed, there is no relevant studies. Although hesitant fuzzy set and rough set research has made much progress, but there are still many aspects still need further development and improvement; as for Picture fuzzy sets it can, for the reclamation of the space is larger. This continues in the existing research results on the basis of discussing the theory of hesitant fuzzy sets and Picture fuzzy sets and its application, including the following Surface: (1) the application of dual hesitant fuzzy aggregation operators and in multiple attribute decision-making. In order to effectively capture the hidden relationship between the various properties, we get the Choquet integral operator is introduced into the dual hesitant fuzzy set to construct a dual hesitant fuzzy Choquet operator (DHFCOA). We will also further (DHFCOA) extended to the generalized dual hesitant fuzzy Choquet order averaging operator (GDHFCOA), studies the corresponding properties of operators, and discuss the relationship between the new operator and the existing operator. The generalized dual hesitant fuzzy Choquet operator based on the average sequence, we propose a multi attribute decision making method. The introduction of parameters, makes the decision-making more flexible decision making can according to choose appropriate parameters to meet the different needs. (2) studied some hesitation triangle fuzzy aggregation operators and its application in multi attribute decision making in reality. Decision making, data are often not independent, but related to each other, therefore, we through the combination of Bonferroni operator and Choquet integral operator to construct a new triangle hesitant fuzzy aggregation operators, obtained a series of new operators, such as triangular fuzzy weighted Bonferroni operator to hesitate, hesitate to triangular fuzzy weighted geometric Bonferroni operator, triangular fuzzy Choquet weighted hesitation Bonferroni operator. We discussed the properties of the new operator as well as the relationship between the operator. The operator proposed, we propose a multi attribute decision making method, through an example to verify the effectiveness of the method, compared with the existing methods and. (3) studied some aggregation operators and the properties of Picture fuzzy sets. We start from the angle of probability, defines the basic operations of fuzzy Picture yuan between, and then construct some Picture fuzzy clustering Set operators such as Picture, fuzzy weighted average operator, fuzzy weighted geometric Picture operator, Picture operator, fuzzy mixed average. Then, we discuss the properties and relations of these operators, and proposes a multi attribute decision making method. Through data examples, we illustrate the practicability and superiority of the method (4). Study on incremental attribute reduction algorithm of rough set. We consider the dynamic changes of object set, a recursive formula for updating entropy, and then proposes a new incremental reduction algorithm.

【学位授予单位】：湖南大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O159

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