本文選題：猶豫模糊集　切入點(diǎn)：對(duì)偶猶豫模糊集　出處：《湖南大學(xué)》2015年博士論文

【摘要】：在紛繁蕪雜的現(xiàn)實(shí)生活里,不確定性現(xiàn)象是廣泛存在的.許多不確定性問(wèn)題難以用現(xiàn)成的數(shù)學(xué)工具諸如概率論、模糊集、區(qū)間數(shù)學(xué)來(lái)處理.為了應(yīng)對(duì)現(xiàn)實(shí)需求,Torra、Cuong以及Pawlak分別提出了猶豫模糊集、Picture模糊集和粗糙集理論,它們都是處理不確定性現(xiàn)象的新工具.猶豫模糊集可以視為模糊集的一種推廣,它允許各個(gè)成員具有多個(gè)隸屬度,從而較好地描摹了人們?cè)谒伎紩r(shí)模棱兩可與猶豫不決.Picture模糊集也可以看作是模糊集的一種推廣,它的每個(gè)成員都用[0,1]上的四個(gè)數(shù)來(lái)刻畫(huà),分別對(duì)應(yīng)著決策者的四種態(tài)度:贊成、中立、反對(duì)、棄權(quán),它恰切地描繪了會(huì)議表決的場(chǎng)景.粗糙集則基于等價(jià)關(guān)系產(chǎn)生劃分,然后采用上下近似算子來(lái)逼近任一給定的集合.相比模糊集而言,猶豫模糊集和Picture模糊集攜帶了更多的信息,因而可以更全面地刻畫(huà)對(duì)象,有利于決策者做出更合理的判斷.針對(duì)猶豫模糊集的研究,主要集中在相似性測(cè)量、距離、聚集算子及其在多屬性決策中的應(yīng)用;而Picture模糊集剛剛被提出,目前還沒(méi)有展開(kāi)相關(guān)的研究.盡管猶豫模糊集和粗糙集的研究已經(jīng)取得了許多進(jìn)展,但仍然有很多方面還需進(jìn)一步發(fā)展與完善;至于Picture模糊集,其可供開(kāi)墾的空間則更大.本文在現(xiàn)有研究成果的基礎(chǔ)上繼續(xù)討論猶豫模糊集和Picture模糊集的理論及其應(yīng)用,主要包括以下幾個(gè)方面:(1)研究了一些對(duì)偶猶豫模糊聚集算子及其在多屬性決策中的應(yīng)用.為了有效地捕捉各個(gè)屬性之間的潛藏關(guān)系,我們把Choquet積分算子引入到對(duì)偶猶豫模糊集中來(lái),構(gòu)造了對(duì)偶猶豫模糊Choquet算子(DHFCOA).我們還進(jìn)一步將(DHFCOA)推廣至廣義對(duì)偶猶豫模糊Choquet序平均算子(GDHFCOA),研究了算子的相應(yīng)性質(zhì),并討論了這些新算子和已有算子之間的關(guān)系.基于廣義對(duì)偶猶豫模糊Choquet序平均算子,我們提出了一種多屬性決策方法.參數(shù)的引入,使得決策更加靈活,決策者可以因地制宜地選擇合適的參數(shù)來(lái)滿足不同的需求.(2)研究了一些三角猶豫模糊聚集算子及其在多屬性決策中的應(yīng)用.現(xiàn)實(shí)的決策問(wèn)題中,數(shù)據(jù)之間往往并不獨(dú)立,而是彼此關(guān)聯(lián),為此,我們通過(guò)結(jié)合Bonferroni算子與Choquet積分算子來(lái)構(gòu)造新的三角猶豫模糊聚集算子,得到了一系列的新算子,比如三角猶豫模糊加權(quán)Bonferroni算子、三角猶豫模糊加權(quán)幾何Bonferroni算子、三角猶豫模糊Choquet加權(quán)Bonferroni算子等.我們討論了這些新算子的性質(zhì)以及各算子間的關(guān)系.利用所提出的算子,我們提出了一種多屬性決策方法,通過(guò)實(shí)例驗(yàn)證了該方法的有效性,并與已有的一些方法作了對(duì)比.(3)研究了Picture模糊集上的一些聚集算子及其性質(zhì).我們從概率角度出發(fā),定義了Picture模糊元之間的基本運(yùn)算,并據(jù)此構(gòu)造了一些Picture模糊聚集算子,如Picture模糊加權(quán)平均算子、Picture模糊加權(quán)幾何算子、Picture模糊混合平均算子等.接下來(lái),我們討論了這些算子的性質(zhì)和關(guān)系,并提出了一種多屬性決策方法.通過(guò)數(shù)據(jù)實(shí)例,我們說(shuō)明了該方法的實(shí)用性與優(yōu)越性.(4)研究了粗糙集上的增量式屬性約簡(jiǎn)算法.我們考慮對(duì)象集的動(dòng)態(tài)變化,建立了更新熵的遞推公式,并進(jìn)而給出了一種新的增量式約簡(jiǎn)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.

【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：O159

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本文編號(hào)：1668752