本文選題：粗糙集　切入點：猶豫模糊軟集　出處：《遼寧工業(yè)大學》2017年碩士論文　論文類型：學位論文

【摘要】：粗糙集、模糊集還有軟集理論都是當代處理不確定性問題的數(shù)學工具。經(jīng)過近些年的發(fā)展,三種理論都得到了相繼推廣,同時,猶豫模糊軟集、軟模糊粗糙集等以這三種理論為基礎的混合型模型也快速地發(fā)展起來。根據(jù)現(xiàn)有的研究成果,本文對猶豫模糊軟集、軟模糊粗糙集進一步擴展。首先,在猶豫模糊軟集的基礎上展開研究,定義廣義猶豫模糊軟集并研究其相關性質;其次,構建兩種廣義猶豫模糊軟集相似度量方法并應用到實際問題中;最后,對軟模糊粗糙集進行推廣,建立軟猶豫模糊粗糙集模型。具體內(nèi)容如下:(1)研究廣義猶豫模糊軟集。在猶豫模糊軟集和廣義模糊軟集理論的基礎上,將猶豫模糊軟集的參數(shù)集賦予猶豫模糊隸屬度,構建廣義猶豫模糊軟集模型;給出廣義猶豫模糊軟子集的定義;定義一種廣義猶豫模糊軟集的擴充,可以將參數(shù)個數(shù)不同的廣義猶豫模糊軟集轉化為參數(shù)個數(shù)相同的廣義猶豫模糊軟集;給出廣義猶豫模糊軟集交、并、補運算的定義,并討論運算的性質;最后通過算例說明以上定義的合理性。(2)針對廣義猶豫模糊軟集的相似度量問題,給出其相似度量Ⅰ。首先,在猶豫模糊集包含度的公理化定義基礎上,建立猶豫模糊集合的三種包含度公式;利用猶豫模糊集的三種包含度公式構造出猶豫模糊集的三種相似度公式;其次依照猶豫模糊集相似度量的公理化定義給出廣義猶豫模糊軟集相似度量的公理化定義,并利用猶豫模糊集的三種相似度公式構造廣義猶豫模糊軟集的相似度公式,同時對該公式加以證明;最后利用廣義猶豫模糊軟集相似度量Ⅰ構建一種決策方法,并將其應用到環(huán)境治理問題中。(3)針對廣義猶豫模糊軟集的相似度量問題,給出其相似度量Ⅱ。首先,在猶豫模糊集包含度的公理化定義基礎上,給出廣義猶豫模糊軟集包含度的公理化定義,并利用猶豫模糊集合的三種包含度公式構造出廣義猶豫模糊軟集間的包含度公式;然后從廣義猶豫模糊軟集的包含度出發(fā)來構造廣義猶豫模糊軟集的相似度公式,這種相似度的計算方法同樣適用于參數(shù)集不同的廣義猶豫模糊軟集;最后將廣義猶豫模糊軟集的相似度Ⅱ應用到關于城市飲水衛(wèi)生評價的聚類分析實例中,通過實例說明了所提出方法的可行性。(4)提出雙論域上的猶豫模糊粗糙集,并討論其性質;研究軟猶豫模糊粗糙集,給出軟猶豫模糊粗糙集上近似和下近似算子,并討論其性質;構建基于軟猶豫模糊粗糙集的決策算法并將其應用到購買汽車的決策問題中;最后討論軟猶豫模糊粗糙集模型與廣義猶豫模糊軟集模型的聯(lián)系,對兩種模型在汽車買賣問題中的實際意義做出說明。
[Abstract]:Rough set, fuzzy set and soft set theory are mathematical tools for dealing with uncertain problems in modern times. Through the development of recent years, three kinds of theories have been popularized one after another, at the same time, hesitant fuzzy soft sets, The hybrid models based on these three theories have also developed rapidly. According to the existing research results, this paper further extends the hesitant fuzzy soft sets and soft fuzzy rough sets. On the basis of hesitating fuzzy soft set, the paper defines generalized hesitant fuzzy soft set and studies its related properties. Secondly, two kinds of similarity measure methods of generalized hesitation fuzzy soft set are constructed and applied to practical problems. This paper generalizes soft fuzzy rough set and establishes soft hesitating fuzzy rough set model. The concrete contents are as follows: 1) the generalized hesitating fuzzy soft set is studied. On the basis of the theory of hesitating fuzzy soft set and generalized fuzzy soft set, The parameter set of the hesitating fuzzy soft set is given the membership degree of the hesitation fuzzy, the model of the generalized hesitant fuzzy soft set is constructed, the definition of the generalized hesitant fuzzy soft subset is given, and the extension of the generalized hesitant fuzzy soft set is defined. The generalized hesitation fuzzy soft set with different parameter number can be transformed into the generalized hesitation fuzzy soft set with the same parameter number, the definition of the intersection of the generalized hesitation fuzzy soft set and the complement operation is given, and the properties of the operation are discussed. Finally, an example is given to illustrate the rationality of the above definition.) for the similarity measurement problem of generalized hesitant fuzzy soft sets, the similarity measure is given. First, on the basis of the axiomatic definition of the inclusion degree of the hesitating fuzzy set, Three kinds of inclusion degree formulas of hesitant fuzzy sets are established, and three similarity formulas of hesitant fuzzy sets are constructed by using the three inclusion degree formulas of hesitating fuzzy sets. Secondly, according to the axiomatic definition of similarity measure of hesitating fuzzy set, the axiomatic definition of similarity measure of generalized hesitation fuzzy soft set is given, and the similarity formula of generalized hesitation fuzzy soft set is constructed by using three similarity formulas of hesitating fuzzy set. At the same time, the formula is proved. Finally, a decision method is constructed by using the similarity measure I of generalized hesitant fuzzy soft sets, and applied to the problem of environmental governance. First of all, based on the axiomatic definition of the inclusion degree of the hesitating fuzzy set, the axiomatic definition of the inclusion degree of the generalized hesitating fuzzy soft set is given. By using the three kinds of inclusion degree formulas of the hesitating fuzzy set, the inclusion degree formula of the generalized hesitant fuzzy soft set is constructed, and the similarity formula of the generalized hesitant fuzzy soft set is constructed from the inclusion degree of the generalized hesitating fuzzy soft set. This similarity calculation method is also suitable for generalized hesitant fuzzy soft sets with different parameter sets. Finally, the similarity 鈪，

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