【摘要】：粗糙集理論是Pawlak教授提出的處理不準(zhǔn)確、不完整和不明晰信息的數(shù)學(xué)方法。模糊集理論是Zadeh教授提出的,用來刻畫模糊現(xiàn)象以及模糊概念的數(shù)學(xué)工具。其后,Atanassov教授推廣了Zadeh教授的模糊集理論,并在模糊集理論的基礎(chǔ)之上,給出了直覺模糊集的概念,該理論給出了隸屬度同時,又給出了非隸屬度和猶豫度的概念,既表達(dá)了“亦此亦彼”,也表達(dá)了“非此非彼”的現(xiàn)象。在分析處理不明確、不完備等信息時,直覺模糊集相較于模糊集具有更強(qiáng)表達(dá)能力。由于直覺模糊集和粗糙集理論在處理不明確性和不完整性問題時,考慮問題出發(fā)角度與側(cè)重方向不是相同的,兩個理論具有很強(qiáng)的互補(bǔ)性。于是,Dubois創(chuàng)造性地將這兩種理論結(jié)合起來進(jìn)行研究,兩種理論的融合已經(jīng)成為了新的研究熱點,引起了許多學(xué)者的研究興趣。近幾年,覆蓋粗糙集、鄰域粗糙集、多粒度粗糙集是粗糙集的重要拓展形式,它們的研究引起了許多學(xué)者的關(guān)注,成為新的研究熱點。目前,將覆蓋粗糙集和直覺模糊集的結(jié)合、鄰域粗糙集與直覺模糊集的結(jié)合,同時從粒度的角度對它們的研究成果較少,對其進(jìn)行研究具有一定的理論價值和實際意義。因此本文在覆蓋理論基礎(chǔ)上,對粗糙集、鄰域粗糙集以及直覺模糊集結(jié)合進(jìn)行了研究,并從粒度的角度出發(fā),對覆蓋粗糙直覺模糊集拓展進(jìn)行了研究,建立了一些模型,研討了這些模型的一些重要性質(zhì),并用算例驗證了有效性。本文的創(chuàng)新點如下:(1)在粗糙集、直覺模糊集和覆蓋理論基礎(chǔ)上,給出了模糊覆蓋粗糙隸屬度和非隸屬度的定義,構(gòu)建了一種新的模型----覆蓋粗糙直覺模糊集,證明了該模型的一些重要性質(zhì),與此同時又定義了一種新的直覺模糊集的相似性度量公式,并用例子進(jìn)行了驗證;(2)把最小描述由單一粒度拓展到了多個粒度,提出了新的基于多粒度的最小描述定義。在此基礎(chǔ)上,給出了多粒度的模糊覆蓋粗糙隸屬度、非隸屬度概念,構(gòu)建了I型、II型多粒度覆蓋粗糙直覺模糊集模型,討論了它們的性質(zhì),并舉例說明;(3)基于不同的屬性集序列和不同的鄰域半徑,定義了雙重粒化準(zhǔn)則,建立基于雙重�；瘻�(zhǔn)則的多粒度鄰域粗糙直覺模糊集模型。并給出該模型的相關(guān)性質(zhì)。然后,提出了樂觀與悲觀多粒度鄰域粗糙直覺模糊集的近似集,并討論了這些模型的一些重要性質(zhì),最后由例子驗證了這些模型的有效性。
[Abstract]:Rough set theory is a mathematical method proposed by Professor Pawlak to deal with inaccurate, incomplete and unclear information. Fuzzy set theory is a mathematical tool for describing fuzzy phenomena and fuzzy concepts proposed by Professor Zadeh. After that, Professor Atanassov generalizes Professor Zadeh's fuzzy set theory and gives the concept of intuitionistic fuzzy set on the basis of fuzzy set theory. It not only expresses the phenomenon of "this is also that", but also expresses the phenomenon of "neither this nor that". The intuitionistic fuzzy sets have stronger expressive ability than fuzzy sets in analyzing and dealing with uncertain and incomplete information. Because the intuitionistic fuzzy set and rough set theory are different from each other when dealing with the problem of uncertainty and incompleteness, the two theories are highly complementary. Therefore, Dubois creatively combines the two theories to study. The fusion of the two theories has become a new research hotspot, which has aroused the interest of many scholars. In recent years, covering rough sets, neighborhood rough sets and multi-grained rough sets are important extension forms of rough sets. At present, the combination of covering rough set and intuitionistic fuzzy set, the combination of neighborhood rough set and intuitionistic fuzzy set, and the research results of them from the angle of granularity have certain theoretical value and practical significance. Therefore, on the basis of covering theory, this paper studies the combination of rough set, neighborhood rough set and intuitionistic fuzzy set, and studies the extension of covering rough intuitionistic fuzzy set from the angle of granularity, and establishes some models. Some important properties of these models are discussed, and the validity of these models is verified by an example. The innovations of this paper are as follows: (1) on the basis of rough set, intuitionistic fuzzy set and covering theory, the definitions of fuzzy covering rough membership degree and non-membership degree are given, and a new model, covering rough intuitionistic fuzzy set, is constructed. Some important properties of the model are proved. At the same time, a new similarity measurement formula of intuitionistic fuzzy sets is defined and verified by an example. (2) the minimum description is extended from single granularity to multiple granularity. A new definition of minimum description based on multi-granularity is proposed. On this basis, the concepts of multi-granularity fuzzy covering rough membership degree and non-membership degree are given, and I type, II type multi-granularity covering rough intuitionistic fuzzy set model are constructed, and their properties are discussed. An example is given to illustrate. (3) based on different attribute set sequences and different neighborhood radius, double granulation criteria are defined, and a multi-granularity neighborhood rough intuitionistic fuzzy set model based on double granulation criteria is established. The related properties of the model are given. Then, the approximate sets of rough intuitionistic fuzzy sets with optimistic and pessimistic multi-granularity neighborhood are proposed, and some important properties of these models are discussed. Finally, the validity of these models is verified by an example.
【學(xué)位授予單位】：河南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP18

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