本文選題：模糊子集 + 粗糙集��； 參考：《聊城大學(xué)》2017年碩士論文

【摘要】：不確定性問題在我們的實(shí)際生產(chǎn)生活中是普遍存在的,而模糊集理論、粗糙集理論均適于解決處理信息系統(tǒng)中的不確定性問題.粗糙集理論、模糊集理論經(jīng)過幾十年的發(fā)展,均形成了相對完備的理論體系.而我國學(xué)者取得了重要的研究成果,并受到國內(nèi)外學(xué)者的廣泛關(guān)注.本文主要研究了模糊粗糙集的基本性質(zhì).在處理現(xiàn)實(shí)中越來越復(fù)雜的信息時(shí),為了更好地進(jìn)行處理、篩選、分類找到對我們有用的信息,我們可以借助模糊粗糙集與粗糙模糊集模型來處理這些復(fù)雜的信息問題.所以本文所做的工作主要包括以下四個(gè)方面:第一,在群中,我們可以由模糊集理論得到的模糊子群,通過與粗糙集理論相結(jié)合,研究粗糙模糊子群,并構(gòu)造出該群中子集的下、上近似算子,我們研究了這個(gè)模型中的關(guān)于模糊代數(shù)方面的一些基本性質(zhì).第二,在群中,借助一個(gè)模糊關(guān)系,可以在這個(gè)代數(shù)關(guān)系中生成一個(gè)模糊近似空間.進(jìn)而構(gòu)造出一個(gè)新的模糊粗糙集模型.研究了這個(gè)新模型中的一個(gè)上、下近似算子的結(jié)構(gòu)性質(zhì),即這個(gè)模糊子群的模糊正規(guī)子群.第三,在粗糙集上,我們可以通過覆蓋的關(guān)系,定義在這個(gè)基礎(chǔ)上的新模型,并且可以進(jìn)一步討論研究這個(gè)基于覆蓋的模糊粗糙集新模型的一些基本的相關(guān)的代數(shù)性質(zhì).第四,借助模糊集的表現(xiàn)定理,通過集合套,構(gòu)造出了一種新的多粒度模糊粗糙集的模型,并且構(gòu)造出此模型中的下、上近似.由這個(gè)模型的上、下近似還得到了一些有趣的結(jié)論.本文的這些研究成果使得在代數(shù)系統(tǒng)中的模糊粗糙集理論與粗糙模糊集的理論更為成熟與豐富,并為以后的關(guān)于此方面的代數(shù)研究提供了更有力的條件.
[Abstract]:Uncertainty problems are common in our actual production and life, while fuzzy set theory and rough set theory are all suitable for solving uncertainty problems in information processing systems. After decades of development, rough set theory and fuzzy set theory have formed a relatively complete theoretical system. Chinese scholars have made important research results, and have received extensive attention from domestic and foreign scholars. In this paper, the basic properties of fuzzy rough sets are studied. In order to deal with more and more complex information in reality, we can deal with these complex information problems by means of fuzzy rough set and rough fuzzy set model in order to better process, filter and classify the useful information for us. So the work of this paper mainly includes the following four aspects: first, in the group, we can get the fuzzy subgroup from the fuzzy set theory, by combining with the rough set theory, we study the rough fuzzy subgroup. The lower and upper approximation operators of the subsets in the group are constructed. We study some basic properties of fuzzy algebras in this model. Secondly, a fuzzy approximate space can be generated in this algebraic relation by means of a fuzzy relation in a group. Then a new fuzzy rough set model is constructed. In this paper, we study the structural properties of an upper and lower approximation operator in this new model, that is, the fuzzy normal subgroup of the fuzzy subgroup. Thirdly, we can define a new model on rough set by covering relation, and we can further study some basic algebraic properties of the new fuzzy rough set model based on covering. Fourthly, by means of the representation theorem of fuzzy sets, a new model of multi-granularity fuzzy rough sets is constructed by means of set jackets, and the lower and upper approximations of this model are constructed. Some interesting conclusions are also obtained from the upper and lower approximations of this model. These results of this paper make the theory of fuzzy rough sets and rough fuzzy sets more mature and rich in algebraic systems, and provide more powerful conditions for further algebraic research in this field.
【學(xué)位授予單位】：聊城大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O159

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本文編號：2082717