本文選題：限制容差關(guān)系 + 程度多粒度粗糙集��； 參考：《安徽工業(yè)大學》2017年碩士論文

【摘要】：由于網(wǎng)絡(luò)技術(shù)和通信技術(shù)的飛速發(fā)展,涌現(xiàn)出類型多樣的海量數(shù)據(jù),各個領(lǐng)域都期待從海量的、雜亂無章的、噪聲數(shù)據(jù)中獲取有用的知識。粗糙集(rough set,RS)在獲取模糊性、不確定的知識方面展現(xiàn)出巨大的優(yōu)勢。它不需要任何其它先驗知識和附加信息,依靠數(shù)據(jù)集合本身的屬性,便可以挖掘出數(shù)據(jù)中隱含的有價值的信息。多粒度粗糙集(Multi-Granulation Rough Set,MGRS)是一種新的粗糙集擴展模型,它從多個粒度空間對目標概念進行近似逼近,在邊界區(qū)域的范圍縮小,目標概念的表示精度提高方面,具有明顯的優(yōu)勢。實際生活中,由于測量偏差等因素,常常存在一些不完備的,但隱藏著豐富知識的數(shù)據(jù)。為了從不完備信息系統(tǒng)中獲得更加準確的知識,本文結(jié)合程度粗糙集,研究不完備MGRS模型和粒度約簡方法。本文主要工作如下:(1)介紹經(jīng)典粗糙集的基礎(chǔ)知識,給出一些實例形象地解釋粗糙集的基本概念。針對完備系統(tǒng)和不完備系統(tǒng),介紹目前MGRS的發(fā)展與研究現(xiàn)狀。(2)分別介紹了基于容差關(guān)系、相似關(guān)系、限制容差關(guān)系的單粒度粗糙集拓展模型和MGRS拓展模型,分析不同關(guān)系下各個粗糙集模型的優(yōu)缺點。(3)針對不完備信息系統(tǒng),提出基于限制容差關(guān)系的程度MGRS,包括程度樂觀MGRS和程度悲觀MGRS。分析程度樂觀MGRS和程度悲觀MGRS的不足之處,提出一種基于限制容差關(guān)系的可變程度MGRS模型。研究這三種模型的相關(guān)性質(zhì)與聯(lián)系。通過實例和實驗分析可變程度MGRS的優(yōu)越性。(4)考慮粒度的權(quán)重,基于限制容差關(guān)系,提出不完備加權(quán)程度MGRS,并討論其性質(zhì)。定義不完備加權(quán)程度MGRS的粒度矩陣、核粒度和粒度重要性公式。提出一種粒度約簡方法,在獲取核粒度的基礎(chǔ)上,以粒度重要性作為啟發(fā)式信息選擇粒度,獲得最終的粒度約簡集。
[Abstract]:Due to the rapid development of network technology and communication technology, massive data of various types have emerged. All fields expect to obtain useful knowledge from mass, disorderly and noisy data. Rough set sets (RS) show great advantages in acquiring fuzzy and uncertain knowledge. It does not need any other prior knowledge and additional information. It can mine the valuable information hidden in the data by relying on the attributes of the data set itself. Multi-granulation Rough set (MGRS) is a new rough set extension model, which approximates the concept of target from multiple granularity spaces, and has obvious advantages in reducing the range of boundary area and improving the precision of representation of target concept. In real life, because of the measurement deviation and other factors, there are often some incomplete, but hidden knowledge of the data. In order to obtain more accurate knowledge from incomplete information system, this paper studies incomplete MGRS model and granularity reduction method combining degree rough set. The main work of this paper is as follows: (1) introduce the basic knowledge of classical rough sets and give some examples to explain the basic concepts of rough sets graphically. For complete systems and incomplete systems, the development and research status of MGRS are introduced. (2) the single granularity rough set extension model and MGRS extension model based on tolerance relation, similarity relation and limiting tolerance relation are introduced respectively. This paper analyzes the advantages and disadvantages of each rough set model under different relationships. (3) aiming at incomplete information systems, the degree MGRS based on restricted tolerance relationship is proposed, including degree optimistic MGRS and degree pessimistic MGRs. By analyzing the disadvantages of degree optimistic MGRS and degree pessimistic MGRS, a variable degree MGRS model based on restricted tolerance relationship is proposed. The related properties and relationships of these three models are studied. The advantage of variable degree MGRS is analyzed by examples and experiments. Considering the weight of granularity, based on the limited tolerance relation, the incomplete weighted degree MGRS is proposed and its properties are discussed. The granularity matrix, kernel granularity and granularity importance formula of incomplete weighted degree MGRS are defined. A granularity reduction method is proposed. Based on the kernel granularity, granularity importance is used as heuristic information to select granularity, and the final granularity reduction set is obtained.
【學位授予單位】：安徽工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP18

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