【摘要】：隨著人類社會(huì)的不斷進(jìn)步,自然界中的分類問題變得更加復(fù)雜化。一些研究對(duì)象沒有特定的屬性,事物的性態(tài)往往具有中立性,對(duì)這類事物的分類必然伴隨模糊性。模糊數(shù)學(xué)為此分類問題提供了良好的理論基礎(chǔ),將模糊集理論與聚類分析相結(jié)合推動(dòng)了分類問題的發(fā)展,越來越多的專家學(xué)者投身于這類問題的研究。但模糊集對(duì)研究對(duì)象模糊程度的刻畫還不夠全面。為了充分挖掘數(shù)據(jù)的有效信息,彌補(bǔ)模糊集的不足,Atanassov于1986年將模糊集理論拓展到了直覺模糊集理論,增加了猶豫度這一新的屬性參數(shù),更加全面地描繪了客觀世界的不確定性本質(zhì)。模糊聚類分析也隨之拓展到了直覺模糊聚類分析,本文在此基礎(chǔ)從以下幾個(gè)方面進(jìn)行了探索性研究。模糊熵可以刻畫模糊集的模糊程度,本文首先根據(jù)直覺模糊熵的概念和定義,從幾何角度解釋了直覺模糊熵,創(chuàng)新性地提出了新的直覺模糊熵公式。其主要思想是以任意直覺模糊點(diǎn)到信息熵最小點(diǎn)的距離,與到信息熵最大、最小點(diǎn)的距離之和的比值作為該直覺模糊點(diǎn)的直覺模糊熵的大小依據(jù),并進(jìn)行歸一化處理,使得計(jì)算公式規(guī)范、合理。其次本文還以模糊度與猶豫度為依據(jù)構(gòu)造了新的直覺模糊熵公式,該公式簡單易操作,并較好地刻畫了研究對(duì)象的模糊程度。本文還提出了構(gòu)造直覺模糊數(shù)作為直覺模糊相似度的新方法,其主要思想是以模糊集間隸屬度距離與非隸屬度距離的最小值作為相似度的非隸屬度,再以1與隸屬度距離、非隸屬度距離的最大值的差作為隸屬度。該計(jì)算公式同時(shí)考慮到不同指標(biāo)對(duì)結(jié)果的貢獻(xiàn)程度不同,增加了各維屬性指標(biāo)的權(quán)重系數(shù),使得計(jì)算結(jié)果更加符合實(shí)際意義。該計(jì)算公式的形式簡單,良好的反映了研究對(duì)象的接近程度,為后文的直覺模糊聚類分析奠定了基礎(chǔ)。最后本文以20個(gè)空中目標(biāo)進(jìn)行分類的問題作為算例,考察了研究對(duì)象的7個(gè)屬性指標(biāo)。利用第三章提出的直覺模糊熵公式確定各指標(biāo)的屬性權(quán)重,再運(yùn)用第四章提出的直覺模糊相似度計(jì)算公式計(jì)算每兩個(gè)空中目標(biāo)的加權(quán)相似度。采用最大樹和等價(jià)關(guān)系兩種聚類算法進(jìn)行分析,并得到了與專家預(yù)測近乎相同的結(jié)果,說明了本文提出的算法的可靠性。
[Abstract]:With the development of human society, the classification problem in nature becomes more complicated. Some objects of study have no specific attributes, and the nature of things is often neutral, the classification of such things must be accompanied by fuzziness. Fuzzy mathematics provides a good theoretical basis for classification problems. The combination of fuzzy set theory and clustering analysis promotes the development of classification problems. More and more experts and scholars devote themselves to the study of such problems. But the description of the fuzzy degree of the research object by fuzzy set is not comprehensive enough. In order to fully mine the effective information of data and make up for the deficiency of fuzzy set, Atanassov extended the theory of fuzzy set to intuitionistic fuzzy set theory in 1986, adding the new attribute parameter of degree of hesitation. A more comprehensive description of the uncertain nature of the objective world. Fuzzy clustering analysis is extended to intuitionistic fuzzy clustering analysis. Fuzzy entropy can depict the fuzzy degree of fuzzy set. Firstly, according to the concept and definition of intuitionistic fuzzy entropy, this paper explains intuitionistic fuzzy entropy from the angle of geometry, and puts forward a new formula of intuitionistic fuzzy entropy innovatively. Its main idea is to take the distance from any intuitionistic fuzzy point to the minimum point of information entropy and the ratio of the sum of distance to the maximum and minimum point of information entropy as the basis for the size of the intuitionistic fuzzy entropy of the intuitionistic fuzzy point, and to normalize it. The calculation formula is standardized and reasonable. Secondly, a new intuitionistic fuzzy entropy formula is constructed based on ambiguity and hesitancy. The formula is simple and easy to operate, and describes the fuzzy degree of the object well. A new method of constructing intuitionistic fuzzy number as intuitionistic fuzzy similarity is also presented in this paper. The main idea of this method is to take the minimum value of membership distance and non-membership distance between fuzzy sets as the non-membership degree of similarity, and then to use 1 and membership degree distance. The difference of the maximum distance between non-membership degrees is taken as membership degree. At the same time, the formula takes into account the different contribution of different indexes to the results, and increases the weight coefficients of each dimension attribute index, which makes the calculation results more in line with the practical significance. The formula is simple in form and well reflects the degree of closeness of the object of study, which lays a foundation for intuitionistic fuzzy clustering analysis in the following papers. Finally, taking 20 aerial targets for classification as an example, 7 attribute indexes of the objects are investigated. The attribute weight of each index is determined by the intuitionistic fuzzy entropy formula proposed in chapter 3, and the weighted similarity of each two air targets is calculated by using the intuitionistic fuzzy similarity formula proposed in chapter 4. Two clustering algorithms, maximum tree and equivalence relation, are used to analyze, and the results are almost the same as that of expert prediction, which shows the reliability of the proposed algorithm.
【學(xué)位授予單位】：西華師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O159

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