基于熵权相似度的直觉模糊聚类分析研究及其应用
发布时间：2018-11-07 06:59
【摘要】：随着人类社会的不断进步,自然界中的分类问题变得更加复杂化。一些研究对象没有特定的属性,事物的性态往往具有中立性,对这类事物的分类必然伴随模糊性。模糊数学为此分类问题提供了良好的理论基础,将模糊集理论与聚类分析相结合推动了分类问题的发展,越来越多的专家学者投身于这类问题的研究。但模糊集对研究对象模糊程度的刻画还不够全面。为了充分挖掘数据的有效信息,弥补模糊集的不足,Atanassov于1986年将模糊集理论拓展到了直觉模糊集理论,增加了犹豫度这一新的属性参数,更加全面地描绘了客观世界的不确定性本质。模糊聚类分析也随之拓展到了直觉模糊聚类分析,本文在此基础从以下几个方面进行了探索性研究。模糊熵可以刻画模糊集的模糊程度,本文首先根据直觉模糊熵的概念和定义,从几何角度解释了直觉模糊熵,创新性地提出了新的直觉模糊熵公式。其主要思想是以任意直觉模糊点到信息熵最小点的距离,与到信息熵最大、最小点的距离之和的比值作为该直觉模糊点的直觉模糊熵的大小依据,并进行归一化处理,使得计算公式规范、合理。其次本文还以模糊度与犹豫度为依据构造了新的直觉模糊熵公式,该公式简单易操作,并较好地刻画了研究对象的模糊程度。本文还提出了构造直觉模糊数作为直觉模糊相似度的新方法,其主要思想是以模糊集间隶属度距离与非隶属度距离的最小值作为相似度的非隶属度,再以1与隶属度距离、非隶属度距离的最大值的差作为隶属度。该计算公式同时考虑到不同指标对结果的贡献程度不同,增加了各维属性指标的权重系数,使得计算结果更加符合实际意义。该计算公式的形式简单,良好的反映了研究对象的接近程度,为后文的直觉模糊聚类分析奠定了基础。最后本文以20个空中目标进行分类的问题作为算例,考察了研究对象的7个属性指标。利用第三章提出的直觉模糊熵公式确定各指标的属性权重,再运用第四章提出的直觉模糊相似度计算公式计算每两个空中目标的加权相似度。采用最大树和等价关系两种聚类算法进行分析,并得到了与专家预测近乎相同的结果,说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.
【学位授予单位】：西华师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159
本文编号：2315575
[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.
【学位授予单位】：西华师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159
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