区间二型模糊相似度与包含度

相似度与包含度是模糊集合理论中的两个重要概念,但对于二型模糊集合的研究还较为少见．鉴于此,提出了新的区间二型模糊相似度与包含度．首先选择了二者的公理化定义;然后基于公理化定义提出了新的计算公式,并讨论了二者的相互转换关系;最后通过实例来验证二者的性能,并将区间二型模糊相似度与Yang-Shih聚类方法相结合,用于高斯区间二型模糊集合的聚类分析,得到了合理的层次聚类树．仿真实例表明新测度具有一定的实用价值．     

Parameterized attribute reduction with Gaussian kernel based fuzzy rough sets

Fuzzy rough sets are considered as an effective tool to deal with uncertainty in data analysis, and fuzzy similarity relations are used in fuzzy rough sets to calculate similarity between objects. On the other hand in kernel tricks, a kernel maps data into a higher dimensional feature space where the resulting structure of the learning task is linearly separable, while the kernel is the inner product of this feature space and can also be viewed as a similarity function. It has been reported there is an overlap between family of kernels and collection of fuzzy similarity relations. This fact motivates the idea in this paper to use some kernels as fuzzy similarity relations and develop kernel based fuzzy rough sets. First, we consider Gaussian kernel and propose Gaussian kernel based fuzzy rough sets. Second we introduce parameterized attribute reduction with the derived model of fuzzy rough sets. Structures of attribute reduction are investigated and an algorithm with discernibility matrix to find all reducts is developed. Finally, a heuristic algorithm is designed to compute reducts with Gaussian kernel fuzzy rough sets. Several experiments are provided to demonstrate the effectiveness of the idea.     

Value集的模糊嫡、相似度量和距离测度的关系

Vague集理论在各个领域中的广泛应用引起越来越多学者的注意,而模糊墒、相似度量和距离测度是其中的3个关键技术。目前已提出多种关于Vague集的模糊嫡、相似度量和距离测度的计算方法,但这些研究都没有讨论这3个基本概念之间的联系。基于Vague集的模糊嫡、相似度量和距离测度的公理化定义,给出了三者之间的相互诱导关系,建立了模糊墒、相似度量和距离测度之间的联系。     

Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship

In this paper, we introduce an axiomatic definition of an interval-valued fuzzy sets’ inclusion measure which is different from Bustince’s [H. Bustince, Indicator of inclusion grade for interval-valued fuzzy sets, Applications to approximate reasoning based on interval-valued fuzzy sets, International Journal of Approximate Reasoning, 23 (2000) 137-209]. The relationship among the normalized distance, the similarity measure, the inclusion measure, and the entropy of interval-valued fuzzy sets is investigated in detail. Furthermore, six theorems are proposed showing how the similarity measure, the inclusion measure, and the entropy of interval-valued fuzzy sets can be deduced by the interval-valued fuzzy sets’ normalized distance based on their axiomatic definitions. Some formulas have also been put forward to calculate the similarity measure, the inclusion measure, and the entropy of interval-valued fuzzy sets.     

基于模糊等价的毕达哥拉斯模糊集相似度构造方法

毕达哥拉斯模糊集是Zadeh模糊集的一种推广形式,其相似度刻画方法是毕达哥拉斯模糊集理论的重要研究内容.现有的毕达哥拉斯模糊集相似度大多针对具体问题而提出.为推广毕达哥拉斯模糊集理论的应用范围,文中基于模糊等价研究毕达哥拉斯模糊集相似度的一般构造方法.将模糊等价概念推广至毕达哥拉斯模糊数,提出了PFN(Pythagor...     

关于模糊粗糙集的相似度量

基于对不确定性信息处理的背景,定义了模糊粗糙值与模糊粗糙集的相似度量,研究了它们的有关性质。     

Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications

In this paper we propose an entropy measure for interval-valued intuitionistic fuzzy sets, which generalizes three entropy measures defined independently by Szmidt, Wang and Huang, for intuitionistic fuzzy sets. We also give an approach to construct similarity measures using entropy measures for interval-valued intuitionistic fuzzy sets. In particular, the proposed entropy measure for interval-valued intuitionistic fuzzy sets can yield a similarity measure. Several illustrative examples are given to demonstrate the practicality and effectiveness of the proposed formulas. We apply the similarity measure to solve problems on pattern recognitions, multi-criteria fuzzy decision making and medical diagnosis.     

模糊熵、距离测度和相似性测度之间的关系

模糊熵、距离测度和相似性测度是模糊集合的三种重要度量,许多学者对三者之间的关系进行了研究。采用更为严格的定义,通过定义模糊集合之间新的运算研究了三者之间的关系,给出了三者之间的相互诱导公式。对部分公式进行了举例说明。     

直觉区间值模糊集的熵、距离测度和相似测度

熵、距离测度和相似测度是模糊集理论中的三个基本概念.本文中,我们给出了直觉区间值模糊集的熵、距离测度和相似测度的公理化定义并讨论了它们之间的基本关系.有别于以往的交、并运算,我们提出了直觉区间值模糊集的加法、乘法运算,并在此基础上讨论了直觉区间值模糊集的熵、距离测度和相似测度的性质.     

两类正规模糊集的相似度量

基于对不确定性信息处理的背景,讨论了常见的两类正规模糊集的相似度量,给出了正规三角模糊集和正规梯形模糊集相似度量的一般计算公式,研究了它们的有关性质,为基于相似度量的近似推理和模糊控制提供了理论准备.     

模糊粗糙集的相似度量和相似性方向

粗糙集理论是一种新的处理模糊和不确定性知识的软计算工具,在人工智能及认知科学等众多领域已经得到了广泛的应用。相似度量的研究是模糊集理论与粗糙集理论的热点问题之一。文章提出了一种更精确、更合理的相似度量方法,讨论了它的一些性质。然后,在此基础上提出了模糊粗糙集的相似性方向的概念,用于比较两个相似的模糊粗糙集所包含信息的精确性大小,并给出了一个关于相似性方向的判别函数。这在近似推理、模式识别和决策分析等领域有着广泛的应用。最后,通过一个实例,分析说明了这种相似度量方法和相似性方向的判别方法是更合理更有效的。     

基于正规三角模糊集相似度量的模糊推理

文章首先定义了正规模糊集相似度量的一般公式,然后给出了正规三角模糊集相似度量计算的简化公式,在正规三角模糊集相似度量的基础上,提出了一种新的模糊推理的方法——基于正规三角模糊集相似度量的模糊推理,并与Mamdani模糊推理方法做了比较。最后给出了模糊推理的仿真实现。     

Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making

The main feature of Pythagorean fuzzy sets is that it is characterized by five parameters, namely membership degree, nonmembership degree, hesitancy degree, strength of commitment about membership, and direction of commitment. In this paper, we first investigate four existing comparison methods for ranking Pythagorean fuzzy sets and point out by examples that the method proposed by Yager, which considers the influence fully of the five parameters, is more efficient than the other ones. Later, we propose a variety of distance measures for Pythagorean fuzzy sets and Pythagorean fuzzy numbers, which take into account the five parameters of Pythagorean fuzzy sets. Based on the proposed distance measures, we present some similarity measures of Pythagorean fuzzy sets. Furthermore, a multiple criteria Pythagorean fuzzy group decision‐making approach is proposed. Finally, a numerical example is provided to illustrate the validity and applicability of the presented group decision‐making method.     

An improved similarity measure for generalized fuzzy numbers and its application to fuzzy risk analysis

This paper presents an improved method to compute the degree of similarity between generalized trapezoidal fuzzy numbers. The proposed similarity measure contains many features of fuzzy numbers such as geometric distance, center of gravity (COG), area, perimeter, and height. The previous methods are criticized via presenting some examples. In addition, the performance of the proposed methods is compared by the existing similarity measures using twenty different sets of generalized trapezoidal fuzzy numbers. Furthermore, the proposed method is used for fuzzy risk analysis based on similarity measures. Finally, an example is introduced to illustrate the fuzzy risk analysis.     

Local density adaptive similarity measurement for spectral clustering

Similarity measurement is crucial to the performance of spectral clustering. The Gaussian kernel function is usually adopted as the similarity measure. However, with a fixed kernel parameter, the similarity between two data points is only determined by their Euclidean distance, and is not adaptive to their surroundings. In this paper, a local density adaptive similarity measure is proposed, which uses the local density between two data points to scale the Gaussian kernel function. The proposed similarity measure satisfies the clustering assumption and has an effect of amplifying intra-cluster similarity, thus making the affinity matrix clearly block diagonal. Experimental results on both synthetic and real world data sets show that the spectral clustering algorithm with our local density adaptive similarity measure outperforms the traditional spectral clustering algorithm, the path-based spectral clustering algorithm and the self-tuning spectral clustering algorithm.     

基于海明距离的直觉模糊粗糙集相似度量方法

针对直觉模糊粗糙集的相似度量问题,提出了一种基于海明距离的直觉模糊粗糙集相似度量方法。首先给出了两个直觉模糊粗糙值问的相似度量方法,并揭示了它的若干重要性质。然后,在此基础上,又提出了一种基于海明距离的直觉模糊粗糙集相似度量方法,并证明它也具有同样的性质。最后用数值算例验证了这种方法的有效性。     

一种新的直觉模糊相似矩阵构造方法

基于直觉模糊相似度和相异度,研究了直觉模糊相似矩阵构造问题。给出了直觉模糊相似度和相异度的标准定义,选取了有效的直觉模糊相似度量和相异度量方法;在分析了现有的几种直觉模糊相似矩阵构造方法基础上,提出了一种新的直觉模糊相似矩阵构造方法。通过算例分析,验证了方法的有效性。     

模糊软集之间的相似性度量及应用

研究模糊软集的不确定度量问题,给出模糊软集的包含度、相似度公理化定义;基于模糊蕴含算子提出新的模糊软集包含度与相似度度量方法,该方法具有一定的普遍性,在某种程度上提供不同的模糊蕴含算子就可得到不同的包含度与相似度。基于新的相似度度量方法构造了一种决策方法并应用于金融企业流动性检测中。     

Distance and similarity measures for hesitant fuzzy sets

In this paper, we propose a variety of distance measures for hesitant fuzzy sets, based on which the corresponding similarity measures can be obtained. We investigate the connections of the aforementioned distance measures and further develop a number of hesitant ordered weighted distance measures and hesitant ordered weighted similarity measures. They can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Several numerical examples are provided to illustrate these distance and similarity measures.     

On generalized similarity measures for Pythagorean fuzzy sets and their applications to multiple attribute decision-making

In this paper, we develop a new and flexible method for Pythagorean fuzzy decision-making using some trigonometric similarity measures. We first introduce two new generalized similarity measures between Pythagorean fuzzy sets based on cosine and cotangent functions and prove their validity. These similarity measures include some well-known Pythagorean fuzzy similarity measures as their particular and limiting cases. The measures are demonstrated to satisfy some very elegant properties which prepare the ground for applications in different areas. Further, the work defines a generalized hybrid trigonometric Pythagorean fuzzy similarity measure and discuss its properties with particular cases. Then, based on the generalized hybrid trigonometric Pythagorean fuzzy similarity measure, a method for dealing with multiple attribute decision-making problems under Pythagorean fuzzy environment is developed. Finally, a numerical example is given to demonstrate the flexibility and effectiveness of the developed approach in solving real-life problems.