A novel approach towards bipolar complex fuzzy sets and their applications in generalized similarity measures

The notions of the bipolar complex fuzzy set (BCFS) and complex bipolar fuzzy set (CBFS) have been already given, but these notions of BCFS and CBFS have the problem that they contradict the basic definition of the complex numbers which we discussed in this article, and then we defined the new definition of BCFS. Our defined notion of BCFS is more closed to bipolarity as compared with already existing BCFS and CBFS, and more accurate. BCFS is the fusion of bipolar fuzzy set (BFS) which a decision analyst needs to describe the positive and negative aspects of an object and complex fuzzy set (CFS) which a decision analyst needs to handle two-dimensional (two variables) information. When there is information of two variables with positive and negative aspects then a decision analyst needs BCFS to handle this information. In this article, we also interpreted some basic operations on BCFS like a complement, intersection, and union and explained them with the help of examples. Additionally, we defined the concept of type-1 partially BCFS and type-2 partially BCFS. Further, we interpreted some generalized trigonometric similarity measures such as generalized cosine similarity measure, generalized tangent similarity measure, generalized cotangent similarity measure, and generalized hybrid trigonometric similarity measure for BCFS. The weighted generalized trigonometric similarity measures are also presented in this article. After that, we applied these similarity measures (SMs) in two real-life applications (pattern recognition and medical diagnosis) to show the benefits and advantages of our proposed SMs. Finally, we did a comparison of our demonstrated SMs with some existing SMs to show the superiority, usefulness, and effectiveness of our proposed SMs.     

Vague集上一个新的贴近度公式

基于已有文献给出的一般性Vague集上贴近度的表达式,结合已提出的几个贴近度公式,研究了一个新的贴近度公式具有的性质,揭示了几个贴近度表达式之间的关系。     

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...     

The generalized Dice similarity measures for Pythagorean fuzzy multiple attribute group decision making

The Pythagorean fuzzy set (PFS) is characterized by two functions expressing the degree of membership and the degree of nonmembership, which square sum of them is equal or less than 1. It was proposed as a generalization of a fuzzy set to deal with indeterminate and inconsistent information. In this study, we shall present some novel Dice similarity measures of PFSs and the generalized Dice similarity measures of PFSs and indicates that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based multiple attribute group decision-making models with Pythagorean fuzzy information. Then, we apply the generalized Dice similarity measures between PFSs to multiple attribute group decision making. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for selecting the desirable ERP system.     

基于正弦函数的直觉模糊集相似度测量及其应用

相似度测量是度量两个直觉模糊集相似程度的重要方法,现已有很多测量公式被相继提出,但现有的部分公式在一些实际应用中会出现无法归类或计算过程相对复杂现象。针对这种问题,通过对Tian 提出的余切相似度测量方法的研究,同时考虑隶属度、非隶属度和犹豫度三个方面信息,提出了两个正弦相似度测量公式,证明了公式的正确性,并用几组数值例子将其与其它测量公式进行比较分析,验证了新公式的合理性。最后通过实例说明了该方法的有效性。     

直觉犹豫模糊集的相关系数在群推荐中的应用

在直觉犹豫模糊集描述的群推荐系统中,首先,针对直觉犹豫模糊距离公式计算相似性问题中存在的不足,提出了直觉犹豫模糊集相关系数的概念;其次,给出直觉犹豫模糊集相关系数的聚类算法,并分析采用直觉犹豫模糊集相关系数公式与距离公式计算相似性的区别;最后,利用直觉犹豫模糊集相关系数对电影进行推荐,结论表明了直觉犹豫模糊集相关系数方法的实用性和有效性。     

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。     

Interval-valued intuitionistic fuzzy cosine similarity measures for multiple attribute decision-making

In this work, considering all information carried by the membership degrees, nonmembership degree, and hesitancy degree in interval-valued intuitionistic fuzzy sets (IVIFSs) as 3-D vector representations, we propose a cosine similarity measure and a weighted cosine similarity measure for IVIFSs based on the extension of the cosine similarity measure (angular coefficient) between intuitionistic fuzzy sets in 2-D vector space. Then, the weighted cosine similarity measure for IVIFSs is applied to multiple attribute decision-making problems under the interval-valued intuitionistic fuzzy environment. Through the similarity measure between the ideal alternative and each alternative, the ranking order of all alternatives can be determined and the best alternative can be easily identified as well. Finally, two illustrative examples are given to demonstrate the applications and efficiency of the proposed decision-making method.     

基于信息测度的勾股模糊决策模型及其应用

相对于直觉模糊集，勾股模糊集能够更为全面和有效地表达描述复杂问题中的不确定和非一致信息，使其受到了广泛研究。对于属性评价值为勾股模糊数并且属性指标权重信息数据完全未知的多属性决策问题，以提出的勾股模糊信息测度为基础，设计了新的多属性决策模型。该模型运用对数函数设计了一种新的勾股模糊数信息熵计算方法；引入了勾股模糊相似度概念，并结合对数行数提出勾股模糊数相似度的衡量方法，随后挖掘出勾股模糊数的信息熵和相似度之间的内在联系；运用提出的勾股模糊熵和相似度计算方法，构建新的多属性决策模型，并进行应用研究。实验结果表明，提出的模型合理有效，同时拓展了模型的使用范围。     

Vague集之间的相似度量

分析了Chen给出的一种度量Vague集(值)之间相似程度的度量方法,指出了这种相似度量方法所存在的缺陷.在此基础上,给出了一种新的相似度量方法.由于该方法具有较好的性质,更具合理性,因而是一种较为理想的检测Vague集(值)之间相似程度的度量方法.     

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。     

广义犹豫模糊软集的相似度量及其应用

在广义模糊软集和犹豫模糊软集的基础上给出广义犹豫模糊软集的概念,并研究广义犹豫模糊软集的相似度量。首先利用三种犹豫模糊集合的包含度,构造犹豫模糊集间的相似度量公式。然后在犹豫模糊集相似度基础上给出广义犹豫模糊软集相似度量的公理化定义,并构造广义犹豫模糊软集的相似度量公式,这些公式可以计算参数集不同时两个广义犹豫模糊软集间的相似度。最后利用广义犹豫模糊软集相似度量方法构造了一种决策方法,并将这个决策方法应用于环境治理问题中。通过实例验证了所提出方法的可行性和有效性。     

A novel TODIM-VIKOR approach based on entropy and Jensen–Tsalli divergence measure for picture fuzzy sets in a decision-making problem

The picture fuzzy set (PFS) has grown huge attention in the research area of uncertain information from the last few years. Information measures have been widely studied in various fuzzy environments. Therefore, in this paper, we study the entropy and divergence measures under the picture fuzzy environment. First, the paper introduced a new entropy measure to measure the fuzziness degree associated with a PFS. An example is established to show the capabilities of the proposed entropy measure. Second, the paper defines a new Jensen–Tsalli divergence measure for PFS to evaluate the information of discrimination between two PFS. We also discuss several properties of entropy and divergence measures in detail. Then we present a new method, based on proposed entropy and divergence measure, to determine the objective weights of experts for multicriteria group decision making with picture fuzzy information. The final criteria weights are obtained by combining subjective and objective weights for more reliable weightage of evaluation criteria. By using this comprehensive weight-determination technique, the proposed method can effectively reduce the unreasonable impact of the extreme evaluation data on the evaluation results. Further, a new multi-criteria decision-making approach is developed based on the combining concepts of the TODIM and VIKOR method under the picture fuzzy environment. We used TODIM to obtain the overall dominance degree which considers the bounded rationality of decision makers and VIKOR is used to obtain the compromise ranking of alternatives. Lastly, an application of the proposed integrated model is demonstrated to verify the feasibility and usefulness and the outcomes of the proposed model are compared with the outcomes of the existing approaches to indicate its validity. This integrated method can effectively reduce the distortion of decision information and provide extraordinary evaluation results. The proposed approach is used in detecting the major issues due to which a company is facing such breakdowns.     

计算Vague集贴近度的一种新方法

指出了Chen给出的Vague集的贴近度存在的缺陷,并分析了李凡[1]提出的贴近度。在此基础上,引入了Vague集(值)的距离概念,进而引入并研究了Vague集(值)的贴近度,并证明了这一新的贴近度的性质。     

Fault Diagnoses of Hydraulic Turbine Using the Dimension Root Similarity Measure of Single-valued Neutrosophic Sets

This paper proposes a dimension root distance and its similarity measure of single-valued neutrosophic sets (SVNSs), and then develops the fault diagnosis method of hydraulic turbine by using the dimension root similarity measure of SVNSs. By the similarity measures between the fault diagnosis patterns and a testing sample with single-valued neutrosophic information and the relation indices, we can determine the main fault type and the ranking order of various vibration faults for predicting some possible fault trend. Then, the comparison of the fault diagnoses of hydraulic turbine based of the proposed dimension root similarity measure and the existing cotangent similarity measure of SVNSs is provided to demonstrate the effectiveness and rationality of the proposed fault diagnosis method. The fault diagnosis results of hydraulic turbine show that the proposed fault diagnosis method not only gives the main fault types of hydraulic turbine, but also provides useful information for multifault analyses and future possible fault trends. The developed fault diagnosis method is effective and reasonable in the fault diagnosis of hydraulic turbine under single-valued neutrosophic environment.     

基于对称交互熵的犹豫模糊信息相似度及聚类应用

研究面向犹豫模糊信息的聚类方法。首先,定义犹豫模糊相对熵、对称交互熵,并基于信息论的角度提出一个新的犹豫模糊相似度公式;然后,利用相似度公式构造相似系数矩阵,基于编网聚类方法对犹豫模糊集进行聚类;最后,通过算例验证了所提出方法的有效性。     

Some cosine similarity measures and distance measures between q-rung orthopair fuzzy sets

In this paper, we consider some cosine similarity measures and distance measures between q-rung orthopair fuzzy sets (q-ROFSs). First, we define a cosine similarity measure and a Euclidean distance measure of q-ROFSs, their properties are also studied. Considering that the cosine measure does not satisfy the axiom of similarity measure, then we propose a method to construct other similarity measures between q-ROFSs based on the proposed cosine similarity and Euclidean distance measures, and it satisfies with the axiom of the similarity measure. Furthermore, we obtain a cosine distance measure between q-ROFSs by using the relationship between the similarity and distance measures, then we extend technique for order of preference by similarity to the ideal solution method to the proposed cosine distance measure, which can deal with the related decision-making problems not only from the point of view of geometry but also from the point of view of algebra. Finally, we give a practical example to illustrate the reasonableness and effectiveness of the proposed method, which is also compared with other existing methods.     

On the J-divergence of intuitionistic fuzzy sets with its application to pattern recognition

The importance of suitable distance measures between intuitionistic fuzzy sets (IFSs) arises because of the role they play in the inference problem. A concept closely related to one of distance measures is a divergence measure based on the idea of information-theoretic entropy that was first introduced in communication theory by Shannon (1949). It is known that J-divergence is an important family of divergences. In this paper, we construct J-divergence between IFSs. The proposed J-divergence can induce some useful distance and similarity measures between IFSs. Numerical examples demonstrate that the proposed measures perform well in clustering and pattern recognition.     

Hesitant fuzzy information measures and their applications in multi-criteria decision making

Hesitant fuzzy set (HFS) is a powerful decision tool to express uncertain information more flexibly and comprehensively. The aim of this paper is to propose more reasonable information measures for HFSs in comparison with the existing ones. First, a series of distance measures is suggested for hesitant fuzzy element and hesitant fuzzy sets. These measures are directly calculated from hesitant fuzzy elements without judging the decision-makers’ risk preference and adding any values into the hesitant fuzzy element with the smaller number of elements. Then, some similarity and entropy measures are proposed based on the transforming relationship among the information measures. Additionally, based on the proposed information measures, a TOPSIS method for hesitant fuzzy information is provided. Finally, some numerical examples are used in order to illustrate the proposed decision method and a comparative analysis is made to demonstrate that the suggested measures are more objective and feasible in certain cases.     

基于Vague集相似度量的模糊分类

在区间值模糊集理论和Vague集理论的基础上,提出了一种新的基于Vague集相似度量的模糊分类方法,对Fisher建立的Iris数据库进行了分类实验处理,分类结果的正确率超过95%。该方法计算简单有效,具有一定的实际应用价值。