Generalized Normalized Euclidean Distance Based Fuzzy Soft Set Similarity for Data Classification

Classification is one of the data mining processes used to predict predetermined target classes with data learning accurately. This study discusses data classification using a fuzzy soft set method to predict target classes accurately. This study aims to form a data classification algorithm using the fuzzy soft set method. In this study, the fuzzy soft set was calculated based on the normalized Hamming distance. Each parameter in this method is mapped to a power set from a subset of the fuzzy set using a fuzzy approximation function. In the classification step, a generalized normalized Euclidean distance is used to determine the similarity between two sets of fuzzy soft sets. The experiments used the University of California (UCI) Machine Learning dataset to assess the accuracy of the proposed data classification method. The dataset samples were divided into training (75% of samples) and test (25% of samples) sets. Experiments were performed in MATLAB R2010a software. The experiments showed that: (1) The fastest sequence is matching function, distance measure, similarity, normalized Euclidean distance, (2) the proposed approach can improve accuracy and recall by up to 10.3436% and 6.9723%, respectively, compared with baseline techniques. Hence, the fuzzy soft set method is appropriate for classifying data.

     

基于模糊软集合理论的文本分类方法

为提高文本分类精度,提出一种基于模糊软集合理论的文本分类方法。该方法把文本训练集表示成模糊软集合表格形式,通过约简、构造软集合对照表方法找出待分类文本所属类别,并针对文本特征提取过程中由于相近特征而导致分类精度下降问题给出一种基于正则化互信息特征选择算法,有效地解决了上述问题。与传统的KNN和SVM分类算法相比,模糊软集合方法在文本分类的精度和准度上都有所提高。     

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。     

On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods

In this paper, a kind of novel soft set model called a Z-soft fuzzy rough set is presented by means of three uncertain models: soft sets, rough sets and fuzzy sets, which is an important generalization of Z-soft rough fuzzy sets. As a novel Z-soft fuzzy rough set, its applications in the corresponding decision making problems are established. It is noteworthy that the underlying concepts keep the features of classical Pawlak rough sets. Moreover, this novel approach will involve fewer calculations when one applies this theory to algebraic structures. In particular, an approach for the method of decision making problem with respect to Z-soft fuzzy rough sets is proposed and the validity of the decision making methods is testified by a given example. At the same time, an overview of techniques based on some types of soft set models is investigated. Finally, the numerical experimentation algorithm is developed, in which the comparisons among three types of hybrid soft set models are analyzed.     

Soft fuzzy rough sets and its application in decision making

Recently, the theory and applications of soft set has brought the attention by many scholars in various areas. Especially, the researches of the theory for combining the soft set with the other mathematical theory have been developed by many authors. In this paper, we propose a new concept of soft fuzzy rough set by combining the fuzzy soft set with the traditional fuzzy rough set. The soft fuzzy rough lower and upper approximation operators of any fuzzy subset in the parameter set were defined by the concept of the pseudo fuzzy binary relation (or pseudo fuzzy soft set) established in this paper. Meanwhile, several deformations of the soft fuzzy rough lower and upper approximations are also presented. Furthermore, we also discuss some basic properties of the approximation operators in detail. Subsequently, we give an approach to decision making problem based on soft fuzzy rough set model by analyzing the limitations and advantages in the existing literatures. The decision steps and the algorithm of the decision method were also given. The proposed approach can obtain a object decision result with the data information owned by the decision problem only. Finally, the validity of the decision methods is tested by an applied example.     

Developing soft sensors using hybrid soft computing methodology: a neurofuzzy system based on rough set theory and genetic algorithms

This paper presents a hybrid soft computing modeling approach, a neurofuzzy system based on rough set theory and genetic algorithms (GA). To solve the curse of dimensionality problem of neurofuzzy system, rough set is used to obtain the reductive fuzzy rule set. Both the number of condition attributes and rules are reduced. Genetic algorithm is used to obtain the optimal discretization of continuous attributes. The fuzzy system is then represented via an equivalent artificial neural network (ANN). Because the initial parameter of the ANN is reasonable, the convergence of the ANN training is fast. After the rules are reduced, the structure size of the ANN becomes small, and the ANN is not fully weight-connected. The neurofuzzy approach based on RST and GA has been applied to practical application of building a soft sensor model for estimating the freezing point of the light diesel fuel in fluid catalytic cracking unit.     

Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making

Intuitionistic fuzzy soft set (IFSS) theory acts as a fundamental tool for handling the uncertainty in the data by adding a parameterizing factor during the process as compared to fuzzy and intuitionistic fuzzy set (IFS) theories. In this paper, an attempt has been made to this effect to describe the concept of generalized IFSS (GIFSS), as well as the group-based generalized intuitionistic fuzzy soft set (GGIFSS) in which the evaluation of the object is done by the group of experts rather than a single expert. Based on this information, a new weighted averaging and geometric aggregation operator has been proposed by taking the intuitionistic fuzzy parameter. Finally, a decision-making approach based on the proposed operator is being built to solve the problems under the intuitionistic fuzzy environment. An illustrative example of the selection of the optimal alternative has been given to show the developed method. Comparison analysis between the proposed and the existing operators have been performed in term of counter-intuitive cases for showing the superiority of the approach.     

The normal parameter reduction of soft sets and its algorithm

This paper is concerned with the reduction of soft sets and fuzzy soft sets. Firstly, the problems of suboptimal choice and added parameter set of soft sets are analyzed. Then, we introduce the definition of normal parameter reduction in soft sets to overcome these problems. In addition, a heuristic algorithm of normal parameter reduction is presented. Two new definitions, parameter important degree and decision partition, are proposed for analyzing the algorithm of normal parameter reduction. Furthermore, the normal parameter reduction is also investigated in fuzzy soft sets.     

几何距优化质心结合隶属度约束RFCM的脑MRI图像分割算法

针对现有图像分割算法聚类复杂以及分割精度不够高的问题,提出了基于几何距优化质心和粗糙模糊C-均值（RFCM）相结合的医学图像聚类分割算法。首先建立软集表示的像素集,并计算每个像素与质心之间的距离,然后基于像素和质心之间的最小距离,将像素分组到聚类中。为了将软集应用到粗糙模糊C-均值中,定义了一个模糊软集,进一步将输入图像转换为二值图像,通过计算连通区域的几何距选择适当的质心。最后利用这些新的质心计算更新像素的隶属度值,从而完成模糊聚类划分。在Allen Brain Atlas等三个医学数据库上评估了所提出混合算法的性能,获得的Jaccards系数和分割精度（SA）都优于几种对比算法。实验证明,提出的聚类分割算法具有良好的性能。     

Pythagorean Uncertain Linguistic Variable Hamy Mean Operator and Its Application to Multi-attribute Group Decision Making

Pythagorean fuzzy set (PFS) can provide more flexibility than intuitionistic fuzzy set (IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multi-attribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean (PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable (PULV) and explore some properties of the operator. Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.      

一种改进的模糊软集多参数决策方法

模糊软集多参数决策方法中经常将Zadeh交与代数积使用在数据融合方法中,在一些实际应用中会产生信息缺失,导致决策者无法做出准确的选择。针对这一问题,结合Einstein运算法则提出一种新的数据融合方法,用于解决信息缺失和对象无法排序的问题。所提出的基于模糊软集的多参数决策方法是通过Einstein积运算进行多个参数集合的整合,从而得到一个合成模糊软集,再由合成模糊软集计算得到对照矩阵与得分表,最终得到对象的全排序,为决策者提供判断依据。通过实例结果,可以验证新方法在决策问题中的正确性和有效性。     

基于F-SVMs的多模型建模方法

针对全局模型难以精确描述复杂工业过程的问题,提出一种基于模糊支持向量机(F-SVMs)的多模型(F-SVMs MM)建模方法。用模糊支持向量分类算法(F-SVC)对输入数据进行预处理,得到多模型模糊隶属度;用模糊支持回归算法(F-SVR)建立多模型(MM)估计器。应用该方法对pH中和滴定过程进行建模,仿真结果表明,F-SVMs MM跟踪性能好、泛化能力强,比USOCPN方法和标准支持向量机(SVMs)方法具有更好的性能和推广能力。     

方差辗转的软集参数约简算法

软集是一种处理不确定数据的理论、工具,通常用于决策论中。软集的参数约简是指删除对决策几乎没有影响的冗余参数,自从0-1线性规划算法提出以来,软集的参数约简问题基本得到了解决,但0-1线性规划算法实现复杂,需要依赖整数规划算法。在此,考虑软集的实际应用背景,将软集与概率论结合,设计出一个在大数据背景下的软集参数约简方法——方差辗转法,该算法的时间复杂度为O(m~2n),而0-1线性规划通常视为NP难问题。方差辗转法实现简单,在物集(或全集)较小,不超过属性集大小的2倍时,效果较差,但随着物集(或全集)大小的增长,效率会逐步上升,最终运算效率会全面优于0-1线性规划算法的,对于约简稠密度高的软集效率会更高。     

一种应用软粗糙模糊集的多属性决策方法

将软粗糙模糊集应用于多属性决策问题,用软粗糙模糊集分析模糊知识表达系统,定义了软模糊决策系统、决策分类模糊软集依赖度、条件双射软集对决策分类模糊软集的重要性、软模糊决策系统的约简、软模糊决策系统的决策规则等概念,借助这些概念给出了一种基于软粗糙模糊集的多属性决策算法,通过实例分析说明了该算法的可行性。     

Group decision making in medical system: An intuitionistic fuzzy soft set approach

In medical system, there may be many critical diseases, where experts do not have sufficient knowledge to handle those problems. For these cases, experts may provide their opinion only about certain aspects of the disease and remain silent for those unknown features. Feeling the need of prioritizing different experts based on their given information, this article uses a novel concept for assigning confident weights to different experts which are mainly based on their provided information. Experts provide their opinions about various symptoms using intuitionistic fuzzy soft matrix (IFSM). In this article, we propose an algorithmic approach based on intuitionistic fuzzy soft set (IFSS) which explores a particular disease reflecting the agreement of all experts. This approach is guided by the group decision making (GDM) model and uses cardinals of IFSS as novel concept. We have used choice matrix (CM) as an important parameter which is based on choice parameters of individual expert. This article has also validated the proposed approach using distance measurements and consents of the majority of experts. The effectiveness of the proposed approach is demonstrated using a suitable case study.     

On Pythagorean fuzzy decision making using soft likelihood functions

Multicriteria decision making (MCDM) is to select the optimal candidate which has the best quality from a finite set of alternatives with multiple criteria. One important component of MCDM is to express the evaluation information, and the other one is to aggregate the evaluation results associated with different criteria. For the former, Pythagorean fuzzy set (PFS) is employed to represent uncertain information in this paper, and for the latter, the soft likelihood function developed by Yager is used. To address MCDM issues from a new perspective, the likelihood function of PFS is first proposed in this study and, to improve some of its limitations, the ordered weighted averaging (OWA)-based soft likelihood function is defined, which introduces the attitudinal characteristic to identify decision makers' subjective preferences. In addition, the defined soft likelihood function of PFS is extended by weighted OWA operator considering the importance weight of the argument. Several illustrative cases are provided based on the presented (weighted) OWA-based soft likelihood functions in Pythagorean fuzzy environment for MCDM problem.     

基于半监督模糊C均值算法的遥感影像分类

遥感影像数据因其固有的不确定性与复杂性,导致传统的无监督分类算法难以对其准确建模。基于模糊集理论的模式识别方法可以有效地表达数据的模糊性,其中二型模糊集能更好地刻画类间多重不确定性,而半监督法可以利用少量先验知识来解决算法对数据的泛化性问题,因此提出一种基于半监督的自适应区间二型模糊C均值遥感影像分类方法（SS-AIT2FCM）。首先,结合半监督和进化论思想,提出一种新的模糊权重指数选取方法,以提升自适应区间二型模糊C均值聚类算法的鲁棒性与泛化性,使算法更适用于光谱混叠严重、覆盖面积大、地物丰富的遥感数据分类;然后,通过对少量标记样本的软约束监督,对区间二型模糊算法迭代过程进行优化指导,来挖掘数据的最优表达。实验选用了北京颐和园区域的SPOT5多光谱遥感影像数据和广东横琴岛区域的Landsat TM多光谱遥感影像数据,对现有流行的模糊分类算法和SS-AIT2FCM的分类结果进行了比较。结果表明,SS-AIT2FCM获得了更高的分类精度与更清晰的类别边界,且有较好数据泛化能力。     

A complete fuzzy discriminant analysis approach for face recognition

In this paper, some studies have been made on the essence of fuzzy linear discriminant analysis (F-LDA) algorithm and fuzzy support vector machine (FSVM) classifier, respectively. As a kernel-based learning machine, FSVM is represented with the fuzzy membership function while realizing the same classification results with that of the conventional pair-wise classification. It outperforms other learning machines especially when unclassifiable regions still remain in those conventional classifiers. However, a serious drawback of FSVM is that the computation requirement increases rapidly with the increase of the number of classes and training sample size. To address this problem, an improved FSVM method that combines the advantages of FSVM and decision tree, called DT-FSVM, is proposed firstly. Furthermore, in the process of feature extraction, a reformative F-LDA algorithm based on the fuzzy k-nearest neighbors (FKNN) is implemented to achieve the distribution information of each original sample represented with fuzzy membership grade, which is incorporated into the redefinition of the scatter matrices. In particular, considering the fact that the outlier samples in the patterns may have some adverse influence on the classification result, we developed a novel F-LDA algorithm using a relaxed normalized condition in the definition of fuzzy membership function. Thus, the classification limitation from the outlier samples is effectively alleviated. Finally, by making full use of the fuzzy set theory, a complete F-LDA (CF-LDA) framework is developed by combining the reformative F-LDA (RF-LDA) feature extraction method and DT-FSVM classifier. This hybrid fuzzy algorithm is applied to the face recognition problem, extensive experimental studies conducted on the ORL and NUST603 face images databases demonstrate the effectiveness of the proposed algorithm.