On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions

The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets （IVIFSs） is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized Hamming distance, the weighted Hamming distance, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance, etc. Then, by combining the Hausdorff metric with the Hamming distance, the Euclidean distance and their weighted versions, two other similarity measures between IVIFSs, i. e., the weighted Hamming distance based on the Hausdorff metric and the weighted Euclidean distance based on the Hausdorff metric, are defined, and then some of their properties are studied. Finally, based on these distance measures, some similarity measures between IVIFSs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information.

Power Aggregation Operators and Similarity Measures Based on Improved Intuitionistic Hesitant Fuzzy Sets and their Applications to Multiple Attribute Decision Making

Intuitionistic hesitant fuzzy set(IHFS)is amixture of two separated notions called intuitionistic fuzzy set(IFS)and hesitant fuzzy set(HFS),as an important technique to cope with uncertain and awkward information in realistic decision issues.IHFS contains the grades of truth and falsity in the formof the subset of the unit interval.The notion of IHFS was defined by many scholars with different conditions,which contain several weaknesses.Here,keeping in view the problems of already defined IHFSs,we will define IHFS in another way so that it becomes compatible with other existing notions.To examine the interrelationship between any numbers of IHFSs,we combined the notions of power averaging(PA)operators and power geometric(PG)operators with IHFSs to present the idea of intuitionistic hesitant fuzzy PA(IHFPA)operators,intuitionistic hesitant fuzzy PG(IHFPG)operators,intuitionistic hesitant fuzzy power weighted average(IHFPWA)operators,intuitionistic hesitant fuzzy power ordered weighted average(IHFPOWA)operators,intuitionistic hesitant fuzzy power ordered weighted geometric(IHFPOWG)operators,intuitionistic hesitant fuzzy power hybrid average(IHFPHA)operators,intuitionistic hesitant fuzzy power hybrid geometric(IHFPHG)operators and examined as well their fundamental properties.Some special cases of the explored work are also discovered.Additionally,the similarity measures based on IHFSs are presented and their advantages are discussed along examples.Furthermore,we initiated a new approach to multiple attribute decision making(MADM)problem applying suggested operators and a mathematical model is solved to develop an approach and to establish its common sense and adequacy.Advantages,comparative analysis,and graphical representation of the presented work are elaborated to show the reliability and effectiveness of the presented works.

Interval-Valued Intuitionistic Fuzzy-Rough Sets

This paper combines interval-valued intuitionistic fuzzy sets and rough sets.It studies rougheness in interval-valued intuitionistic fuzzy sets and proposes one kind of interval-valued intuitionistic fuzzy-rough sets models under the equivalence relation in crisp sets.That extends the classical rough set defined by Pawlak.

Interval-valued intuitionistic fuzzy aggregation operators

The notion of the interval-valued intuitionistic fuzzy set （IVIFS） is a generalization of that of the Atanassov＇s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVlFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the t.ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.

Intuitionistic fuzzy C-means clustering algorithms

Intuitionistic fuzzy sets(IFSs) are useful means to describe and deal with vague and uncertain data.An intuitionistic fuzzy C-means algorithm to cluster IFSs is developed.In each stage of the intuitionistic fuzzy C-means method the seeds are modified,and for each IFS a membership degree to each of the clusters is estimated.In the end of the algorithm,all the given IFSs are clustered according to the estimated membership degrees.Furthermore,the algorithm is extended for clustering interval-valued intuitionistic fuzzy sets(IVIFSs).Finally,the developed algorithms are illustrated through conducting experiments on both the real-world and simulated data sets.

Intuitionistic fuzzy hierarchical clustering algorithms

Intuitionistic fuzzy set （IFS） is a set of 2-tuple arguments, each of which is characterized by a membership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set （IVIFS）, whose components are intervals rather than exact numbers. IFSs and IVIFSs have been found to be very useful to describe vagueness and uncertainty. However, it seems that little attention has been focused on the clustering analysis of IFSs and IVIFSs. An intuitionistic fuzzy hierarchical algorithm is introduced for clustering IFSs, which is based on the traditional hierarchical clustering procedure, the intuitionistic fuzzy aggregation operator, and the basic distance measures between IFSs： the Hamming distance, normalized Hamming, weighted Hamming, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance. Subsequently, the algorithm is extended for clustering IVIFSs. Finally the algorithm and its extended form are applied to the classifications of building materials and enterprises respectively.

Target Priority Determination Methods by Interval-Valued Intuitionistic Fuzzy Sets with Unknown Attribute Weights

The paper aims at the problem of multi-targets threat degree being hard to be evaluated accurately in complex air defense battlefield environments. Combined with multi-sensors information fusion and interval-valued intuitionistic fuzzy sets(IVIFS) theories, the target priority determination is studied. The score and accuracy functions of IVIFS are improved with thinking about the hesitating information in order to increase the rationality.Then, the influence factors of target priority and the nonlinear relationship between the influence factors and target priority are analyzed. Next, the algorithms for calculating the factor weights and sensor weights are given. Based on the theory of IVIFS and technique for order preference by similarity to an ideal solution(TOPSIS), two methods of target priority determination based on the IVIFS and TOPSIS are proposed. At last, an application example verifies the effectiveness and flexibility of the proposed algorithms.

Interval-Valued Dual Hesitant Fuzzy Hamacher Aggregation Operators for Multiple Attribute Decision Making

As an generalization of hesitant fuzzy set, interval-valued hesitant fuzzy set and dual hesitant fuzzy set, interval-valued dual hesitant fuzzy set has been proposed and applied in multiple attribute decision making. Hamacher t-norm and t-conorm is an generalization of algebraic and Einstein t-norms and t-conorms. In order to combine interval-valued dual hesitant fuzzy aggregation operators with Hamacher t-norm and t-conorm. We first introduced some new Hamacher operation rules for interval-valued dual hesitant fuzzy elements. Then, several interval-valued dual hesitant fuzzy Hamacher aggregation operators are presented, some desirable properties and their special cases are studied. Further, a new multiple attribute decision making method with these operators is given,and an numerical example is provided to demonstrate that the developed approach is both valid and practical.

NOTES ON “MULTICRITERIA FUZZY DECISION-MAKING METHOD BASED ON A NOVEL ACCURACY FUNCTION UNDER INTERVAL-VALUED INTUITIONISTIC FUZZY ENVIRONMENT”

This note points outs the inappropriateness of an accuracy function introduced by Ye [Ye, J. （2009）. Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment. Expert Systems with Applications, 36 （3）： 6899-6902] and its misleading use for comparing two interval-valued intuitionistic fuzzy numbers.

遥感影像直觉模糊集分割法

针对传统模糊聚类算法在影像分割中忽略影像成像过程带来的光谱测度不确定性及聚类过程中像素类属非隶属性的问题,本文提出了一种基于直觉模糊集的遥感影像分割算法。首先,设计直觉模糊发生器,并通过最大熵法分析影像光谱测度不确定性,求解波段指数以将遥感影像转化为直觉模糊集,从而对影像的光谱测度不确定性进行建模。然后,在聚类过程中同时考虑像素类属隶属度和像素类属非隶属度,结合直觉模糊集间距离定义目标函数,提高算法对类属模糊信息的处理能力,实现遥感影像的精准分割。最后,分别利用本文算法和比较算法对模拟影像和真彩色遥感影像进行分割试验。分割结果的定性、定量评价表明,本文算法能够更好地处理影像本身和聚类过程中的不确定性,获得更高精度的影像分割结果。

基于直觉模糊集的三支决策模型

三支决策理论是处理不确定决策问题的重要理论基础,近年来其已成为国内外学者的研究热点。在决策粗糙集、三支决策和直觉模糊集理论的基础上,对基于直觉模糊集的三支决策的模型进行深入研究,提出了三支决策的两描述模型、三描述模型,然后将其拓展为一般模型。该一般模型使用犹豫度重新设计了阈值参数,通过隶属度函数对事件对象进行评估,最后用淮河表层沉积物中有机氯农药污染情况的真实例子来验证该模型的有效性。

基于三角模糊数犹豫直觉模糊集的多属性智能决策

通过剖析现实生活中数据对象复杂性以及决策人思考的犹豫模糊性,提出了基于三角模糊数的犹豫直觉模糊集决策方法。首先,给出了三角模糊数犹豫直觉模糊集的定义,构建并证明了三角犹豫直觉模糊元及模糊数的基本运算法则和集成算子。其次,通过对三角犹豫直觉模糊元的得分函数和精确函数的定义,实现了三角犹豫直觉模糊数下的对象间的取值比较,针对三角犹豫直觉模糊数下多属性决策分析中的不确定性权重求解难题,提出了一种基于得分函数和最大熵理论的最优权重求解模型,并构建遗传算法模型实施最优化求解。最后,给出了三角犹豫直觉模糊数下的多属性智能决策算法,并以算例证明了所提方法的可行性和有效性。

基于区间直觉犹豫模糊集的高速列车系统关键部件辨识

关键部件作为系统可靠性分析的重要组成以及系统维修策略制定的重要基础,其辨识方法与识别结果的准确性一直是研究热点与难点.为有效识别关键部件保证高速列车系统安全可靠性运行,本文提出一种新的基于区间直觉犹豫模糊集的关键部件辨识方法.首先通过回顾现有复杂系统网络建模方法及其优缺点,归纳总结部件的提取规则与部件间作用关系的定义和类型,提出由局部到整体的高速列车系统全局拓扑网络模型构建方法.其次鉴于现有针对同一高速列车同一节车辆同一部件的故障维修记录数据量少、随机性大等特点,提出将节点属性值区间化,构建节点属性的区间直觉犹豫模糊集,其中节点属性包括由故障数据分析获得的节点可靠性属性值以及由所建全局拓扑网络得到的拓扑属性.最后利用区间直觉犹豫模糊积分算子综合节点的多种属性辨识系统中的关键部件.以转向架系统的拓扑结构以及历史故障数据为基础的实例分析表明,所提出的辨识方法能够准确的识别出系统中的关键部件,且与专家经验的分析结果基本一致.

直觉模糊集熵的一种计算公式

为进一步精确度量直觉模糊集的模糊性,改进了直觉模糊集的模糊度的公理化形式,并给出了直觉模糊集的模糊度计算公式.利用直觉模糊集的模糊度和犹豫度,给出了直觉模糊集熵的计算公式,并举例验证了该计算公式的有效性.

直觉模糊集TOPSIS在边坡地震稳定性评价中的应用

为准确评价岩土边坡地震稳定性,建立基于直觉模糊集逼近理想解排序(TOPSIS)法的边坡地震稳定性评价模型。首先综合考虑定量与定性指标,选取岩土体特征、新构造运动特性、坡高、坡角、年降水量、场地地震烈度等6个因素为边坡地震稳定性评价指标;然后针对定性指标与指标权重的模糊性,利用直觉模糊集对其进行表示,并结合TOPSIS构建边坡地震稳定性评价模型;最后利用模型对16处边坡地震稳定性进行评价,结果与实际相符。研究结果表明:基于直觉模糊集TOPSIS法的岩土边坡地震稳定性评价模型可用来处理指标权重和定性指标的模糊性,与突变级数法、属性数学、灰色聚类法、综合指标法、模糊因素法等方法相比,用其得到的评价结果更准确。

基于语言值有序对三元组的多类型数据标准化方法

为了标准化处理多类型数据,基于语言值二元组,提出语言值有序对三元组表示模型,研究语言值有序对三元组及其性质,给出语言值有序对三元组之间的相似度.讨论语言值有序对三元组加权平均算子,构造模糊集、直觉模糊集、犹豫模糊集、语言真值直觉模糊集与语言值有序对三元组的标准化转化模型.结合语言值有序对三元组之间的相似度,将模糊集、直觉模糊集、犹豫模糊集、语言真值直觉模糊集的转化模型应用于模式识别中.最后,通过医院智能分诊的实例说明文中方法的合理性和有效性.

基于新的区间直觉模糊集相似性测度的模式识别

有关区间值直觉模糊数(集)的相似性研究较少,并且现有的方法在处理实际问题时效果较差。针对这个问题,提出了区间值直觉模糊数(集)相似性测度的新方法,包含了隶属度,非隶属度,犹豫度,以及后者对前两者的影响,将隶属度,非隶属度,犹豫度的相似度表示成三元组的形式,用TOPSIS的思想处理该三元组,得出一种新的有效的相似性度,证明其合理性。将其应用到模式识别实例中,验证其有效性。

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。

直觉对偶犹豫模糊集的集结算子及其应用

在对偶犹豫模糊集与直觉模糊集的基础上,提出了直觉对偶犹豫模糊集的概念和基本运算,构造了直觉对偶犹豫模糊集的算术加权平均集结算子和几何加权平均算子,并考虑有序和广义的情况,分别给出相对应的公式。同时针对某些算子的特殊性质,给出了详细描述和证明。针对模糊集的多属性群决策问题,提出了一种新的基于直觉对偶犹豫模糊集的集结算子的多属性群决策方法,通过一个实例说明了该方法的实用性和有效性。

基于直觉犹豫模糊集的TOPSIS法

直觉犹豫模糊集集成了直觉模糊集和犹豫模糊集的优势,能更有效地刻画决策者偏好不一致的情况。距离测度一直是研究的热点问题,但尚没有文献研究直觉犹豫模糊集间的距离测度,因此本文定义了直觉犹豫模糊集间的Hamming距离、Euclidean距离和广义距离,同时考虑每个元素的权重,定义了加权距离。犹豫度是直觉犹豫模糊集的重要特性,因此在考虑犹豫度的基础上,又定义了一些距离测度。这些距离测度不仅考虑了直觉犹豫模糊数间的差异,同时考虑了犹豫度的影响,决策者可以根据对直觉犹豫模糊数和犹豫度之间偏好的不同,设置不同的偏好值得到距离测度。然后基于这些距离测度,又提出了直觉犹豫模糊环境下的TOPSIS法。最后通过实例说明了所提出的TOPSIS法的合理性与实用性。