Cartesian product over interval valued intuitionistic fuzzy sets

The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to the interval valued intuitionistic fuzzy set(IVIFS). On the basis of fuzzy set(FS), the IFS is a generalization concept. And the IFS is generalized to the IVIFS.In this paper, the definition of the sixth Cartesian product over IVIFSs is first introduced and its some properties are explored.We prove some equalities based on the operation and the relation over IVIFSs. Finally, we present one geometric interpretation and a numerical example of the sixth Cartesian product over IVIFSs.

Reliability Analysis of a Powerloom Plant Using Interval Valued Intuitionistic Fuzzy Sets

In this paper, we investigate the reliability analysis of a powerloom plant by using interval valued intuitionistic fuzzy sets (IVIFS). Herein, we modeled a powerloom plant as a gracefully degradable system having two units A(n) and B(m) connected in series. The reliability ofncomponents of unitAandmcomponents of unitBis assumed to be an IVIFS defined over the universe of discourse [0, 1]. Thus, the reliability of the system obtained is an IVIFS that covers the inherited uncertainty in data collection and reliability evaluation of a powerloom plant.

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.

特征匹配驱动的IVIFSs相似性测度模型研究

直觉模糊集(intuitionistic fuzzy sets,IFSs)的隶属关系表征并不完全适用于区间直觉模糊集(interval-valued intuitionistic fuzzysets,IVIFSs),故其相似性测度模型与特征条件难以实现完全匹配。首先,运用记分函数和精确函数来刻画IVIFSs的特征条件,分析了现有IVIFSs相似性测度模型与特征条件匹配的冲突性;其次,基于其几何距离和重心设计了一种新的IVIFSs相似性测度模型;最后,通过理论证明和实证研究分析了该模型的优越性和应用价值。

精确函数在IVIFS多准则决策中的应用

模糊数和区间直觉模糊集(interval-valued intuitionistic fuzzy set,IVIFS)被用于解决不确定和不精确数值的模型问题。从1989年开始,众多学者先后进行了模糊数和区间直觉模糊集排序的研究,但至今还没有给出适合排列任意2个区间直觉模糊集的通用方法。在分析现有区间直觉模糊集的得分函数和精度函数存在的不足后,提出了一种新的精确函数。首先,针对区间直觉模糊环境下的多准则决策问题,利用区间直觉模糊加权算子对各备选方案对应的模糊信息进行聚合,得出综合属性值;其次,依据新的精确函数计算出各备选方案的得分,比较各备选方案的排序情况和综合准确度,选择最理想方案;最后,通过实例验证了该方法的实用性和有效性。

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.

双论域区间值直觉模糊vague粗糙集及其应用

区间值直觉模糊集可诱导出vague集和粗糙集,而后两者的结合具有不确定性深入分析的优势.立足双论域区间值直觉模糊粗糙集,引入vague集进行融合扩张,研究双论域区间值直觉模糊vague粗糙集.首先,定义区间值直觉模糊vague相容类,构建双论域区间值直觉模糊vague粗糙集模型,提出关于双逼近近似和三支决策区域的计算算法,并确立该模型的精确度、粗糙度、依赖度.然后,研究该模型的近似算子与不确定性度量的性质.最后,采用医疗例子进行模型计算、度量测量、性质验证,并得到关于患者临床诊断的患病分析与治疗决策.

基于区间值直觉模糊集和云模型的FMEA风险评估方法

针对传统故障模式和影响分析(failure mode and effect analysis,FMEA)方法存在评价使用精确数量化造成专家风险评估信息的丢失、忽略风险指标之间的相对重要性以及由于专家有限理性导致的评价固有的随机性等问题,利用区间值直觉模糊集和云模型构建了一种改进的FMEA风险评估方法。首先,引入区间值直觉模糊集(IVIFS)来描述专家评价信息的复杂性和不确定性,通过运用区间值直觉模糊熵,计算专家权重和风险因子的权重;其次,采用云模型的方法,通过比较各支持云模型和反对云模型与正、负理想云模型的正、负相似度,获得故障模式评价值的综合相似度,通过对综合相似度大小排序得到各故障模式风险排序;最后,以自动扶梯的梯级、踏板和胶带风险评估为例进行分析,验证该评估方法的实用性和可行性。

区间值直觉Fuzzy集的结构

引进区间值直觉 Fuzzy集的截集的概念 。

基于区间直觉模糊集的绿色施工承包商选择

为了避免从专家库随机抽取的评标专家具有的绿色施工经验水平不同,同时提高中标承包商的绿色施工能力,必须建立科学合理的绿色施工承包商评价模型。首先结合传统施工项目评标指标和绿色施工评价指标建立承包商评价指标体系;然后引入区间直觉模糊集,通过相关系数、模糊熵理论分别计算专家权重和指标权重,再基于TOPSIS法选择最优绿色施工承包商;最后通过实例分析表明该模型的有效性。

覆盖变精度粗糙区间直觉模糊集模型探究

概述区间直觉模糊集的基本理论,利用所定义的平均隶属度、平均非隶属度,建立基于覆盖的变精度粗糙区间直觉模糊集的4种模型,并讨论这4种模型的一些相关性质、与现有模型的关系以及4种模型之间的关系;最后,对4种模型进行实例分析。

基于IVIFE-GRPM方法的雷达装备维修性评估

针对雷达装备在鉴定定型阶段的维修性评估问题,首先建立了定性与定量指标相结合的雷达装备维修性评估指标体系;其次,考虑对事物判断的犹豫度,避免权值为0的情况,采用了改进的区间直觉模糊熵(IVIFE)对指标进行赋权;最后运用灰关联投影评价模型(GRPM)进行了评估.实例分析验证了该方法的可行性,为鉴定定型阶段雷达装备维修性评估提供一种思路.

基于加权双向投影的决策专家权重确定方法

针对现有单向投影法存在相似度误判的问题,提出一种区间数矩阵加权双向投影公式,其能更好地度量矩阵间的相似性关系,进而提出基于加权双向投影的专家权重确定方法。首先将每位决策专家的决策矩阵进行集结形成平均决策矩阵,然后通过专家个体隶属度矩阵、非隶属度矩阵与群体平均隶属度矩阵、非隶属度矩阵的加权双向投影值来获得专家个体与群体的相似度,进而通过相似度确定每位专家的权重。不仅充分利用了决策数据,还解决了现有投影法相似度误判的问题。最后通过3种具体的决策实例分析,验证了所提方法的有效性以及适用性。

基于区间直觉模糊TOPSIS法的水资源空间均衡评价

为更好体现指标值的模糊性以及评价结果的客观性,将区间直觉模糊集引入水资源空间均衡评价,构建包含水资源禀赋和水资源利用两个子系统的评价指标体系。采用改进的区间直觉模糊TOPSIS法计算相似度、区间直觉模糊熵法确定权重,构造不均衡系数,建立基于改进区间直觉模糊TOPSIS法的水资源空间均衡评价模型。将模型应用于山西省2015-2019年水资源空间均衡评价,结果表明:山西省水资源空间均衡等级总体为中部均衡、北部较均衡、南部较不均衡,其中太原市为水资源空间不均衡等级;该模型能够反映各地级市水资源空间均衡程度并揭示其空间不均衡的原因,有效评价水资源空间均衡。

基于GIS和区间直觉模糊集的铁路线网规划评价

为了综合全面地反映城市群高速铁路规划线网的总体性能,评价比选出最优规划方案,针对复杂多因素约束条件下评价指标信息的非“二分法”特性,本文在GIS技术支持下,尝试提出了基于区间直觉模糊集的城市群高速铁路线网评价模型。该模型从区间直觉模糊数的几何意义出发,基于熵值最大化原理,求出指标的权重,获得不同决策者对各个方案的评价值。最后,综合不同决策者意见得出各个方案的最终评价值。以辽中南城市群高速铁路线网规划评价为例,进行了基于区间直觉模糊集的城市群高速铁路线网方案评价。分析表明提出的方法能够描述决策者判断过程中的犹豫程度,可以更细腻、更全面地描述评价指标的自然属性,从而使评价结果更符合客观实际情况。