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.

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.

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.

On Rough Intuitionistic Fuzzy Ideals（Filters） in Lattices

In this paper, we introduce a new algebraic structure, called a rough intuitionistic fuzzy ideal(filter) which is a generalized intuitionistic fuzzy ideal(filter) of a lattice and study some related properties of such ideals(filters).

Ordered Semigroups Characterized by Their Intuitionistic Fuzzy Generalized Bi-ideals

In this paper,we define intuitionistic fuzzy generalized bi-ideals in ordered semigroups and characterize regular and left weakly regular ordered semigroups in terms of intuitionistic fuzzy generalized bi-ideals.

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.

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.

基于TIFANP-TOPSIS-TIFCE法的大跨桥梁安全状态评估方法

针对传统方法子指标的不确定性问题,提出了一种基于三角直觉模糊网络分析法(triangular intuitionistic fuzzy analytic network process,TIFANP)、优劣解距离法(technique for order preference by similarity to an ideal solution,TOPSIS)和三角直觉模糊综合评价(triangular intuitionistic fuzzy comprehensive evaluation,TIFCE)的大跨桥梁安全状态评估方法。首先,建立大跨桥梁安全状态分层指标体系,采用TIFANP法确定考虑指标相互影响后的权重;其次,引入TOPSIS法分配指标各截面权重,进而获得子指标取值;然后,将桥梁安全状态划分为5级,通过TIFCE法构建指标在不同等级的隶属度和非隶属度函数,据此建立对应判断矩阵,并进行桥梁安全状态指数综合计算;最后,以某大跨悬索桥监测数据为依托,验证了所提方法的有效性。结果表明:所提方法能够更合理地处理评价指标间的相互影响以及专家评分时的不确定,可为运营期大跨桥梁安全状态的准确评估提供新思路。

布尔代数上的直觉Fuzzy同余关系

引入了布尔代数上的直觉Fuzzy同余关系的概念,讨论了布尔代数上的直觉Fuzzy同余关系与布尔代数的直觉Fuzzy子代数(直觉Fuzzy理想)之间的关系,以及布尔代数上的直觉Fuzzy同余关系在布尔代数同态下的象和逆象,并给出了商布尔代数的同构定理。

基于直觉模糊环境的海上风机选型

选择合适的海上风力发电机机型对海上风电场的长期高效运行起着至关重要的作用。针对决策者在风机选型决策过程中存在不确定性和主观偏好等问题,提出一种改进的多准则决策(multi-criteria decision making, MCDM)框架及方法:在权重求解算法中将群体决策和直觉模糊数与层次分析法相结合,提出群体直觉模糊层次分析法(group intuitionistic fuzzy analytic hierarchy process, GIAHP)计算指标权重;在备选方案排序算法中将余弦距离引入接近理想点法(technique for order preference by similarity to an ideal solution, TOPSIS),提出多距离TOPSIS确定备选方案排序。最后以山东省海上风电场风机选型为例,并通过敏感性分析验证框架及方法的鲁棒性。该框架及方法为中国海上风电场风机选型提供理论依据,可确保海上风电场长期稳定运行。

布尔代数的(λ,μ)直觉模糊点理想

在布尔代数中引入了(λ,μ)直觉模糊点理想的概念并讨论其性质,证明了布尔代数的(,μ)直觉模糊点理想的交,同态像及其同态逆像仍然是布尔代数的(λ,μ)直觉模糊点理想。

SOME NEW SIMILARITY MEASURES FOR INTUITIONISTIC FUZZY VALUES AND THEIR APPLICATION IN GROUP DECISION MAKING

We first propose a series of similarity measures for intuitionistic fuzzy values （IFVs） based on the intuitionistic fuzzy operators （Atanassov 1995）. The parameters in the proposed similarity measures can control the degree of membership and the degree of non-membership of an IFV, which can reflect the decision maker’s risk preference. Moreover, we can obtain some known similarity measures when some fixed values are assigned to the parameters. Furthermore, we apply the similarity measures to aggregate IFVs and develop some aggregation operators, such as the intuitionistic fuzzy dependent averaging operator and the intuitionistic fuzzy dependent geometric operator, whose prominent characteristic is that the associated weights only depend on the aggregated intuitionistic fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results. Based on these aggregation operators, we develop some group decision making methods, and finally extend our results to interval-valued intuitionistic fuzzy environment.

改进TOPSIS的多态融合直觉模糊威胁评估

针对防空作战中的目标威胁评估问题,提出一种新的多时刻融合直觉模糊集排序模型。首先,依据目标威胁属性的主、客观权重得到综合权重。然后,通过逼近理想解排序法来衡量直觉模糊集信息量的大小,利用直觉模糊熵来表征直觉模糊集信息的可靠性,并结合决策者的风险偏好,构建了基于信息量和不确定性的直觉模糊集排序模型,得出单时刻的目标威胁排序。最后,利用泊松分布逆形式构建了时间序列权重以融合多个时刻的决策信息,得出最终的目标威胁排序。仿真结果表明,所提算法综合了多时刻的决策信息,并可根据决策者的风险偏好进行调整,灵活性强,可靠性高。

基于TOPSIS的直觉模糊多属性群决策方法

针对直觉模糊信息环境下的多属性群决策问题,对专家给出的直觉模糊集决策矩阵进行规范化处理,利用直觉模糊集的相关理论,提出基于直觉模糊熵的属性权重确定方法;为了便于度量任意两个专家之间决策信息的相似度,将各专家给出的直觉模糊集决策矩阵转化决策向量,提出基于直觉模糊相似度的专家权重确定方法;利用逼近于理想解的排序方法(TOPSIS)对专家群的决策信息进行综合集成,给出备选方案优劣排序。结合算例验证方法的有效性。

布尔代数的直觉模糊子代数和直觉模糊理想

引入了布尔代数的直觉模糊子代数、直觉模糊理想和直觉模糊商布尔代数的概念,给出了布尔代数的直觉模糊子集是直觉模糊子代数(直觉模糊理想)的充要条件,讨论了布尔代数的直觉模糊子代数(直觉模糊理想)在布尔代数同态下的像和逆像,并证明了当I是布尔代数R的直觉模糊真理想时,R/I是布尔代数。

基于熵和协相关度的直觉模糊多属性决策方法

针对决策信息为直觉模糊集且属性权重完全未知的多属性决策问题,提出了一种基于直觉模糊熵和协相关度的决策方法。对于直觉模糊集的直觉性和模糊性,从公理化定义出发,给出了一种改进的直觉模糊熵的定义。然后基于所有属性总不确定信息量最小化准则,利用提出的直觉模糊熵建立非线性规划模型,从而得到属性权重公式。接着,由统计学中变量间相关系数的构造思想,提出直觉模糊集协相关度的概念,并探讨了与相关系数类似的性质,且进一步得出各对象与理想对象加权的协相关度公式。最后给出了一种新的多属性决策途径,并将所提方法成功应用于教授评选的实例中,通过计算各个教师的协相关度确定最佳候选人,实现最优决策。该方法操作合理,算法易于实现,计算结果可靠,可用于多种决策问题。

基于TOPSIS的区间直觉模糊多属性决策法

对基于区间直觉模糊信息的多属性决策问题进行了研究。给出了区间直觉模糊数之间的距离公式,并定义了区间直觉模糊正、负理想点,进而提出了一种基于TOPSIS的区间直觉模糊多属性决策方法。最后进行了实例分析。