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.

A Novel Incremental Attribute Reduction Algorithm Based on Intuitionistic Fuzzy Partition Distance

Attribute reduction,also known as feature selection,for decision information systems is one of the most pivotal issues in machine learning and data mining.Approaches based on the rough set theory and some extensions were proved to be efficient for dealing with the problemof attribute reduction.Unfortunately,the intuitionistic fuzzy sets based methods have not received much interest,while these methods are well-known as a very powerful approach to noisy decision tables,i.e.,data tables with the low initial classification accuracy.Therefore,this paper provides a novel incremental attribute reductionmethod to dealmore effectivelywith noisy decision tables,especially for highdimensional ones.In particular,we define a new reduct and then design an original attribute reduction method based on the distance measure between two intuitionistic fuzzy partitions.It should be noted that the intuitionistic fuzzypartitiondistance iswell-knownas aneffectivemeasure todetermine important attributes.More interestingly,an incremental formula is also developed to quickly compute the intuitionistic fuzzy partition distance in case when the decision table increases in the number of objects.This formula is then applied to construct an incremental attribute reduction algorithm for handling such dynamic tables.Besides,some experiments are conducted on real datasets to show that our method is far superior to the fuzzy rough set based methods in terms of the size of reduct and the classification accuracy.

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.

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.

Big Data Clustering Optimization Based on Intuitionistic Fuzzy Set Distance and Particle Swarm Optimization forWireless Sensor Networks

Big data clustering plays an important role in the field of data processing in wireless sensor networks.However,there are some problems such as poor clustering effect and low Jaccard coefficient.This paper proposes a novel big data clustering optimization method based on intuitionistic fuzzy set distance and particle swarm optimization for wireless sensor networks.This method combines principal component analysis method and information entropy dimensionality reduction to process big data and reduce the time required for data clustering.A new distance measurement method of intuitionistic fuzzy sets is defined,which not only considers membership and non-membership information,but also considers the allocation of hesitancy to membership and non-membership,thereby indirectly introducing hesitancy into intuitionistic fuzzy set distance.The intuitionistic fuzzy kernel clustering algorithm is used to cluster big data,and particle swarm optimization is introduced to optimize the intuitionistic fuzzy kernel clustering method.The optimized algorithm is used to obtain the optimization results of wireless sensor network big data clustering,and the big data clustering is realized.Simulation results show that the proposed method has good clustering effect by comparing with other state-of-the-art clustering methods.

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。

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.

区间值直觉Fuzzy度量空间及其完备性

给出区间值直觉Fuzzy数的定义 ,并引入区间值直觉Fuzzy数间的区间值直觉Fuzzy距离 ,建立区间值直觉Fuzzy度量空间并讨论其完备性 .

基于后悔理论的多属性决策方法及其在就业选择中的应用

针对决策者在决策过程所产生的心理行为和决策属性权重未知的决策问题,提出基于后悔理论的语言直觉模糊多属性决策方法并用于就业选择。基于Jensen-Shannon散度提出语言直觉模糊JS距离,并通过对比分析验证其合理性。将给出的JS距离和后悔理论相结合,利用后悔值最小化和欣喜值最大化构建赋权模型,并与决策效用值聚合给出备选方案排序。将提出的方法应用于某计算机系学生对就业的选择实例中,通过与其他决策方法进行比较分析,证明了所提方法在就业选择中的有用性和有效性。

基于加权直觉模糊兰氏距离的密度峰值聚类算法

利用传统的聚类算法对直觉模糊集进行聚类分析时,存在对异常值敏感、复杂度较高的问题,不适用于大规模直觉模糊数据的聚类。针对上述问题,提出了一种基于密度峰值思想和加权兰氏距离的直觉模糊聚类算法(WIFDPL),用来提高算法对直觉模糊数据的检测精度,降低算法的复杂度。由于现有直觉模糊距离算子不满足距离度量的定义,提出了一种新的直觉模糊兰氏距离算子,减少了数据的偏移程度,降低了对异常值的敏感程度;由于凝聚型层次聚类算法复杂度较高,采用密度峰值聚类算法对直觉模糊集进行聚类,显著提高了算法的运行效率。实验结果表明,利用改进的直觉模糊兰氏距离提高了聚类精度,且新算法复杂度较低,更适用于大规模直觉模糊集的聚类。

基于距离区间数算子的故障模式与影响分析方法

现有故障模式与影响分析(FMEA)方法在属性值为直觉模糊数且风险程度采用确定距离算子度量的情况下,评判专家通常难以精准地描述相关不确定性问题。因此,首先在有序加权距离算子、区间数的理论以及区间数排序方法研究基础上,提出了直觉模糊混合欧氏距离区间数(IFHEDIN)算子及其优良性质。其次,构建基于不确定IFHEDIN算子,改进FMEA方法,以进行产品或者系统故障模式的可靠性分析,并对风险等级进行计算与排序。最后,以实际医院放射肿瘤治疗过程中,故障模式的风险分析以及评价为例,论证了所提方法的有效性、可靠性以及精准性,为相关医疗诊断管理者进行风险应对和控制提供决策支持。

EXTENSION OF THE TOPSIS METHOD BASED ON PROSPECT THEORY AND TRAPEZOIDAL INTUITIONISTIC FUZZY NUMBERS FOR GROUP DECISION MAKING

Considering the decision maker＇s risk psychological factors and information ambiguity under uncertainty, a novel TOPSIS based on prospect theory （PT） and trapezoidal intuitionistic fuzzy numbers （YrIFNs） for group decision making is investigated, in which the criteria values and the criteria weights take the form of TrIFNs, and weights of decision makers are unknown. Firstly, distance measures for TrIFNs are used to induce value function under trapezoidal intuitionistic fuzzy environment. Secondly, the concepts of distance measures and trapezoidal intuitionistie fuzzy weighted averaging operator are employed to induce the weights of decision makers and thus the decision makers＇ options can be aggregated. Then the PT-based separation measures and relative closeness coefficient are defined and an algorithm for ranking alternatives under trapezoidal intuitionistic fuzzy environment is proposed. Finally, a numerical example further illustrates the practicality and effectiveness of the proposed TOPSIS method.

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.

高阶隐写直觉模糊集距离安全性测度

在隐写安全性研究滞后于隐写算法发展的前提下,隐写安全性研究成为亟待解决的问题。根据隐写通信过程的模糊不确定性,对隐写数据采用n阶Markov链建模,提出了隐写系统直觉模糊集距离安全性测度,并证明了该安全性测度的有界性、交换性和一致性。仿真实验表明,该安全性测度具有对不同隐写算法的度量区分能力。与确定模式下安全性相比较,在相同数据统计模型下,直觉模糊集距离安全性测度获得了更全面的隐蔽性评价。

剩余型直觉模糊推理的模糊取式反向三Ⅰ算法的性质研究

借助直觉模糊推理的反向三Ⅰ算法,针对直觉模糊推理取式(IFMP)的问题,提出了直觉模糊推理取式反向三Ⅰ算法的连续性与鲁棒性.选用直觉模糊距离,验证了在直觉模糊距离下,模糊推理的反向三Ⅰ算法的IFMP问题具有较好的连续性、逼近性及鲁棒性.

基于直觉模糊马氏距离的船舶绿色度评价

为准确评估船舶与环境的友好程度,引入船舶绿色度概念,提出一种运用模糊多属性决策模型选择最优备选方案的方法。从环境协调性、经济合理性、技术先进性和安全舒适性等4方面构建绿色船舶评价指标体系。采用群决策理论和模糊熵确定指标权重,利用新定义的直觉模糊马氏距离和优劣解距离法对备选船舶的绿色度进行排序。通过实例和对比分析,验证所提方法的有效性和稳健性,并阐述其应用价值。