Assessment and sequencing of air target threat based on intuitionistic fuzzy entropy and dynamic VIKOR

In view of the fact that traditional air target threat assessment methods are difficult to reflect the combat characteristics of uncertain, dynamic and hybrid formation, an algorithm is proposed to solve the multi-target threat assessment problems. The target attribute weight is calculated by the intuitionistic fuzzy entropy(IFE) algorithm and the time series weight is gained by the Poisson distribution method based on multi-times data. Finally,assessment and sequencing of the air multi-target threat model based on IFE and dynamic Vlse Kriterijumska Optimizacija I Kompromisno Resenje(VIKOR) is established with an example which indicates that the method is reasonable and effective.

Dynamic Weapon Target Assignment Based on Intuitionistic Fuzzy Entropy of Discrete Particle Swarm

Aiming at the problems of convergence-slow and convergence-free of Discrete Particle Swarm Optimization Algorithm(DPSO) in solving large scale or complicated discrete problem, this article proposes Intuitionistic Fuzzy Entropy of Discrete Particle Swarm Optimization(IFDPSO) and makes it applied to Dynamic Weapon Target Assignment(WTA). First, the strategy of choosing intuitionistic fuzzy parameters of particle swarm is defined, making intuitionistic fuzzy entropy as a basic parameter for measure and velocity mutation. Second, through analyzing the defects of DPSO, an adjusting parameter for balancing two cognition, velocity mutation mechanism and position mutation strategy are designed, and then two sets of improved and derivative algorithms for IFDPSO are put forward, which ensures the IFDPSO possibly search as much as possible sub-optimal positions and its neighborhood and the algorithm ability of searching global optimal value in solving large scale 0-1 knapsack problem is intensified. Third, focusing on the problem of WTA, some parameters including dynamic parameter for shifting firepower and constraints are designed to solve the problems of weapon target assignment. In addition, WTA Optimization Model with time and resource constraints is finally set up, which also intensifies the algorithm ability of searching global and local best value in the solution of WTA problem. Finally, the superiority of IFDPSO is proved by several simulation experiments. Particularly, IFDPSO, IFDPSO1~IFDPSO3 are respectively effective in solving large scale, medium scale or strict constraint problems such as 0-1 knapsack problem and WTA problem.

Entropy-based procedures for intuitionistic fuzzy multiple attribute decision making

The class of multiple attribute decision making （MADM） problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score function is first used to calculate the score of each attribute value and a score matrix is constructed, and then it is transformed into a normalized score matrix. Based on the normalized score matrix, an entropy-based procedure is proposed to derive attribute weights. Furthermore, the additive weighted averaging operator is utilized to fuse all the normalized scores into the overall scores of alternatives, by which the ranking of all the given alternatives is obtained. This paper is concluded by extending the above results to interval-valued intuitionistic fuzzy set theory, and an illustrative example is also provided.

Entropy measures of type-2 intuitionistic fuzzy sets and type-2 triangular intuitionistic trapezodial fuzzy sets

In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all of the constructive principles. Further, a novel concept of the type-2 triangular in- tuitionistic trapezoidal fuzzy set （T2TITrFS） is developed, and a geometric interpretation of the T2TITrFS is given to comprehend it completely or correctly in a more intuitive way. To deal with a more general uncertain complex system, the constructive principles of an entropy measure of T2TITrFS are therefore proposed on the basis of the axiomatic definition of the type-2 intuitionisic fuzzy entropy measure. This paper elicits a formula of type-2 triangular intuitionistic trapezoidal fuzzy entropy and verifies that it does sa- tisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2TITrFS in describing the uncertainty of the type-2 intuitionistic fuzzy information and illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.

Introduce a Novel PCA Method for Intuitionistic Fuzzy Sets Based on Cross Entropy

In this paper, a new method for Principal Component Analysis in intuitionistic fuzzy situations has been proposed. This approach is based on cross entropy as an information index. This new method is a useful method for data reduction for situations in which data are not exact. The inexactness in the situations assumed here is due to fuzziness and missing data information, so that we have two functions (membership and non-membership). Thus, method proposed here is suitable for Atanasov’s Intuitionistic Fuzzy Sets (A-IFSs) in which we have an uncertainty due to a mixture of fuzziness and missing data information. For the demonstration of the application of the method, we have used an example and have presented a conclusion.

Multi-attribute decision making method for air target threat evaluation based on intuitionistic fuzzy sets

The function of the air target threat evaluation （TE） is the foundation for weapons allocation and senor resources management within the surface air defense. The multi-attribute evaluation methodology is utilized to address the issue of the TE in which the tactic features of the detected target are treated as evaluation attributes. Meanwhile, the intuitionistic fuzzy set （IFS） is employed to deal with information uncertainty in the TE process. Furthermore, on the basis of the entropy weight and inclusion-comparison probability, a hybrid TE method is developed. In order to accommodate the demands of naturalistic decision making, the proposed method allows air defense commanders to express their intuitive opinions besides incorporating into the threat features of the detected target. An illustrative example is provided to indicate the feasibility and advantage of the proposed method.

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.

Consensus intuitionistic fuzzy group decision-making method for aircraft cockpit display and control system evaluation

A novel group decision-making （GDM） method based on intuitionistic fuzzy sets （IFSs） is developed to evaluate the ergonomics of aircraft cockpit display and control system （ACDCS）. The GDM process with four steps is discussed. Firstly, approaches are proposed to transform four types of common judgement representations into a unified expression by the form of the IFS, and the features of unifications are analyzed. Then, the aggregation operator called the IFSs weighted averaging （IFSWA） operator is taken to synthesize decision-makers’ （DMs’） preferences by the form of the IFS. In this operator, the DM’s reliability weights factors are determined based on the distance measure between their preferences. Finally, an improved score function is used to rank alternatives and to get the best one. An illustrative example proves the proposed method is effective to valuate the ergonomics of the ACDCS.

A Knowledge Measure with Parameter of Intuitionistic Fuzzy Sets

A new knowledge measure with parameter of intuitionistic fuzzy sets (IFSs) is presented based on the membership degree and the non-membership degree of IFSs, which complies with the extended form of Szmidt-Kacprzyk axioms for intuitionistic fuzzy entropy. And a sufficient and necessary condition of order property in the Szmidt-Kacprzyk axioms is discussed. Additionally, some numerical examples are given to illustrate the applications of the proposed knowledge measure and some conventional entropies and knowledge measures of IFSs. The experimental results show that the results of the parametric model proposed in this paper are more accurate than those of most of the classic models.

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.

Group Decision Making With Consistency of Intuitionistic Fuzzy Preference Relations Under Uncertainty

Intuitionistic fuzzy preference relation(IFPR) is a suitable technique to express fuzzy preference information by decision makers(DMs). This paper aims to provide a group decision making method where DMs use the IFPRs to indicate their preferences with uncertain weights. To begin with, a model to derive weight vectors of alternatives from IFPRs based on multiplicative consistency is presented. Specifically, for any IFPR,by minimizing its absolute deviation from the corresponding consistent IFPR, the weight vectors are generated. Secondly,a method to determine relative weights of DMs depending on preference information is developed. After that we prioritize alternatives based on the obtained weights considering the risk preference of DMs. Finally, this approach is applied to the problem of technical risks assessment of armored equipment to illustrate the applicability and superiority of the proposed method.

Solving Intuitionistic Fuzzy Linear Programming Problem—II

Under non-random uncertainty, a new idea of finding a possibly optimal solution for linear programming problem is examined in this paper. It is an application of the intuitionistic fuzzy set concept within scope of the existing fuzzy optimization. Here, we solve a linear programming problem (LPP) in an intuitionistic fuzzy environment and compare the result with the solution obtained from other existing techniques. In the process, the result of associated fuzzy LPP is also considered for a better understanding.

Anomaly Detection of Complex Networks Based on Intuitionistic Fuzzy Set Ensemble

Ensemble learning for anomaly detection of data structured into a complex network has been barely studied due to the inconsistent performance of complex network characteristics and the lack of inherent objective function. We propose the intuitionistic fuzzy set（IFS）-based anomaly detection, a new two-phase ensemble method for anomaly detection based on IFS, and apply it to the abnormal behavior detection problem in temporal complex networks.Firstly, it constructs the IFS of a single network characteristic, which quantifies the degree of membership,non-membership and hesitation of each network characteristic to the defined linguistic variables so that makes the unuseful or noise characteristics become part of the detection. To build an objective intuitionistic fuzzy relationship, we propose a Gaussian distribution-based membership function which gives a variable hesitation degree. Then, for the fuzzification of multiple network characteristics, the intuitionistic fuzzy weighted geometric operator is adopted to fuse multiple IFSs and to avoid the inconsistence of multiple characteristics. Finally, the score function and precision function are used to sort the fused IFS. Finally, we carry out extensive experiments on several complex network datasets for anomaly detection, and the results demonstrate the superiority of our method to state-of-the-art approaches, validating the effectiveness of our method.

基于IFE动态直觉模糊法的空战目标威胁评估

针对传统空战多目标威胁评估难以与动态作战态势相结合的缺陷和不足,提出了基于直觉模糊熵(intuitionistic fuzzy entropy,IFE)与动态直觉模糊法相结合的空战多目标威胁评估方法。该方法通过直觉模糊集确定目标属性矩阵,采用IFE算法对目标属性赋权;采用泊松分布法处理多时刻态势信息,计算时间序列权重;建立动态直觉模糊空战多目标威胁评估数学模型,并进行了仿真研究。仿真结果表明该算法是合理和有效的。

覆盖粗糙直觉Fuzzy集模型的一点注记

通过对一类覆盖粗糙直觉模糊集模型中粗糙度定义的分析,对其所存在疏漏进行了改进;再将粗糙熵的概念引入到该模型,研究直觉模糊集的不确定度量;通过例子说明该度量的有效性。

基于dynFWA-IFE的空中目标威胁评估方法

针对现代战场中数据模糊,无法准确判断空中目标威胁情况的问题,提出一种基于动态搜索烟花算法-直觉模糊熵(dynamic search fireworks algorithm-intuitionistic fuzzy entropy,dynFWA-IFE)的空中目标威胁评估方法。该方法运用dynFWA优化求解最小IFE的非线性规划模型,得到威胁指标权重后代入直觉模糊集中的隶属度数据,从而评估空中目标的威胁情况。实验证明该方法能够准确对空中目标威胁程度进行排序,为作战指挥提供情报服务。

直觉模糊系统下的属性约简算法及其应用

信息熵是研究信息粒不确定性度量的一种重要方法,并且可以应用于信息系统的属性约简和综合评估中。本文提出了比较两个直觉模糊值大小的新方法,定义了直觉模糊集中香农熵形式的熵度量。以直觉模糊决策系统为背景,结合直觉模糊集理论,基于直觉模糊相似关系分别构造了直觉模糊信息熵和条件熵,利用直觉模糊条件熵给出属性重要度的计算公式,设计了基于直觉模糊条件熵的启发式属性约简算法。在此基础上,通过属性重要度得到了属性指标的权重,进而提出了一种综合评估方法,并将其应用于安全审计风险的研究中,得到可接受的安全风险评估方法,通过结果对比分析,验证了该方法的可靠性和有效性。

防空反导一体化指挥协同效能评估

针对当前防空反导一体化指挥协同缺乏科学效能评估方法问题,构建了效能评估指标体系,构造了一个差值平方根直觉模糊熵,以此来确定评估指标权重和评估专家权重,运用改进的TOPSIS方法进行效能评估,并通过与传统的模糊综合评价方法对比分析,验证改进评估方法的科学性和可靠性,评估结果可为指战员提供作战辅助决策。

基于自信息熵的直觉模糊决策系统的属性约简

针对在直觉模糊集中,利用下近似构建的约简只考虑了下近似而忽略了上近似,从而导致一些信息丢失的问题,基于直觉模糊集的上、下近似提出了3种熵度量,并将其应用于直觉模糊决策信息系统的约简之中。在直觉模糊决策信息系统上定义用于描述直觉模糊关系的3种不确定性度量,分别为平均决策指数、平均安全决策指数以及平均风险决策指数,并在此基础上依次提出了条件信息熵、条件粗糙熵和自信息熵,基于自信息熵给出了相应的约简定义以及属性约简算法。在多个数据集上的实验表明,所提出的属性约简算法与其他算法相比,约简结果更具有优越性以及鲁棒性。

基于前景理论的多阶段混合信息决策方法

针对属性值为混合信息的多阶段决策问题,考虑决策者风险偏好态度,提出一种新的基于动态参考点的前景理论决策方法。通过定义直觉模糊熵,将混合信息一致化为信息效用值,并在传统单阶段参考点设置方法的基础上引入目标参考点,综合发展状态和发展趋势计算得到具有决策者风险偏好波动特点的动态参考点;进一步通过熵权法确定属性的权重范围,并构建考虑偏差度的目标优化模型,在引入前景理论的基础上测算各备选方案的动态前景值。将该决策方法应用到商业银行对小微企业贷款融资的选择案例中,对比分析说明方法的合理性和可行性。