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...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.展开更多
As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making proble...As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making problems are becoming more and more complex,it also becomes more and more difficult to appropriately depict decision makers’cognitive information in decision-making process.In order to describe the decision information more comprehensively,we define a pythagorean probabilistic hesitant triangular fuzzy set(PPHTFS)by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set.Firstly,the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element(PPHTFE)are proposed,and the comparison rule of two PPHTFEs is given.Then,some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed,and their properties are also studied.Finally,a multi-attribute decision-making(MADM)model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information,and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.展开更多
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,TO...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。展开更多
作战试验的条件制定与结果评估对于检验、提高装备的作战效能具有重要意义。本文首先重点分析了空空导弹作战试验的考核目的、考核原则,设置了具体的考核点;在此基础上运用模糊质量功能展开法(Quality Function Deployment,QFD)方法建...作战试验的条件制定与结果评估对于检验、提高装备的作战效能具有重要意义。本文首先重点分析了空空导弹作战试验的考核目的、考核原则,设置了具体的考核点;在此基础上运用模糊质量功能展开法(Quality Function Deployment,QFD)方法建立了作战效能以及作战适用性质量屋,获得作战效能和作战适用性在导弹总体作战性能中的权重;最后,用本文的评估流程对国外先进中距空空导弹进行评估。展开更多
This paper is concerned with a technique for order performance by similarity to ideal solution（TOPSIS） method for fuzzy multi-attribute decision making,in which the information about attribute weights is partly know...This paper is concerned with a technique for order performance by similarity to ideal solution（TOPSIS） method for fuzzy multi-attribute decision making,in which the information about attribute weights is partly known and the attribute values take form of triangular fuzzy numbers.Considering the fact that the triangular fuzzy TOPSIS results yielded by different distance measures are different from others,a comparative analysis of triangular fuzzy TOPSIS ranking from each distance measure is illustrated with discussion on standard deviation.By applying the most reasonable distance,the deviation degrees between attribute values are measured.A linear programming model based on the maximal deviation of weighted attribute values is established to obtain the attribute weights.Therefore,alternatives are ranked by using TOPSIS method.Finally,a numerical example is given to show the feasibility and effectiveness of the method.展开更多
The objective of this work was to determine the location of emergency material warehouses. For the site selection problem of emergency material warehouses, the triangular fuzzy numbers are respectively demand of the d...The objective of this work was to determine the location of emergency material warehouses. For the site selection problem of emergency material warehouses, the triangular fuzzy numbers are respectively demand of the demand node, the distance between the warehouse and demand node and the cost of the warehouse, a bi-objective programming model was established with minimum total cost of the system and minimum distance between the selected emergency material warehouses and the demand node. Using the theories of fuzzy numbers, the fuzzy programming model was transformed into a determinate bi-objective mixed integer programming model and a heuristic algorithm for this model was designed. Then, the algorithm was proven to be feasible and effective through a numerical example. Analysis results show that the location of emergency material warehouse depends heavily on the values of degree a and weight wl. Accurate information of a certain emergency activity should be collected before making the decision.展开更多
基金supported by the National Natural Science Foundation of China(7137115670971017)the Research Grants Council of the Hong Kong Special Administrative Region,China(City U112111)
文摘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.
基金supported by the Key Research and Development Project of Hunan Province(2019SK2331)the Natural Science Foundation of Hunan Province(2019JJ40099,2019JJ40100,2020JJ4339)+2 种基金the Key Scientific Research Project of Hunan Education Department(18A317,19A202)the Scientific Research Fund of Hunan Provincial Education Department(20B272)the Innovation Foundation for Postgraduate of Hunan Institute of Science and Technology(YCX2020A34).
文摘As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making problems are becoming more and more complex,it also becomes more and more difficult to appropriately depict decision makers’cognitive information in decision-making process.In order to describe the decision information more comprehensively,we define a pythagorean probabilistic hesitant triangular fuzzy set(PPHTFS)by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set.Firstly,the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element(PPHTFE)are proposed,and the comparison rule of two PPHTFEs is given.Then,some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed,and their properties are also studied.Finally,a multi-attribute decision-making(MADM)model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information,and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.
文摘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。
文摘作战试验的条件制定与结果评估对于检验、提高装备的作战效能具有重要意义。本文首先重点分析了空空导弹作战试验的考核目的、考核原则,设置了具体的考核点;在此基础上运用模糊质量功能展开法(Quality Function Deployment,QFD)方法建立了作战效能以及作战适用性质量屋,获得作战效能和作战适用性在导弹总体作战性能中的权重;最后,用本文的评估流程对国外先进中距空空导弹进行评估。
基金supported by the National Natural Science Foundation of China (70473037)the Key Project of National Development and Reform Commission (1009-213011)
文摘This paper is concerned with a technique for order performance by similarity to ideal solution（TOPSIS） method for fuzzy multi-attribute decision making,in which the information about attribute weights is partly known and the attribute values take form of triangular fuzzy numbers.Considering the fact that the triangular fuzzy TOPSIS results yielded by different distance measures are different from others,a comparative analysis of triangular fuzzy TOPSIS ranking from each distance measure is illustrated with discussion on standard deviation.By applying the most reasonable distance,the deviation degrees between attribute values are measured.A linear programming model based on the maximal deviation of weighted attribute values is established to obtain the attribute weights.Therefore,alternatives are ranked by using TOPSIS method.Finally,a numerical example is given to show the feasibility and effectiveness of the method.
基金Project(71071162)supported by the National Natural Science Foundation of China
文摘The objective of this work was to determine the location of emergency material warehouses. For the site selection problem of emergency material warehouses, the triangular fuzzy numbers are respectively demand of the demand node, the distance between the warehouse and demand node and the cost of the warehouse, a bi-objective programming model was established with minimum total cost of the system and minimum distance between the selected emergency material warehouses and the demand node. Using the theories of fuzzy numbers, the fuzzy programming model was transformed into a determinate bi-objective mixed integer programming model and a heuristic algorithm for this model was designed. Then, the algorithm was proven to be feasible and effective through a numerical example. Analysis results show that the location of emergency material warehouse depends heavily on the values of degree a and weight wl. Accurate information of a certain emergency activity should be collected before making the decision.
