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双语推荐:三角模糊数直觉模糊数

研究了属性值为三角直觉模糊数的多属性决策问题,提出了一种基于权重函的决策方法。给出了三角直觉模糊数的定义、运算法则和截集;定义了三角直觉模糊数关于隶属函和非隶属函的精确值和模糊度,以及精确值的指标和模糊度的指标,给出了三角直觉模糊数的排序方法,并将其应用到属性值为三角直觉模糊数的多属性决策问题中;给出了属性值为三角直觉模糊数的多属性决策的步骤;通过值算例分析和验证了该方法的有效性。
This paper studies the multi-attribute group decision making problems where the attribute values are triangular intuitionistic fuzzy numbers (TIFNs), and proposes a new decision making method on the basis of weight function. Firstly, this paper introduces the concept, arithmetic operations and cut sets of TIFNs. Secondly, this paper defines the crisp value and ambiguities of the membership function and the non-membership function for TIFNs as well as the crisp value-index and ambiguity-index, then develops a crisp value and ambiguity based ranking method and uses the method to solve multi-attribute decision making problems. Thirdly, this paper gives the steps of triangular intuitionistic multiple attribute decision making. Finally, an illustrative example shows the effectiveness of the proposed method.

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针对决策信息为三角模糊数直觉模糊数(TFNIFN)且属性间存在相互关联的多属性群决策(MAGDM)问题,提出了一种基于三角模糊数直觉模糊加权 Bonferroni 平均(TFNIFWBM)算子的决策方法。首先,基于TFNIFN的运算法则和Bonferroni平均(BM)算子,定义了三角模糊数直觉模糊BM算子和TFNIFWBM算子;然后,研究了这些算子的一些性质,建立基于TFNIFWBM算子的MAGDM模型,结合排序方法进行决策。最后通过MAGDM算例验证了该算子的有效性与可行性。
With respect to the problems of multiple attribute group decision-making (MAGDM)in which the attribute values were in the form of triangular fuzzy number intuitionistic fuzzy numbers (TFNIFN)and attributes were associated with each other,this paper presented a method based on triangular fuzzy number intuitionistic fuzzy weighted Bonferroni means (TFNIF-WBM)operator.Firstly,according to the TFNIFN’s operational laws and Bonferroni means(BM)operator,this method de-fined triangular fuzzy number intuitionistic fuzzy Bonferroni means(TFNIFBM)operator and TFNIFWBM operator.Then,it re-searched the related properties,constructed a multi-attribute group decision making model based on TFNIFWBM operator, which was for making decisions combining with sort methods.Finally,this paper gave an illustrative example of MAGDMprob-lems to demonstrate the effectiveness and feasibility of the proposed operator.
针对决策信息为三角模糊数直觉模糊数(TFNIFN)且属性间存在相互关联的多属性群决策(MAGDM)问题,提出了一种基于三角模糊数直觉模糊PG(TFNIFPG)算子的决策方法.首先,基于TFNIFN的运算法则和PG(Power Geometric)算子,定义了TFNIFPG算子.然后,研究了该算子的一些性质,建立基于TFNIFPG算子的MAGDM模型,结合排序方法进行决策.最后通过某项目投资算例验证了该算子的有效性与可行性.
With respect to the multiple attribute group decision-making(MAGDM)problem,a method based on triangu-lar fuzzy number intuitionistic fuzzy powergeometric (TFNIFPG)operator was presented.The attribute values of MAGDM are in the form of triangular fuzzy number intuitionistic fuzzy numbers (TFNIFN),and the attributes are associated with each oth-er.Firstly,according to the TFNIFN’s operational laws and power geometric (PG)operator,TFNIFPG operator was defined. Then the related properties were researched and a multiple attribute decision group model was constructed based on TFNIFPG operator.The model used sort methods to make decision.Finally,an illustrative example of proj ect investment was proposed to demonstrate the effectiveness and feasibility of the proposed operator.
军事航线优选是一类典型的多属性决策问题,需综合考虑多个定性和定量的决策指标,且由于航行和战场环境的复杂性,决策信息具有高阶模糊不确定性。鉴于三角直觉模糊数能较好地描述高阶模糊不确定性信息,本文利用三角直觉模糊数表示待选航线相对于决策指标的评估值。在此基础上,定义了三角直觉模糊正、负理想解及其与待选航线的距离,建立待选航线与正理想解之间相对贴近度的计算方法,据此给出所有待选航线的优劣排序。值实例说明该方法的有效性和实用性,可为解决军事航线优选问题提供新的途径。
The aim of this paper is to research the military route selection problems with the ratings of alternatives on attributes expressed using triangular intuitionistic fuzzy numbers (TIFNs). Firstly, a distance measure of TIFNs is developed to calculate differences between each alternative and the positive ideal-solution as well as the negative ideal-solution. Secondly, based on these distances the relative closeness degrees to the positive ideal-solution are calculated. Thus, the ranking order of all alternatives is obtained. A numerical example is examined to demonstrate the implementation process of the method proposed in this paper. So, a new method is given for solving the military route selection problems with intuitionistic fuzzy information.

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针对准则值均为模糊数的风险型多准则决策问题,提出一种基于前景理论和VIKOR的多准则决策方法。首先,进行区间三角模糊数、梯形模糊数直觉模糊数和语言值的无量纲化处理;然后,基于各个准则各种状态下各个方案的准则值排序,确定中位参考点以及各个方案在各个准则下的综合前景值;接着,基于前景价值矩阵,给出基于VIKOR的扩展方法;最后,通过具体实例验证了所提出方法的有效性和可行性。
According to the multi-criteria decision making problems with fuzzy criteria values, a decision making approach based on the prospect theory and the VIKOR method is proposed. Firstly, the interval numbers, the triangular fuzzy number, the trapezoidal fuzzy number, the intuitionistic fuzzy number and the linguistic information are nondimensionalized. Then, the median reference points are given based on the order of all the alternatives with different criteria under all the conditions, thus the comprehensive prospect values of each alternative under each criterion are obtained. Furthermore, the extended VIKOR method is proposed based on the prospect value matrix. Finally, an example illustrates the feasibility and effectiveness of the proposed method.

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针对高速铁路调度指挥人因风险排序问题,从人因失误概率、人因失误探测度、人因失误重要度和事故严酷度四个方面构建风险评价指标体系。考虑到人因风险指标的模糊性和不确定性,用直觉三角模糊数描述各指标值,基于直觉模糊熵计算指标客观权重,然后建立基于TOPSIS法的高铁列车调度指挥人因失误风险排序模型。最后,基于实例验证了排序模型的实用性。
Error probability, error detectability, error importance and accident severity were used to evaluate hu-man error risk .Due to the uncertainties and imprecisions , the risk factors were characterized with intuitionistic tri-angular fuzzy numbers .The objective weights of four factors were calculated based on intuitionistic fuzzy entropy . Then, a risk prioritization model of human error for high-speed railway dispatchers based on intuitionistic triangular fuzzy TOPSIS was constructed .A case example was presented to demonstrate the practicality of proposed approach .

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文章针对航空公司服务质量评价过程存在的不确定性和非可加性,在三角直觉模糊数模糊测度和VIKOR等理论的基础上构建非可加直觉模糊VIKO多准则评价方法,从"保证性"、"服务人员"、"有形性"、"可靠性"四个方面建立评价指标体系。基于此对六家航空公司的服务质量的进行了评价。被评价航空公司的服务质量由高到低大致可以分为三等级:第一等级为中国国际航空公司和四川航空公司;第二等级为海南航空公司;第三等级为东方航空公司、南方航空公司和深圳航空公司。另外,与可加多准则评价方法对比研究的结果显示指标间的非可加性对评价结果有较明显的影响。
In order to seize the characteristics of non-additive and uncertainty in the evaluation procedure , this paper const-ruct a non-additive VIKOR method in intuitionistic fuzzy settings based on the integration of VIKOR , fuzzy measure and intuitionistic fuzzy theory. This paper also established evaluation criteria for airline service quality with four dimensions: "Reliab-ility","Employees'' service","Tangibles" and "Assurance". Six airline''s services are assessed with the help of the criteria and the method. The results show that the service performance of the six airlines could be divided into three levels: the first level includes airline A1 and A5, second includes A4. The remain belong to third level. Comparative studies are also carried out which results suggested that the property of non-additive between criteria obviously impact on the results.

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