New approach to multiple attribute decision making with interval numbers

In an ambiguous decision domain, the evaluation values of alternatives against attributes would be interval numbers because of the inherent, uncertain property of the problems. By using a number of linear programming models, Bryson and Mobolurin propose an approach to compute attribute weights and overall values of the alternatives in the form of interval numbers. The intervals of the overall values of alternatives are then transformed into points or crisp values for comparisons among the alternatives. However, the attribute weights are different because of the use of linear programming models in Bryson and Mobolurin＇s approach. Thus, the alternatives are not comparable because different attribute weights are employed to calculate the overall values of the alternatives. A new approach is proposed to overcome the drawbacks of Bryson and Mobolurin＇s approach. By transforming the decision matrix with intervals into the one with crisp values, a new linear programming model is proposed, to calculate the attribute weights for conducting alternative ranking.

Interval Neutrosophic Prioritized OWA Operator and Its Application to Multiple Attribute Decision Making

On the basis of prioritized aggregated operator and prioritized ordered weighted average(POWA)operator,in this paper,the authors further present interval neutrosophic prioritized ordered weighted aggregation(INPOWA)operator with respect to interval neutrosophic numbers(INNs).Firstly,the definition,operational laws,characteristics,expectation and comparative method of INNs are introduced.Then,the INPOWA operator is developed,and some properties of the operator are analyzed.Furthermore,based on the INPOWA operator and the comparative formula of the INNs,an approach to decision making with INNs is established.Finally,an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Interval-Valued Dual Hesitant Fuzzy Hamacher Aggregation Operators for Multiple Attribute Decision Making

As an generalization of hesitant fuzzy set, interval-valued hesitant fuzzy set and dual hesitant fuzzy set, interval-valued dual hesitant fuzzy set has been proposed and applied in multiple attribute decision making. Hamacher t-norm and t-conorm is an generalization of algebraic and Einstein t-norms and t-conorms. In order to combine interval-valued dual hesitant fuzzy aggregation operators with Hamacher t-norm and t-conorm. We first introduced some new Hamacher operation rules for interval-valued dual hesitant fuzzy elements. Then, several interval-valued dual hesitant fuzzy Hamacher aggregation operators are presented, some desirable properties and their special cases are studied. Further, a new multiple attribute decision making method with these operators is given,and an numerical example is provided to demonstrate that the developed approach is both valid and practical.

Dynamic Multi-Attribute Decision Analysis on Three-Parameter Interval Grey Number of Upper(Lower)Deviation Quasi-Normal Distribution

Aiming at the dynamic multi-attribute decision making problem where the weight of each decision stage and attribute weight are completely unknown and the attribute value is unknown distributed three-parameter interval grey number,a threeparameter interval grey number dynamic multiattribute grey target decision making method with attribute value following quasi-normal distribution is proposed.Firstly,the position relationship between the“center of gravity”point and the kernel of the threeparameter interval grey number is discussed.According to the characteristicthat the attribute value obeys the quasi-normal distribution,anew weight isgiventothe“centerof gravity”point,and a new distance measure formula of the three-parameter interval grey number is defined.Secondly,according to the principle of maximum entropy,the objective programming model is constructed to determine the stage weight and attributeweight.Then,the schemes aresorted according to thesize of the comprehensive bull's-eye distance Finally an example is given to illustrate the effectiveness of the decision model.

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.

Optimized interval 2-tuple linguistic aggregation operator based on PGSA and its application in MAGDM

This study proposes a multiple attribute group decisionmaking(MAGDM)approach on the basis of the plant growth simulation algorithm(PGSA)and interval 2-tuple weighted average operators for uncertain linguistic weighted aggregation(ULWA).We provide an example for illustration and verification and compare several aggregation operators to indicate the optimality of the assembly method.In addition,we present two comparisons to demonstrate the practicality and effectiveness of the proposed method.The method can be used not only to aggregate MAGDM problems but also to solve multi-granularity uncertain linguistic information.Its high reliability,easy programming,and high-speed calculation can improve the efficiency of ULWA characteristics.Finally,the proposed method has the exact characteristics for linguistic information processing and can effectively avoid information distortion and loss.

水利工程施工的IT2FS-MARCOS风险评价

为解决专家决策的主观性造成的风险评价不确定性和不同风险参数权重下考虑多种风险因子评价问题,这里提出一种基于IT2FS-MARCOS法的水利工程施工风险评价方法。首先确定水利工程施工风险指标评估体系,运用最优最劣法(BWM)融合基于层间相关性的客观赋权法(CRITIC)的组合赋权法对各风险参数的权重进行分析;然后引入区间2型模糊集(IT2FS)改进多准则决策中的基于折衷方案的备选方案排序法(MARCOS)计算各风险因素的效用函数值,基于效用函数值进行风险因素分析和评价。结合工程实例应用,表明:地质、天气条件和作业计划安排等风险因素危险程度较高,其中地质条件对该施工项目安全威胁最大,为水利工程施工需重点管理的风险因子。该模型的特点是不仅考虑了专家评价的模糊性,而且采用多准则决策方法避免对风险参数简单加权,与优劣解距离法(TOPSIS)相比,本方法与工程实际符合得更好,有望为处理水利工程不确定信息下的风险评价提供一种新的思路。

An ideal interval method of multi-objective decision-making for comprehensive assessment of water resources renewability

In order to estimate water resources renewability scientifically, an Ideal Interval Method of Multiple Objective Decision-Making (IIMMODM) is presented. This method is developed through improving an ideal point method of multiple objective decision-making. The ideal interval is obtained with assessment standard instead of ideal points. The weights are decided by using the basic point and gray code accelerating genetic algorithm. This method has synthesized the expert’s suggestion and avoided giving a mark for the objective again. It could solve the complicated problem of compatible or incompatible multi-objective assessment. The principle of IIMMODM is presented in this paper. It is used to assess the water resources renewability for nine administrative divisions in the Yellow River basin. The result shows that the water resources renewability in the Yellow River basin is very low. Compared with the gray associate analysis method, fuzzy synthesis method and genetic projection pursuit method, the IIMMODM is easier to use. Compared with the ideal point method of multiple objective decision-making, the IIMMODM has good robustness, which is applicable to the comprehensive assessments of water resources.

一种基于集对分析的区间数多属性决策方法

针对属性权重和决策矩阵均为区间数的多属性决策问题,提出了一种基于集对分析的排序方法。通过借鉴集对分析理论把论域三划分的思想,把区间评价值转化成联系数的形式,给出了两个具有直观意义、计算简便的排序准则,并分析其合理性。分析过程中发现,区间数权重向量和区间数决策矩阵的方案评价向量具有不同的自由度,因此需要对它们采用不同的处理方法。最后,通过算例表明算法排序有效。与已有的数学规划等方法相比,该方法计算更为简便,排序准则具有直观的意义。

三参数区间数多属性决策的后悔理论方法

本文将后悔理论方法用于解决三参数区间数多属性决策问题.首先,提出一种将三参数区间数转换为两参数区间数的方法,避免了传统三参数区间数在大小比较方面不确定信息的遗失.其次,依据两参数区间数决策信息计算不同状态下备选方案及正理想方案各属性的效用值,从而可得各备选方案的后悔–欣喜值及综合感知效用值.然后,针对权重范围已知的情况,通过构建备选方案综合感知效用最大化优化模型求得属性权重;针对权重信息完全未知的情况,提出一种基于注水原理的属性权重求解方法.最后,利用属性权重加权求和方法得到备选方案综合效用值,从而通过比较综合效用值得到方案的排序结果.

属性权重信息不完全的区间数多属性决策方法

针对属性权重信息不完全且属性值以区间数形式给出的多属性决策问题,提出了一种逼近于理想点(TOPSIS)的决策分析方法.首先对属性权重信息不完全的区间数多属性决策问题进行了描述;然后依据传统的,TOPSIS方法的基本思路,给出了解决属性权重信息不完全的区间数多属性决策问题的计算步骤,其核心是通过构建并求解二次规划模型,得到每个方案与正理想点、负理想点的差异值,进而计算出每个方案与理想点的相对接近度,即可得到所有方案的排序结果. 最后通过给出一个算例说明了该方法.

区间数多属性决策中决策矩阵的规范化方法

决策矩阵的规范化是多属性决策分析中的一个重要组成部分，针对具有不确定性区间数的决策矩阵的规范化问题，给出了两类实用的规范化方法，即基于区间数运算的规范化方法和基于误差传递的规范化方法·最后，给出了算例并说明了两类方法各自的特点·

区间数多指标决策的一种TOPSIS方法

针对具有不确定性区间数的多指标决策问题 ,给出了一种逼近于理想点 (TOPSIS)的分析方法·首先对区间数多指标决策问题和区间数运算法则进行了描述 ;然后依据传统的TOPSIS方法的基本思路 ,给出了解决区间数多指标决策问题的计算步骤·该分析方法具有简单、实用的特点 ,它克服了以往研究此类决策问题时所遇到的区间数难以排序的问题·最后给出了一个算例·

区间数多属性决策中一种带有可能度的排序方法

为解决具有不确定性区间数的多属性决策中的方案排序问题，在考虑落在区间内的评价值（即被认为随机变量）服从正态分布的情况下，针对方案综合评价值所在的区间存在相互交叉部分的情形，提出了关于区间数之间相互比较的可能度的概念，并相应给出了带有可能度的方案排序方法。

权重为区间数的多指标决策问题的逼近理想点法

通过引进区间数数量乘法运算 ,将权重为区间数的多指标决策问题转化为指标取值为区间数的多指标决策问题。在此基础上 ,定义了区间数正理想方案和区间数负理想方案 ,由此给出了权重为区间数的多指标决策问题的逼近理想点法 ,该方法简单实用 ,所需信息少。运用该方法分析了一个实际问题。

水环境质量综合评价的多目标决策-理想区间法

对水环境质量综合评价中应用的多目标决策 理想点法进行了分析,认为实际上水环境质量评价标准是区间概念而非点的概念,因而传统的多目标决策 理想点法把评价标准处理成理想点存在一定缺陷。为了克服这种缺陷,提出了一种多目标决策 理想区间法(MODMIIM)。介绍了MODMIIM的原理,给出了它的构成方法,并把它应用到水环境质量综合评价中。MODMIIM与PP模型和神经网络法相比,简单、有效;与多目标决策 理想点法相比,具有更大的适用性。MODMIIM可广泛应用于各种环境质量综合评价中。

突发事件应急响应的多属性风险决策方法研究

针对突发事件发展演变的多状态并导致不同结果的情形,提出了一种突发事件应急响应的多属性风险决策方法。首先描述了突发事件应急响应的多属性风险决策问题;然后依据方案应对突发事件不同状态的损益信息构建具有区间数信息形式的综合决策矩阵,并在此基础上计算各应急方案的综合评价值。进一步地,给出了一个基于概率计算的综合评价值排序方法,进而确定应急方案的排序结果。最后,通过一个算例说明了本文提出方法的可行性和有效性。

不确定性多属性决策中确定属性熵权的一种方法

针对属性值以区间数形式给出的不确定性多属性决策中确定属性权重的问题,提出了一种区间数熵权的确定方法·依据多属性决策中传统熵权确定方法的思路,首先,通过构建两个最优化模型,求得区间熵;然后根据传统熵权确定公式及区间数运算法则得到以区间数形式表示的属性熵权·该方法具有概念清晰、实用的特点,得出的属性熵权能够较好地反映各属性信息的差异程度·最后通过一个算例说明了该方法的实用性和有效性·

考虑决策者心理行为的区间数多属性决策方法

针对考虑决策者心理行为的区间数多属性决策问题,提出一种决策分析方法.首先,针对决策者参照依赖的心理行为特征,依据前景理论计算每个方案在各属性下的评价值相对于参照点的益损值,并构建益损决策矩阵;然后,考虑决策者损失规避的心理行为特征,基于TODIM方法的基本思想,计算决策者对每个方案的益损值的总体感知价值,并依据总体感知价值的大小对所有方案进行排序.最后,通过一个算例说明了该方法的可行性和有效性.