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.

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.

A refined risk explicit interval linear programming approach for optimal watershed load reduction with objective-constraint uncertainty tradeoff analysis

To enhance the effectiveness of watershed load reduction decision making, the Risk Explicit Interval Linear Programming （REILP） approach was developed in previous studies to address decision risks and system returns. However, REILP lacks the capability to analyze the tradeoff between risks in the objective function and constraints. Therefore, a refined REILP model is proposed in this study to further enhance the decision support capability of the REILP approach for optimal watershed load reduction. By introducing a tradeofffactor （α） into the total risk function, the refined REILP can lead to different compromises between risks associated with the objective functions and the constraints. The proposed model was illustrated using a case study that deals with uncertainty- based optimal load reduction decision making for Lake Qionghai Watershed, China. A risk tradeoff curve with different values of a was presented to decision makers as a more flexible platform to support decision formulation. The results of the standard and refined REILP model were compared under 11 aspiration levels. The results demon- strate that, by applying the refined REILP, it is possible to obtain solutions that preserve the same constraint risk as that in the standard REILP but with lower objective risk, which can provide more effective guidance for decision makers.

Linear goal programming approach to obtaining the weights of intuitionistic fuzzy ordered weighted averaging operator

The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.

属性权重不确定条件下的区间直觉模糊多属性决策

在区间直觉模糊集(Interval-valued intuitionistic fuzzy set,IVIFS)的框架内,重点研究了属性权重在一定约束条件下和属性权重完全未知的多属性群决策问题.首先利用区间直觉模糊集成算子获得方案在属性上的综合区间直觉模糊决策矩阵,进一步依据逼近理想解排序法(Technique for order preference by similarity to an ideal solution,TOPSIS)的思想计算候选方案和理想方案的加权距离,最后确定方案排序.其中针对属性权重在一定约束条件下的决策问题,提出了基于区间直觉模糊集精确度函数的线性规划方法,用以解决属性权重求解问题.针对属性权重完全未知的决策问题,首先定义了区间直觉模糊熵,其次通过熵衡量每一属性所含的信息量来求解属性权重.实验结果验证了决策方法的有效性和可行性.

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。

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.

基于灰色关联度求解指标权重的改进方法

针对决策过程中指标权重的确定问题,在分析现有权重确定方法不足的基础上,提出了一种基于灰色关联度求解指标权重的改进方法,并对其性质进行了研究。该方法是对决策者给出的主观权重经验判断矩阵进行充分挖掘,提取出一个公共比较权重数列,并建立一个简易的数学模型,使确定的权重同时反映主观程度和客观程度。算例分析说明了该改进方法的简单性与实用性。

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.

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。

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·

一种新的区间数多属性决策的集结方法

对于属性权重和决策矩阵元素均为区间数的多属性决策问题,提出了一种新的方案综合属性区间的集结方法。通过给出与区间权重向量相对应的属性有效权重向量的定义及其具体表达形式,改变已有方法需要求解数学规划模型的做法,运用区间数的数乘运算和加法运算集结方案的有效综合属性区间值,并利用一种对区间数排序的方法,比较各方案的有效综合属性区间值来确定方案的优劣。最后,给出了一个数值例子,结果表明方法简单、有效,易于实现。

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·

基于模糊决策方法的含风电场电力系统机组组合

结合基于置信区间的风电功率不确定性分析方法和模糊决策方法,提出了计及风电功率预测不确定性风险的含风电场的电力系统模糊机组组合模型。该模型采用模糊决策方法实现了机组发电成本和系统失负荷风险最小的目标,解决了已有模型中未给出置信区间选取依据的不足。此外,该模型采用贴合实际的风电预测不确定模型,保证了该模型的实用性。采用混合整数线性规划(mixed integer linear programming,MILP)方法对所提出的模型进行求解。通过对含风电场的IEEE RTS 26测试系统进行仿真,验证了该模型的有效性和优越性。

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。