基于区间梯形二型犹豫模糊数的多准则决策方法及其在工程决策中的应用

针对犹豫语言决策问题,提出了基于区间梯形二型犹豫模糊数的多准则决策方法。首先,给出了区间梯形二型模糊数的定义。然后,构建了区间梯形二型犹豫模糊数的期望值和贴近度函数。在此基础上,建立了区间梯形二型犹豫模糊数的排序模型,并提出了基于该排序模型的区间梯形二型犹豫模糊多准则决策方法。最后,通过工程决策实例论证了该方法的有效性和可行性。     

不完全语言信息下的多准则群决策方法研究

针对决策者所给的自然语言信息缺失判断矩阵,提出了一种基于群体满意度最大的不完全语言信息多准则群决策规划模型.首先分析决策者所给的多准则语言评价信息矩阵,进而通过三角模糊数将多准则语言评价信息矩阵转化为三角模糊数矩阵;其次根据满意度函数构建不完全语言信息多准则群决策规划模型;最后通过实例验证本方法的可行性及有效性.实例表明该方法计算简单,易操作.     

多属性决策中的一种最优组合赋权方法研究

在多属性决策中权系数的确定是非常重要的。从最大地利用信息这个角度，综合各种赋权法的特点，以离差平方和为准则建立了最优组合赋权模型。并以实例表明该方法有效性。     

IVIFS环境下基于模糊熵和得分函数的多准则决策方法

在区间直觉模糊环境和各准则的信息完全未知的条件下,本文提出了一个基于模糊熵和得分函数的多准则决策方法.基于区间直觉模糊集的准则形式,本文给出了模糊熵模型,从而可以确定各准则的权重.在决策方法方面,作者提出了区间直觉模糊集的加权记分函数和加权精确函数,解决了记分函数无法解决的加权问题的难题,同时给出了一种新的决策方法.最后,文章通过实例说明了该方法的可行性和有效性.     

基于共识性测度的概率语言多准则群决策方法研究

针对准则值为概率语言术语集的决策问题,提出一种基于共识性测度的概率语言多准则群决策方法.首先,方法定义概率语言共识性测度公式,据此判断个体决策信息是否满足共识性检验.其次,建立考虑决策者协作意愿的群体共识反馈调整模型及权重惩罚体系.此外,利用网络层次分析法(ANP)和共识性测度公式构建指标定权模型,模型可有效解决指标间互相影响导致的权重计算失准问题.随后,提出改进的TODIM决策方法,结合准则权系数及通过共识性检验的群决策矩阵,对方案进行择优排序.最后,通过算例分析验证了该方法的有效性.     

蕴含权重的偏序集多准则决策法

针对偏序集方法不能解决含有权重的多准则决策问题,提出一种“隐式”赋权的偏序决策方法。首先将含有m个方案和n个准则的决策问题表示成偏序集,之后按权重由大到小的顺序,对准则进行逐步相加形成n个新的准则,得到一个新的偏序集。根据偏序集间的包含关系,证明了新偏序集不仅蕴含了权重信息,而且比初始偏序集有更强的排序能力。结果表明,该法在应用中仅需获取权重排序信息,无需精确权重,适用于权重难以确定的多准则决策问题。以三峡库区水质评价为例,例子表明新方法明显优于原有的偏序决策方法,能够对13个方案进行聚类和排序,而原有方法在该例中几乎难以应用。     

偏好信息为模糊互反判断矩阵的模糊多属性决策法

研究只有部分权重信息且决策者对方案的偏好信息以模糊互反判断矩阵形式给出的模糊多属性决策问题。提出了一种基于目标规划模型的模糊多属性决策方法。该法首先基于模糊互反判断矩阵，利用转换函数将决策信息一致化，建立了一个目标规划模型．通过求解该模型确定属性的权重，然后运用加性加权法求出各方案的模糊综合属性值，并利用已有的三角模糊数排序公式求得决策方案的排序。文章最后把该法应用于解决风险投资领域中的项目评估问题。     

基于语言值软集的多准则群决策方法及其应用

在语言值评估集上引进适当的运算,建立语言值逻辑代数系统,并利用虚拟术语指标不丢失信息的特点,扩展语言值逻辑代数系统为连续语言值逻辑代数系统。通过加权平均算子将全部专家对各决策方案的语言值评估信息集结,得到专家群对全部决策方案就全部准则的集中评估,全部集中评估值构成决策方案上的语言值软集。建立优化模型计算最优准则权重,利用最优准则权重将专家关于各准则的语言值评估结果进行集结,得到各专家对全部决策方案的评估值,评估值全体可看成专家群上的语言值软集,这里参数集为决策方案集。建立基于决策方案上的语言值软集的粗糙近似模型——语言值粗糙近似模型,通过计算各专家对全部决策方案的评估值关于语言值粗糙近似模型的下近似和上近似,得到专家群上的语言值下近似软集和上近似软集。通过对全部决策方案评估集及其语言值粗糙下近似、上近似进行加权算术平均,分别得到三个决策方案上的语言值模糊集。通过三个语言值模糊集对全部决策方案排序。最后,应用基于语言值软集的多准则群决策方法对电子商务监管系统安全进行多准则综合决策评估,说明本文提出的多准则群决策方法是有效的和合理的。     

多目标决策的中心方法之统一探讨

该文从统一的角度研究了多目标决策的中心方法的结构及其收敛性质．提出了形式一般的、可采用三种曲线搜索规则的中心方法之算法模型并在很弱的条件下证明了其全局收敛性以此为基础．讨论了模型中的搜索方向等参量的取法，给出了两类可实现的算法．该文结果统一和推广了已有的单（多）目标决策的中心方法．数值结果表明该算法是有效的．     

一种新的模糊TOPSIS决策方法

TOPSIS方法是多准则决策中常用的一种方法.但是该方法无法有效处理决策中的模糊信息,本文提出了一种模糊环境下的TOPSIS方法.在用三角模糊数对语言变量表示的基础上,决策过程中的各个准则的权重和各个备选方案的等级均采用语言变量来描述,这些语言变量由专家确定.为降低决策中的计算量,引入了模糊数的等级均值积分表示,在决策过程中将模糊数计算转化为简单的实数运算.这一优点使得决策中可以避免求解模糊数之间的距离和对模糊数排序.利用一个多准则决策的算例验证了该方法的有效性.     

A method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations

This paper proposes a method for solving stochastic multiple criteria decision making (MCDM) problems, where evaluations of alternatives on considered criteria are random variables with known probability density functions or probability mass functions. Probabilities on all possible results of pairwise comparisons of alternatives are first calculated using Probability Theory. Then, all possible results of pairwise comparisons are classified into superior, indifferent and inferior ones using a predefined identification rule. Consequently, the probabilities on all possible results of pairwise comparisons are partitioned into superior, indifferent and inferior probabilities. Furthermore, based on the derived probabilities, an algorithm is developed to rank the alternatives. Finally, a numerical example is used to illustrate the feasibility and validity of the proposed method.     

Multi-criteria decision-making method based on normal intuitionistic fuzzy-induced generalized aggregation operator

Normal intuitionistic fuzzy numbers (NIFNs), which use normal fuzzy numbers to express their membership and non-membership functions, can reflect the evaluation information exactly in different dimensions. In this paper, we are committed to apply NIFNs to multi-criteria decision-making (MCDM) problems, and meanwhile some new aggregation operators are proposed, including normal intuitionistic fuzzy weighted arithmetic averaging operator, normal intuitionistic fuzzy weighted geometric averaging operator, normal intuitionistic fuzzy-induced ordered weighted averaging operator, normal intuitionistic fuzzy-induced ordered weighted geometric averaging operator and normal intuitionistic fuzzy-induced generalized ordered weighted averaging operator (NIFIGOWA). Based on the NIFIGOWA operator, an approach is introduced to solve MCDM problems where the criteria values are NIFNs and the criteria weight information is fixed. Finally, the proposed method is compared to the existing methods by virtue of a numerical example to verify its feasibility and rationality.     

A new decision support model in multi-criteria decision making with intuitionistic fuzzy sets based on risk preferences and criteria reduction

In this paper, we propose a new model for decision support to address the ‘large decision table’ (eg, many criteria) challenge in intuitionistic fuzzy sets (IFSs) multi-criteria decision-making (MCDM) problems. This new model involves risk preferences of decision makers (DMs) based on the prospect theory and criteria reduction. First, we build three relationship models based on different types of DMs’ risk preferences. By building different discernibility matrices according to relationship models, we find useful criteria for IFS MCDM problems. Second, we propose a technique to obtain weights through discernibility matrix. Third, we also propose a new method to rank and select the most desirable choice(s) according to weighted combinatorial advantage values of alternatives. Finally, we use a realistic voting example to demonstrate the practicality and effectiveness of the proposed method and construct a new decision support model for IFS MCDM problems.     

Graph-based multi-agent decision making

In lots of practical multi-criteria decision making (MCDM) problems, there exist various and changeable relations among the criteria which cannot be handled well by means of the existing methods. Considering that graphic or netlike structures can be used to describe the relationships among several individuals, we first introduce the graphic structure into MCDM and formalize the relations among criteria. Then, we develop a new tool, called graph-based multi-agent decision making (GMADM) model, to deal with a kind of MCDM problems with the interrelated criteria. In the model, the graphic structure is paid sufficient attention to in two main aspects: (1) how the graphic structure has influence on the benefits of agents (or the criteria values); and (2) the relation between the graphic structure and the importance weights of agents (criteria). In this case, we can select the best plan(s) (or alternative(s)) according to the overall benefits (the overall criteria values) resulting from the model. Moreover, a fuzzy graph-based multi-agent decision making (FGMADM) method is developed to solve a common kind of situations where the graphic structure of agents is uncertain (confidential or false). Three examples are used to illustrate the feasibility of these two developed methods.     

Interactive outranking approaches for multicriteria decision-making problems with imprecise information

PROMETHEE is a powerful method, which can solve many multiple criteria decision making (MCDM) problems. It involves sophisticated preference modelling techniques but requires too much a priori precise information about parameter values (such as criterion weights and thresholds). In this paper, we consider a MCDM problem where alternatives are evaluated on several conflicting criteria, and the criterion weights and/or thresholds are imprecise or unknown to the decision maker (DM). We build robust outranking relations among the alternatives in order to help the DM to rank the alternatives and select the best alternative. We propose interactive approaches based on PROMETHEE method. We develop a decision aid tool called INTOUR, which implements the developed approaches.     

Nonessential objectives within network approaches for MCDM

In Gal and Hanne [Eur. J. Oper. Res. 119 (1999) 373] the problem of using several methods to solve a multiple criteria decision making (MCDM) problem with linear objective functions after dropping nonessential objectives is analyzed. It turned out that the solution does not need be the same when using various methods for solving the system containing the nonessential objectives or not. In this paper we consider the application of network approaches for multicriteria decision making such as neural networks and an approach for combining MCDM methods (called MCDM networks). We discuss questions of comparing the results obtained with several methods as applied to the problem with or without nonessential objectives. Especially, we argue for considering redundancies such as nonessential objectives as a native feature in complex information processing. In contrast to previous results on nonessential objectives, the current paper focuses on discrete MCDM problems which are also denoted as multiple attribute decision making (MADM).     

Fractional Minmax Goal Programming: A Unified Approach to Priority Estimation and Preference Analysis in MCDM

A special minmax goal programming model with fractional goals is formulated and then used as the basis for developing two specific MCDM methods: (1) a method to derive priorities for decision elements from pairwise comparison matrices in the AHP framework; (2) a method to assess an additive value function by analysing some preference information expressed over the set of alternatives on a ratio scale. For both methods a common iterative solution procedure is proposed by using a linear programming formulation.     

Some issues in mathematical modelling of multiple criteria decision-making problems

Models for analyzing and solving multiple criteria decision-making (MCDM) problems are difficult to evaluate and compare, because they are intended for diverse orderings of a set of feasible alternatives. These models are based on a variety of assumptions about the decision maker's preferences and use different types of preference information. In this paper, a conceptual framework is developed for evaluating and comparing discrete alternative MCDM models available for a given decision situation. The procedure employed in the framework guides the user through an analysis of the decision situation making it possible for a decision maker or analyst to select the most appropriate MCDM model from among several alternative feasible models.     

基于犹豫毕达哥拉斯模糊环境下的TODIM方法

在决策过程中TODIM方法能有效的捕捉决策者的心理行为。犹豫毕达哥拉斯模糊集不但能反映正反两个方面的不确定性,而且能反映决策者的犹豫程度。本文将TODIM方法扩展到犹豫毕达哥拉斯模糊集。首先定义了犹豫毕达哥拉斯模糊环境下的测量函数,用于比较两个犹豫毕达哥拉斯模糊数的大小,其次计算每个备选方案相对其它备选方案的相对优势度,然后根据相对优势度选出最佳方案。最后,用航空公司服务质量的评估来说明本文给出方法的可行性和有效性。     

Extension of VIKOR method for decision making problem based on hesitant fuzzy set

The multiple criteria decision making (MCDM) methods VIKOR and TOPSIS are all based on an aggregating function representing “closeness to the ideal”, which originated in the compromise programming method. The VIKOR method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum of an “individual regret” for the “opponent”, which is an effective tool in multi-criteria decision making, particularly in a situation where the decision maker is not able, or does not know to express his/her preference at the beginning of system design. The TOPSIS method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative-ideal solution, but it does not consider the relative importance of these distances. And, the hesitant fuzzy set is a very useful tool to deal with uncertainty, which can be accurately and perfectly described in terms of the opinions of decision makers. In this paper, we develop the E-VIKOR method and TOPSIS method to solve the MCDM problems with hesitant fuzzy set information. Firstly, the hesitant fuzzy set information and corresponding concepts are described, and the basic essential of the VIKOR method is introduced. Then, the problem on multiple attribute decision marking is described, and the principles and steps of the proposed E-VIKOR method and TOPSIS method are presented. Finally, a numerical example illustrates an application of the E-VIKOR method, and the result by the TOPSIS method is compared.