A method for multiple attribute decision-making with the fuzzy preference relation on alternatives

This paper investigates the multiple attribute decision-making (MADM) problem with preference information on alternatives. A new method is proposed to solve the MADM problem, where the decision maker (DM) gives his/her preference on alternatives in a fuzzy relation. To reflect the DM's subjective preference information, a linear goal programming model is constructed to determine the weight vector of attributes and then to rank the alternatives. Finally, a numerical example is used to illustrate the use of the proposed method.     

An interactive sorting method for additive utility functions

In this paper, we consider the problem of placing alternatives that are defined by multiple criteria into preference-ordered categories. We consider a method that estimates an additive utility function and demonstrate that it may misclassify many alternatives even when substantial preference information is obtained from the decision maker (DM) to estimate the function. To resolve this difficulty, we develop an interactive approach. Our approach occasionally requires the DM to place some reference alternatives into categories during the solution process and uses this information to categorize other alternatives. The approach guarantees to place all alternatives correctly for a DM whose preferences are consistent with any additive utility function. We demonstrate that the approach works well using data derived from ranking global MBA programs as well as on several randomly generated problems.     

Multiple-attribute group decision making with different formats of preference information on attributes.

Interval utility values, interval fuzzy preference relations, and interval multiplicative preference relations are three common uncertain-preference formats used by decision-makers to provide their preference information in the process of decision making under fuzziness. This paper is devoted in investigating multiple-attribute group-decision-making problems where the attribute values are not precisely known but the value ranges can be obtained, and the decision-makers provide their preference information over attributes by three different uncertain-preference formats i.e., 1) interval utility values; 2) interval fuzzy preference relations; and 3) interval multiplicative preference relations. We first utilize some functions to normalize the uncertain decision matrix and then transform it into an expected decision matrix. We establish a goal-programming model to integrate the expected decision matrix and all three different uncertain-preference formats from which the attribute weights and the overall attribute values of alternatives can be obtained. Then, we use the derived overall attribute values to get the ranking of the given alternatives and to select the best one(s). The model not only can reflect both the subjective considerations of all decision-makers and the objective information but also can avoid losing and distorting the given objective and subjective decision information in the process of information integration. Furthermore, we establish some models to solve the multiple-attribute group-decision-making problems with three different preference formats: 1) utility values; 2) fuzzy preference relations; and 3) multiplicative preference relations. Finally, we illustrate the applicability and effectiveness of the developed models with two practical examples.     

一种结合主客观信息的多属性决策方法

研究了具有模糊偏好信息的模糊多属性决策问题．提出一种结合主观偏好信息与客观信息的综合特征向量方法．主观偏好信息由决策方案的模糊偏好互补矩阵和属性权重的两两比较互反矩阵组成，客观信息由客观决策矩阵组成．给出了求解模糊多属性决策问题的最小二乘偏差估计方法．通过建立二次规划模型决定属性权重向量，并对方案进行排序．最后，给出了使用该方法的数值例子．     

部分权重信息下对方案有偏好的多属性决策法

研究只有部分权重信息且对方案有偏好的多属性决策问题．首先对方案的偏好信息以互反判断矩阵和互补判断矩阵这两种形式给出的情形，分别建立一个目标规划模型，通过求解这两个模型可确定属性的权重；然后提出一种基于目标规划模型的多属性决策方法；最后通过实例说明了该方法的可行性和有效性。     

Possibilistic programming approach for fuzzy multidimensional analysis of preference in group decision making

Multiple attribute decision making (MADM) problems are the most encountered problems in decision making. Fuzziness is inherent in decision making process and linguistic variables are well suited to assessing an alternative on qualitative attributes using fuzzy rating. A few techniques in MADM assess the weights of attributes based on preference information on alternatives. But they are not practical any more when the set of all paired comparison judgments from decision makers (DMs) on attributes are not crisp and also we have to deal with fuzzy decision matrix. This paper investigates the generation of a possibilistic model for multidimensional analysis of preference (LINMAP). The model assesses the fuzzy weights as well as locating the ideal solution with fuzzy decision making preference on attributes and fuzzy decision matrix. All of the information is assumed as triangular fuzzy numbers (TFNs). This method is developed in group decision making environments and formulates the problem as a possibilistic programming with multiple objectives.     

Establishing dominance and potential optimality in multi-criteria analysis with imprecise weight and value

The model presented in this paper does not require exact estimations of decision parameters such as attribute weights and values that may often be considerable cognitive burden of human decision makers. Information on the decision parameters is only assumed to be in the form of arbitrary linear inequalities which form constraints in the model. We consider two criteria, dominance and potential optimality, to check whether or not each alternative is outperform for a fixed feasible region denoted by the constraints. In particular, we develop a method to identify potential optimality of alternatives when all (or subsets) of the attribute values as well as weights are imprecisely know. This formulation becomes a nonlinear programming problem hard to be solved generally so that we provide in this paper how this problem is transformed into a linear programming equivalent.Scope and purposeMost managerial decisions involve choosing an optimal alternative from a number of available alternatives. Researchers have proposed a lot of methods to assist decision makers in choice making with a set of, usually conflicting, criteria or attributes. Many of these approaches require exact (or precise) information about either or both attribute values and/or trade-off weights. In some practice, however, it is not easy for decision makers to provide such exact data because, for example, intangible attributes to reflect social and environmental impacts may be included. To cope with such problem, a mathematical programming model-based approach to multi-criteria decision analysis is presented in this paper when both attribute weights and marginal values are imprecisely identified. A weighted additive rule is used to evaluate the performance of alternatives. We then show how to obtain non-dominated and potentially optimal alternatives in order to support choice making.     

Group decision making with incomplete information: a dominance and quasi‐optimality volume‐based approach using Monte‐Carlo simulation

In this paper, we present a comprehensive framework for multiattribute group decision making considering that neither information about individual preferences nor the importance of individual decision makers for the group is available in exact form. We study several different forms of incomplete preference information, including a ranking of attribute weights, ranking of values of alternatives in each attribute, and ranking of value differences. Our approach is based on relative volumes in parameter space and allows for probabilistic statements about different results, including optimality or quasi‐optimality of alternatives, or relations between alternatives.     

区间型多属性决策的心态指标法

针对决策者偏好信息和属性值均为区间数的多属性决策问题,提出一种新的决策方法.该方法将区间型决策矩阵转化为带心态指标的决策矩阵,通过求解主、客观偏好的总绝对偏差最小与各方案综合属性值差距最大的双目标规划问题,客观地确定了属性的权重,从而给出各方案的排序结果.当决策者处于不同心态时,可以通过调整其心态指标来进行决策,因而更加符合实际.应用实例表明了该方法的有效性和实用性.     

基于方案偏好和部分权重信息的模糊多属性决策方法

研究了只有部分权重信息且决策者对方案的偏好信息以三角模糊数互反判断矩阵形式给出的模糊多属性决策问题.首先为得到属性权重,给出一种结合主观模糊偏好信息和客观决策信息的极小化极大偏差模型;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;最后,通过算例说明了该方法的可行性和有效性.     

A method based on interval-valued fuzzy soft set for multi-attribute group decision-making problems under uncertain environment

In this paper, we develop a new method for multiple attributes group decision-making problems under uncertain environment, in which the information about attribute weights is incompletely known or completely unknown, and each maker’s decision information is expressed by an interval-valued fuzzy soft set. Moreover, this paper takes account of the decision makers’ attitude toward risk. In order to get the weight vector of the attributes, we construct the score matrix of the final fuzzy soft set. From the score matrix and the given attribute weights information, we establish an optimization model to determine the weights of attributes. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. According to these models, a method based on interval-valued fuzzy soft set, which considers the decision makers’ risk attitude under uncertain environment, is given to rank the alternatives. Finally, a numerical example is used to illustrate the applicability of the proposed approach.     

MAGDM Linear-Programming Models With Distinct Uncertain Preference Structures

Group decision making with preference information on alternatives is an interesting and important research topic which has been receiving more and more attention in recent years. The purpose of this paper is to investigate multiple-attribute group decision-making (MAGDM) problems with distinct uncertain preference structures. We develop some linear-programming models for dealing with the MAGDM problems, where the information about attribute weights is incomplete, and the decision makers have their preferences on alternatives. The provided preference information can be represented in the following three distinct uncertain preference structures: 1) interval utility values; 2) interval fuzzy preference relations; and 3) interval multiplicative preference relations. We first establish some linear-programming models based on decision matrix and each of the distinct uncertain preference structures and, then, develop some linear-programming models to integrate all three structures of subjective uncertain preference information provided by the decision makers and the objective information depicted in the decision matrix. Furthermore, we propose a simple and straightforward approach in ranking and selecting the given alternatives. It is worth pointing out that the developed models can also be used to deal with the situations where the three distinct uncertain preference structures are reduced to the traditional ones, i.e., utility values, fuzzy preference relations, and multiplicative preference relations. Finally, we use a practical example to illustrate in detail the calculation process of the developed approach.      

An stochastic multiattribute acceptability analysis‐based method for the multiattribute project portfolio selection problem with rank‐level information

In many cases of practical multiattribute project portfolio selection problems, it is hard to obtain accurate measurements of attributes and precise preference information. Even after a long and costly information gathering, the attribute measurements and the preference information can still be uncertain or inaccurate. Considerable cost saving will be obtained if the selection of an optimal project portfolio can be done using rank‐level information based on some or all the attributes, without knowing the preference information. In this paper, we propose a stochastic multiattribute acceptability analysis‐based method that can deal with mixed rank and cardinal attribute measurements and uses little or no weight information. In the proposed stochastic multiattribute acceptability analysis‐based method, the decision makers need not to express their preferences explicitly or implicitly, so it is particularly useful when no weight information is available at all. A numerical example involving selection of photovoltaic plants in an industrial province in Eastern China is provided to demonstrate the proposed method.     

Information fusion for intuitionistic fuzzy decision making: An overview

Intuitionistic fuzzy decision making is to find the suitable method for ranking alternatives based on the provided intuitionistic fuzzy information or some related attributes. To date, many studies have focused on intuitionistic fuzzy decision making problems and various decision making methodologies and approaches have been proposed. To provide a clear perspective on the information fusion for intuitionistic fuzzy decision making, this paper presents an overview on the existing intuitionistic fuzzy decision making theories and methods from the perspective of information fusion, involving the determination of attribute weights, the aggregation of intuitionistic fuzzy information and the ranking of alternatives. Some potential challenges in future research are meanwhile pointed out. In addition, we provide a survey of recent applications of the discussed theories and methods in various fields.     

对方案有偏好的直觉模糊多属性决策方法

对属性权重信息不完全、属性值和决策者对方案的偏好信息均以直觉模糊数表示的多属性决策问题提出一种决策方法。首先根据决策者对方案的偏好信息建立多目标规划模型,求出属性权重,接着利用觉模糊加权算术平均算子求出方案的综合属性值,由直觉模糊数的得分函数和精确函数确定方案的排序,最后通过实例证明了该方法的实用性和有效性。     

Large-scale group decision making with multiple stakeholders based on probabilistic linguistic preference relation

A large number of stakeholders take part in the process of decision making, namely, large-scale group decision making (LGDM) problems. Every stakeholder utilises a linguistic preference relation (LPR) to represent her/his preference information for alternatives. Then, a probabilistic LPR (PLPR) is established to represent the group preference. However, some stakeholders may only provide partial preference information about the alternatives. Thus, a PLPR with incomplete probabilities can be used to manage LGDM problems in complex environments. Based on the defined expected multiplicative consistency of PLPR, a probability computation model is established by mathematical programming to derive the missing probabilities of PLPR. In addition, an iterative algorithm to improve the consistency is proposed to obtain the PLPR with satisfactory consistency. Finally, a real-world investment decision-making problem with multiple stakeholders is solved to demonstrate the effectiveness of the proposed method.     

Attribute weights determination models for consensus maximization in multiple attribute group decision-making

Multiple attribute group decision making (MAGDM) is an important research field of decision science. A critical aspect of MAGDM is to determine the weights of attributes. In this paper, we study the MAGDM problem in which the attributes are given in real numbers or interval numbers, and the information about attribute weights is completely unknown or partially known. We first get the group opinion by fusing all individual opinion with each decision-makers' importance and introduce the deviation variable of each individual opinion and the group opinion. Then, we develop a quadratic programming model by means of minimizing the sum of all the deviation values, and a simple and straightforward formula for determining attribute weights can be derived from solving the developed models. We also establish a generalized model for solving MAGDM problems with partial weight information on attributes. In addition, we establish some similar models for MAGDM with interval attribute values. At last, we apply our models to a practical problem of a military unit purchasing new artillery weapons.     

MADM based on distance and correlation coefficient measures with decision-maker preferences under a hesitant fuzzy environment

In multiple attribute decision making (MADM), hesitant fuzzy sets (HFSs) are powerful tools for expressing uncertain and vague information. Recently, MADM problems with hesitant fuzzy information have attracted increasing attention, and many MADM methods have been developed. However, only a limited amount of research has considered MADM problems that simultaneously determine attribute weights and decision-maker (DM) preferences. Therefore, we propose an MADM approach for such problems under a hesitant fuzzy environment. First, we derive extended distance and correlation coefficient measures for HFSs that are more reasonable and effective when the DM preferences are considered. We then apply the extended distance measure to subjective and objective preference information to determine attribute weights, and use these to calculate the weighted correlation coefficient between the ideal choice and each alternative. Further, we determine the ranking order of all alternatives, from which it is easy to identify the best choice. Finally, we present an example that demonstrates the practicality of the proposed approach.     

一类基于优势关系的不完全信息多属性决策方法

针对属性权重和属性值信息均不完全,且含有非线性形式的多属性决策问题,提出一种基于优势关系实现方案择优与排序的决策方法.首先定义方案优势、弱优势和潜在优关系,构建等价的非线性规划模型,确定优势和潜在优方案;然后揭示、论证了非劣集与潜在优集的关系,提出了方案优势度指标,并据此给出了方案择优与排序的实现步骤;最后,提出采用变量替换法求解非线性决策模型.实例计算结果表明,所提出的方法是可行且有效的.     

基于乘法偏好关系的群一致性偏差熵多属性群决策方法研究

在多属性群决策中, 针对每一个属性下决策者都有一个关于决策方案的乘法偏好关系的决策问题, 提出一种基于乘法偏好关系的群一致性偏差熵多属性群决策方法. 此方法考虑到不同属性下的决策者具有不同的权重, 并通过迭代运算可以达到群一致性水平, 从而得出最终的不同属性下决策者的权重; 同时, 可以利用偏差熵模型来求解属性权重, 利用这两个权重最终获得一个综合各方意见的群一致性乘法偏好关系. 最后通过算例分析验证了所提出方法的有效性.