A generic multi-attribute analysis system

This paper describes a generic decision support system based on an additive multiattribute utility model that is intended to allay many of the operational difficulties involved in the multicriteria decision-making process. The system accounts for uncertainty about the alternative consequences and admits incomplete information about the decision-makers’ preferences, which leads to classes of utility functions and weight intervals. The additive model is used to assess, on the one hand, average overall utilities, on which the ranking of alternatives is based and, on the other, minimum and maximum overall utilities, which give further insight into the robustness of this ranking. When the information obtained is not meaningful enough so as to definitively recommend an alternative, an iteration process can be carried out by tightening the imprecise parameters and assessing the non-dominated and potentially optimal alternatives or using Monte Carlo simulation techniques to determine useful information about dominance among the alternatives.     

A method for large group decision-making based on evaluation information provided by participators from multiple groups

Large group decision-making (LGDM) is a special group decision-making (GDM) problem, in which a large number of persons take part in decision process, while research concerning this issue is still relatively scarce. The objective of this paper is to develop a method to solve the LGDM problem, in which a large number of persons from multiple groups take part in the decision process and express their personal evaluations on the alternatives according to the pre-established identifier set. In the method, the percentage distribution on evaluations of each group concerning each alternative is determined. The decision weight of each group concerning each alternative is obtained by aggregating the subjective weight, which is provided by the organizer, and the objective weight, determined according to the level of consensus among participators' evaluations. According to the percentage distributions and decision weights, the dominance degrees on pairwise comparisons of alternatives are calculated, and a ranking of alternatives can be determined using the PROMETHEE II method. Finally, an example is given to illustrate the use of the proposed method.     

一种信息不完全确定的多准则语言群决策方法

针对权系数信息不完全确定且方案的准则值为确定语言等级或位于两个连续语言等级之间,甚至缺失的群决策问题,提出一种群体语言决策方法．该方法利用证据推理算法得到方案属于各语言等级的信任度,利用二元语义对方案进行语言集结;然后结合决策者和准则权重的不完全确定信息及方案与理想方案的二元语义问的距离构建非线性规划模型．利用遗传算法求解所得模型,计算得到各方案的排序．实例计算表明了该方法的可行性和有效性．     

Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets

In this paper, a new method for handling multicriteria fuzzy decision-making problems based on intuitionistic fuzzy sets is presented. The proposed method allows the degrees of satisfiability and non-satisfiability of each alternative with respect to a set of criteria to be represented by intuitionistic fuzzy sets, respectively. Furthermore, the proposed method allows the decision-maker to assign the degrees of membership and non-membership of the criteria to the fuzzy concept “importance.” The method proposed here can provide a useful way to efficiently help the decision-maker to make his decision.     

An algorithm for projecting a reference direction onto thenondominated set of given points

We consider the problem of searching nondominated alternatives in a discrete multiple criteria problem. The search procedure is based on the use of a reference direction. A reference direction reflects the desire of the decision maker (DM) to specify a search direction. To find a set of given alternatives related somehow to the reference direction specified by the DRI, the reference direction has to be projected onto the set of nondominated alternatives. Our purpose is to develop an efficient algorithm for making this projection. The projection of each given reference direction determines a nondominated ordered subset. The set is provided to a decision maker for evaluation. The decision maker will choose the most preferred alternative from this subset and continues the search from this alternative with a new reference direction. The search will end when no direction of improvement is found. A critical point in the procedure is the efficiency of the projection operation. This efficiency of our algorithm is considered theoretically and numerically. The projection is made by parametrizing an achievement scalarizing function originally proposed by Wierzbicki (1980) to project any single point onto the nondominated set     

Identifying and eliminating dominated alternatives in multi-attribute decision making with intuitionistic fuzzy information

Multi-attribute decision making under uncertainty is a usual task in our daily life. In the decision making process, the decision information provided by the decision maker (or expert) over alternatives may take the form of intuitionistic fuzzy numbers, and the weight information on attributes is usually incomplete. To this issue, we first transform the original decision matrix, whose elements are intuitionistic fuzzy numbers expressed by pairs of satisfaction degrees and dissatisfaction degrees, into its expected decision matrix, whose elements are composed of satisfaction degrees and hesitation degrees. We introduce the concept of dominated alternative, and give a method to identify the dominated alternatives. Then we develop an interactive method for eliminating any dominated alternatives by updating the decision maker's preferences gradually so as to find out the optimal one eventually. A further extension of the interactive method to interval-valued intuitionistic fuzzy situations is given, and the solution process of this interactive method is shown in detail through an illustrative example.     

Clustering and selection of multiple criteria alternatives using unsupervised and supervised neural networks

There are decision-making problems that involve grouping and selecting a set of alternatives. Traditional decision-making approaches treat different sets of alternatives with the same method of analysis and selection. In this paper, we propose clustering alternatives into different sets so that different methods of analysis, selection, and implementation for each set can be applied. We consider multiple criteria decision-making alternatives where the decision-maker is faced with several conflicting and non-commensurate objectives (or criteria). For example, consider buying a set of computers for a company that vary in terms of their functions, prices, and computing powers. In this paper, we develop theories and procedures for clustering and selecting discrete multiple criteria alternatives. The sets of alternatives clustered are mutually exclusive and are based on (1) similar features among alternatives, and (2) preferential structure of the decision-maker. The decision-making process can be broken down into three steps: (1) generating alternatives; (2) grouping or clustering alternatives based on similarity of their features; and (3) choosing one or more alternatives from each cluster of alternatives. We utilize unsupervised learning clustering artificial neural networks (ANN) with variable weights for clustering of alternatives, and we use feedforward ANN for the selection of the best alternatives for each cluster of alternatives. The decision-maker is interactively involved by comparing and contrasting alternatives within each group so that the best alternative can be selected from each group. For the learning mechanism of ANN, we proposed using a generalized Euclidean distance where by changing its coefficients new formation of clusters of alternatives can be achieved. The algorithm is interactive and the results are independent of the initial set-up information. Some examples and computational results are presented.     

A Bayesian network for recurrent multi-criteria and multi-attribute decision problems: Choosing a manual wheelchair

This paper discusses recurrent multi-criteria, multi-attribute decision problems. Because of the possibility of decision-maker ignorance or low decision-maker involvement the decision problem structuring is done once for all by a group of experts and does not involve the implication of the decision makers. We propose an original model based on Bayesian networks, which provides a decision process that helps the decision-maker to select an appropriate alternative among a set of alternatives, taking into account multiple criteria that are often conflicting. Our model makes it possible to represent in the same model the decision case (i.e., the decision-maker characteristics, contextual characteristics, their needs and preferences), the set of alternatives with the different attributes, and the choice criteria. The model allows us to compute the value of three essential elements: the importance of each criterion, which is based on the decision-case characteristics; each criterion’s evaluation index in terms of the alternative; and each criterion’s satisfaction index. The recurrent problem of choosing a manual wheelchair (MWC) illustrates the construction and use of our model.     

A method for stochastic multiple criteria decision making based on dominance degrees

This paper proposes a method for solving the stochastic multiple criteria decision making (SMCDM) problem, where consequences of alternatives with respect to criteria are represented by random variables with probability distributions. Firstly, definitions and related analysis of dominance degree of one probability distribution over another are given. Then, by calculating the dominance degrees, the dominance degree matrix of alternative pairwise comparisons with respect to each criterion is built. Further, using PROMETHEE II method, an overall dominance degree matrix of alternative pairwise comparisons is constructed, and a net flow of each alternative is calculated. Based on the obtained net flows, a ranking of alternatives is determined. Finally, numerical examples for the three cases are given to illustrate the use of the proposed method.     

Improved method of multicriteria fuzzy decision-making based on vague sets

An improved method is presented, which provides improved score functions to measure the degree of suitability of each of a set of alternatives, with respect to a set of criteria presented with vague values. The improved algorithm for score functions is introduced by taking into account the effect of an unknown degree (hesitancy degree) of the vague values on the degree of suitability to which each alternative satisfies the decision-maker’s requirement. The meaning of the proposed function is more transparent than that of other existing functions, which are not reasonable in some cases. The proposed function illustrates that it has stronger discrimination in comparison with previous functions. The applicability of this improved multicriteria fuzzy decision-making approach is also demonstrated by means of examples. The improved method can be used to rank the decision alternatives according to the decision criteria. The functions proposed in this paper can provide a more useful technique than previous functions, in order to efficiently help the decision-maker.     

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.     

Consensus in innovation contest categorisation by means of fuzzy partitions

Consensus decision-making is fuzzy by nature, yet fuzzy consensus decision-making in a medium to large number of decisions is not widely used since it demands additional information that requires extra decision-maker effort. Consensus decision-making rests on properly measured agreement. This paper proposes a fuzzy measure of agreement through fuzzy kappa based on fuzzy partitions. These fuzzy partitions enable decision-makers to assess their decisions with a degree of confidence. A fuzzy partition is built for each decision-maker considering his/her confidence degrees when categorising a set of alternatives or solutions. This enables decision-makers to more easily capture the fuzzy nature of the decision. In addition, this paper presents a real-life experiment based on a innovation contest to show the feasibility of using confidence degrees in real-life applications compared to traditional consensus decision-making. The results suggest that the use of confidence degrees improves the level of agreement in the consensus decision-making process through fuzzy kappa coefficients, and it also improves the level of agreement in the consensus decision-making process.     

考虑偏好反转的区间不确定多属性决策方法

针对实际决策中的不确定性和偏好反转问题, 提出一种区间不确定多属性决策方法. 该方法先用证据推理方法集结区间不确定评估信息, 采用累积前景理论代替主观期望效用理论以构建方案的综合前景价值, 从而应对不确定环境下可能的决策偏好反转, 最后区间可能度用于方案综合前景价值排序. 介绍了决策过程, 给出求解方案综合前景价值的非线性规划模型, 并通过实例验证了方法的可行性、合理性和有效性.     

复杂环境下的平行决策研究

针对复杂环境下决策的不确定性、动态性以及面对大量信息决策不知所措等系列问题,提出了复杂环境下的平行决策研究方法,利用平行决策的分解原理,将复杂决策分解为流决策、平行决策和交叉决策,不仅简化了复杂环境下的决策问题研究,而且从某种程度上能将信息优势适时地转化为决策优势,从而为系统决策获取最终的系统竞争优势提供一定的帮助。     

Extending Malakooti's model for ranking multicriteria alternatives with preference strength and partial information

The paper deals with a multiple attribute decision making methodology when a decision maker (DM) specifies his/her preferences in imprecise ways, which is basically an extended version of Malakooti's prior work. Usually, it is said that the DM is willing, or able, to provide partial information, because of time pressure, lack of domain knowledge, or data and the like. In this paper, we consider two categories of partial preference information. First, partial information is related to holistic preference judgments about some pair of alternatives. Second, in a situation where the characteristics of some attributes considered are abstract, or noncommensurate, it is sometimes difficult to make an exact performance evaluation of alternatives with respect to those attributes. To circumvent this difficulty, we allow the DM to specify partial information on performance evaluations, which is similar to the types of preference judgments on some pairs of alternatives. Prioritizing multiple attribute alternatives under two categories of partial information causes an intractable nonlinear program, which is the first issue we try to resolve in the paper. We further propose a measure of preference strength as a decision rule. With partial information, often the use of strict dominance rule yields a larger number of nondominated candidates than the DM wants. The paper assumes a situation where the DM is not willing to provide additional information to reduce the number of nondominated candidates, but he/she wants to have a single optimal candidate or rank ordering of alternatives. It is then necessary to develop a method like one we propose as a preference strength measure.     

Design a new mixed expert decision aiding system using fuzzy ELECTRE III method for vendor selection

Any decision process deals with two different concerns as its cornerstones, evaluating the alternatives and ranking them based on their performances. In any decision process, the former phase is usually the premise of the latter one. Alternatives’ evaluation is the concept that largely depends on the experts and their expertise, which increase uncertainty in the decision-making process. In addition to all proposed methods for having the experts’ knowledge as evaluations of the alternatives, utilizing expert decision support systems (EDSS) can be a sensible response to such a need. Having evaluated the alternatives in the first phase of a decision-making process, the second phase of the process deals with the ranking the alternatives based on their performances obtained from the first phase. In this paper, we discuss the architecture of a fuzzy system including both modules, utilizing fuzzy concept for dealing with the uncertainty of the problem. Concerning the problem we had been dealt with, our system comprises a fuzzy evaluation module, which is a fuzzy expert system and an appropriate tool for evaluating the existing alternatives promptly and smoothly, without the imposed time delays by the experts to propose their comments and the uncertainty of such expertise-based comments, and a fuzzy ranking module, which is a fuzzy version of ELECTRE III method ranking the alternatives based on their outranking relations and by considering the existing uncertainty in their performances. This way the final ranking is resulted from an independent fuzzy system, which has considered the existing uncertainty in the evaluations not once but twice. Our proposed system has been applied to a real case of vendor selection process in one of the greatest and the most famous companies in the Iranian oil industry, OIEC, and the results are discussed.     

A Model for Decision Making with Missing,Imprecise, and Uncertain Evaluations of Multiple Criteria

In real‐life multicriteria decision making (MCDM) problems, the evaluations against some criteria are often missing, inaccurate, and even uncertain, but the existing theories and models cannot handle such evaluations well. To address the issue, this paper extends the Dempster–Shafer (DS)/analytic hierarchy process (DS/AHP) approach of MCDM to handle three types of ambiguous evaluations: missing, interval‐valued, and ambiguous lottery evaluations. In our extension, the aggregation of criteria's evaluation takes the following six steps: (i) calculate the expected evaluation interval and the ambiguity degree of each group of decision alternatives regarding each criterion, (ii) from them to obtain the preference degree of each group of decision alternatives, (iii) apply the DS/AHP method to obtain the mass function distribution of each group of decision alternatives, (iv) use the Dempster's rule of combination to get the overall mass function of each group of decision alternatives with respect to all criteria, (v) according to the overall mass function to count the belief function and the plausibility function of each decision alternative, and (vi) set the overall preference ordering of decision alternatives by our regret‐avoid ambiguous principle and then find the optimal solution. Finally, we give an example of real estate investment to illustrate how our approach is employed to deal with real‐life MCDM problems.     

α-优势关系下的概率粗糙模型及其应用

讨论优势关系下的区间值信息系统在二维均匀分布的假设条件下,通过定义属性对象xj优于xi的概率Paji,结合相对熵最优准则,建立α-优势关系的概率粗糙模型,探讨了即使出现不可分辨情况,也可通过α-累积概率加以决策.模型应用于雷达作战目标的区间数群决策实例分析中,结果显示:α-优势关系的概率粗糙模型可根据不同的决策者,不同的偏好,在合适的粒度,灵活选择粗细适当的优势关系,进行区间数群决策,模型可行有效.     

An improved iterative stochastic multi-objective acceptability analysis method for robust alternative selection in new product development

Alternative selection in new product development (NPD) is a multi-criteria decision-making (MCDM) problem. It usually starts with incomplete, imprecise or even partially missing information. Currently, most existing methods in dealing with this problem cannot work well if required information is incomplete or missing. It is acknowledged that stochastic multi-objective acceptability analysis (SMAA) can be applied to address MCDM problem with incomplete preference information and uncertain criteria measurements. In SMAA, alternatives are evaluated based on SMAA measurements (acceptability index, central weight vector and confidence factor). The discriminability of SMAA for the optimum alternative heavily depends on differences of SMAA measurements among different alternatives. Usually, a large number of alternatives and high level of uncertainty are involved in alternative selection in NPD. In this situation, the differences among SMAA measurements are not obvious, and therefore SMAA cannot deal with such problem very well. To this end, this paper proposes an improved SMAA method called Iterative-SMAA (I-SMAA) for alternative selection in NPD. In the I-SMAA, an iterative multi-step decision-making process is suggested to improve differences of SMAA measurements among different alternatives, and thus assist decision makers (DMs) to positively discern from the most preferred alternative. To enhance the decision-making efficiency, sensitive criteria are acquired in each iteration by ranking sensitivity analysis. DMs are guided to provide partial preference information and give more accurate criteria measurements for sensitive criteria rather than all criteria. Eventually, to verify the proposed method, a numerical example of the existing literature is solved with the method, and the results are compared. And then, a practical example of a preparation equipment for coal samples is further employed to verify the practicability of the proposed I-SMAA.     

A decision support system for supplier selection based on a strategy-aligned fuzzy SMART approach

This study presents a strategy-aligned fuzzy simple multiattribute rating technique (SMART) approach for solving the supplier/vendor selection problem from the perspective of strategic management of the supply chain (SC). The majority of supplier rating systems obtained their optimal solutions without considering firm operations management (OM)/SC strategy. The proposed system utilizes OM/SC strategy to identify supplier selection criteria. A fuzzy SMART is applied to evaluate the alternative suppliers, and deals with the ratings of both qualitative and quantitative criteria. The final decision-maker incorporates the supply risks of individual suppliers into final decision making. Finally, an empirical study is conducted to demonstrate the procedure of the proposed system and identify the suitable supplier(s).