Multicriteria Decision Making with Cognitive Limitations: A DS/AHP‐Based Approach

In real life, sometimes multicriteria decision making (MCDM) problems are dealt with inevitably under cognitive limitations of human's minds. However, few existing models can directly solve MCDM problems of this kind. Thus, to address the issue, this paper proposes a novel approach, which can: (i) handle the cognitive limitations in MCDM problems by distinguishing the case of complete criteria (i.e., there are no hidden cognitive factors that can deviate rational decisions) from the case of incomplete criteria (i.e., there are some hidden cognitive factors that can deviate rational decisions); (ii) differentiate incomplete and complete relative ranking of the groups of decision alternatives (DAs) over a criterion; and (iii) solve the imprecise and uncertain evaluation of criterion weight as well as the ambiguous evaluations of the groups of DAs regarding a given criterion. Hence, we give a measure to consider the influence of cognitive limitations and give two methods to reduce the influence of cognitive limitations when a decision making needs more rational. Moreover, we illustrate our approach by solving a real‐life problem of estate investment. Finally, we give some experimental results about the reduction of the required number of knowledge judgments in our method compared with the previous methods.     

An expert system for multi-criteria decision making using Dempster Shafer theory

This paper outlines a new software system we have developed that utilises the newly developed method (DS/AHP) which combines aspects of the Analytic Hierarchy Process (AHP) with Dempster–Shafer Theory for the purpose of multi-criteria decision making (MCDM). The method allows a decision maker considerably greater level of control (compared with conventional AHP methods) on the judgements made in identifying levels of favouritism towards groups of decision alternatives. More specifically, the DS/AHP analysis allows for additional analysis, including levels of uncertainty and conflict in the decisions made, for example. In this paper an expert system is introduced which enables the application of DS/AHP to MCDM. The expert system illustrates further the usability of DS/AHP, also including new aspects of analysis and representation offered through using this method. The principal application used to illustrate this expert system is that of identifying those residential properties to visit (view), from those advertised for ales through a real estate brokerage firm.     

基于TOPSIS方法改进的多属性决策模型:最小化偏好反转

针对多属性决策方法(MCDM)中出现的偏好反转问题,提出一种基于TOPSIS方法改进的MCDM模型.该模型用MAX法代替矢量法对数据进行标准化处理,并根据备选方案的相似距离衡量每个选项的优劣性.这种基于距离计算的综合属性评价方法不仅计算简单,而且可以较好地测度选项间的差异,增强决策结果的准确性.同时,将该模型计算的结果与SAW、AHP、TOPSIS、VIKOR方法进行对比分析,发现只存在原选项时,所提出的模型与SAW、AHP方法的排序结果一致,而当添加或删除某个选项时,SAW、AHP、TOPSIS、VIKOR方法均会产生不同程度的偏好反转现象,而所提出的基于TOPSIS改进的模型可以保持选项的相对顺序不变,表明所提出的模型是有效的,且在避免偏好反转问题时较SAW、AHP、TOPSIS、VIKOR方法具有一定的优越性和可靠性.     

Comparison between multiple-choice and analytic hierarchy process: measuring human perception

The objective of this study is to examine the effectiveness of the multiple‐choice method in measuring human perception. Specifically, the results of comparisons of the answers to two questions on the same issue are shown, each formatted in a different way: multiple‐choice (MC) and Analytic Hierarchy Process (AHP). AHP not only clearly identifies the most important alternative but also the preference for each alternative by each decision‐maker. Therefore, using AHP to analyze the decision‐making process results in a precise clarification of preference for alternatives. Based on public opinion research using AHP, two findings are shown: (1) MC and AHP yield different aggregated rankings of alternatives, and (2) AHP reveals that in modified MC format, which gives respondents the option of indicating their second‐best alternatives, the choice of a second‐best alternative is independent of the difference in the degree of importance between the best and the second best.     

Data transformation in the evidential reasoning-based decision making process

This paper describes the application of an evidential reasoning (ER)‐based decision making process to multiple‐criteria decision making (MCDM) problems having both quantitative and qualitative criteria. The ER approach is based on the decision theory and the theory of evidence and it uses the concept of ‘degree of belief’ to assess decision alternatives on each attribute. When faced with MCDM problems, evaluation and selection or ranking of alternatives appear to be both challenging and vital to arrive at a rational and robust decision. In the presence of both qualitative and quantitative evaluations in an MCDM problem, it is necessary, when using the ER‐based decision making process, to transform or convert quantitative data into a belief structure using a number of grades so that the converted belief structure and the original quantitative data are equivalent in values or utilities. This paper suggests three scenarios for data transformation and examines how the ranking of decision alternatives is changed when different scenarios of data transformation are used. Ranking of UK universities using the ER approach is illustrated as an example.     

Hierarchical semi-numeric method for pairwise fuzzy group decision making

Gradual improvements to a single-level semi-numeric method, i.e., linguistic labels preference representation by fuzzy sets computation for pairwise fuzzy group decision making are summarized. The method is extended to solve multiple criteria hierarchical structure pairwise fuzzy group decision-making problems. The problems are hierarchically structured into focus, criteria, and alternatives. Decision makers express their evaluations of criteria and alternatives based on each criterion by using linguistic labels. The labels are converted into and processed in triangular fuzzy numbers (TFNs). Evaluations of criteria yield relative criteria weights. Evaluations of the alternatives, based on each criterion, yield a degree of preference for each alternative or a degree of satisfaction for each preference value. By using a neat ordered weighted average (OWA) or a fuzzy weighted average operator, solutions obtained based on each criterion are aggregated into final solutions. The hierarchical semi-numeric method is suitable for solving a larger and more complex pairwise fuzzy group decision-making problem. The proposed method has been verified and applied to solve some real cases and is compared to Saaty's (1996) analytic hierarchy process (AHP) method.     

A method of aggregation in DS/AHP for group decision-making with the non-equivalent importance of individuals in the group

Group decision-making (GDM) is an active area of research within multi-criteria decision-making (MCDM). This paper develops the nascent DS/AHP method of MCDM as an effective tool in GDM. Attention here is given to the aggregation of evidence from individual members of a decision-making group who are considered non-equivalent in their importance within the group. A discount rate value is defined for each member of the group depending on their perceived individual levels of importance. This discount rate attenuates the evidence from an individual by re-assigning more value to their concomitant level of ignorance. The adjusted evidence from each group member is then combined to derive the group's collective decision. A small real world GDM problem concerning the choice of university course textbooks is utilised throughout the analysis presented.     

A new soft computing model based on linear assignment and linear programming technique for multidimensional analysis of preference with interval type-2 fuzzy sets

Multiple criteria decision making (MCDM) approach plays an important role in life, since it is always necessary to make decisions through various alternatives based on specific criteria. In this paper, interval type-2 fuzzy sets (IT2FSs) are used because in most cases in the real-world the information is incomplete and ambiguous. A new group decision approach with linear assignment method (LAM) is proposed. In addition, weight of each evaluation factor according to subjective and objective data is constructed based on a new developed version of linear programming technique for multidimensional analysis of preference (LINMAP) method. In the proposed method, weights of decision makers (DMs) are computed based on a novel approach that applies a new modified method based on the concept of ideal solutions. Furthermore, a new IT2F-ranking method is introduced. To display the applicability of the presented soft computing method, firstly, a real case study of green supplier selection problem is adopted from the literature and solved. Moreover, the method is applied in a second case study of project evaluation and selection problem. Two applications show that the introduced method presents a proper soft computing framework that can handle real-world uncertain environments. Moreover, the method can consider importance of the DMs and evaluation criteria.     

A new linguistic MCDM method based on multiple-criterion data fusion

Multiple-criteria decision-making (MCDM) is concerned with the ranking of decision alternatives based on preference judgements made on decision alternatives over a number of criteria. First, taking advantage of data fusion technology to comprehensively consider each criterion data is a reasonable idea to solve the MCDM problem. Second, in order to efficiently handle uncertain information in the process of decision making, some well developed mathematical tools, such as fuzzy sets theory and Dempster Shafer theory of evidence, are used to deal with MCDM. Based on the two main reasons above, a new fuzzy evidential MCDM method under uncertain environments is proposed. The rating of the criteria and the importance weight of the criteria are given by experts’ judgments, represented by triangular fuzzy numbers. Then, the weights are transformed into discounting coefficients and the ratings are transformed into basic probability assignments. The final results can be obtained through the Dempster rule of combination in a simple and straight way. A numerical example to select plant location is used to illustrate the efficiency of the proposed method.     

动态环境下的群组专家多准则变权决策方法

为克服经典多准则决策（MCDM）方法不适应动态的决策环境、难以反映方案集对准则集的非线性反馈效应等方面缺陷,通过运用网络分析和数据包络分析技术,提出一种动态环境下的群组专家多准则变权决策方法。较之于经典MCDM方法,新方法主要创新之处在于：给出了MCDM模型的动态演化机理;通过专家对方案所处准则状态予以有偏好（无偏好）判断,提出一种保证信息无损的群组专家信息提取方式;实现了对方案的变权评价,有效反映出蕴含在系统内部的准则集与方案集的非线性交互作用关系。实例验证结果表明,所提方法是科学可行的,能够有效解决救灾方案动态优选、供应商动态评价等实践问题。     

Decision making in equipment selection: an integrated approach with AHP and PROMETHEE

Multi-attribute equipment selection is a very important issue for an effective manufacturing system, since the improper equipment selection might cause many problems affecting productivity, precision, flexibility and quality of the products negatively. On the other hand, selecting the best equipment among many alternatives is a multi-criteria decision making (MCDM) problem. In this study, an integrated approach which employs analytic hierarchy process (AHP) and preference ranking organization method for enrichment evaluations (PROMETHEE) together, is proposed for the equipment selection problem. The AHP is used to analyze the structure of the equipment selection problem and to determine weights of the criteria, and PROMETHEE method is used to obtain final ranking, and to make a sensitivity analysis by changing the weights. Proposed approach is applied to a problem of selecting milling machines to be purchased in an international company. Company management found the application and results satisfactory and implementable in their equipment selection decisions.     

Group decision making with incomplete fuzzy linguistic preference relations

The aim of this paper is to propose a procedure to estimate missing preference values when dealing with incomplete fuzzy linguistic preference relations assessed using a two‐tuple fuzzy linguistic approach. This procedure attempts to estimate the missing information in an individual incomplete fuzzy linguistic preference relation using only the preference values provided by the respective expert. It is guided by the additive consistency property to maintain experts' consistency levels. Additionally, we present a selection process of alternatives in group decision making with incomplete fuzzy linguistic preference relations and analyze the use of our estimation procedure in the decision process. © 2008 Wiley Periodicals, Inc.     

Matrix games with missing,interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles

In a matrix game, the interactions among players are based on the assumption that each player has accurate information about the payoffs of their interactions and the other players are rationally self‐interested. As a result, the players should definitely take Nash equilibrium strategies. However, in real‐life, when choosing their optimal strategies, sometimes the players have to face missing, imprecise (i.e., interval), ambiguous lottery payoffs of pure strategy profiles and even compound strategy profile, which means that it is hard to determine a Nash equilibrium. To address this issue, in this paper we introduce a new solution concept, called ambiguous Nash equilibrium, which extends the concept of Nash equilibrium to the one that can handle these types of ambiguous payoff. Moreover, we will reveal some properties of matrix games of this kind. In particular, we show that a Nash equilibrium is a special case of ambiguous Nash equilibrium if the players have accurate information of each player's payoff sets. Finally, we give an example to illustrate how our approach deals with real‐life game theory problems.     

基于证据距离的改进DS/AHP 多属性群决策方法

证据推理/层次分析(DS/AHP)方法采用了AHP法的层次结构模型和证据理论的分析过程,为不确定多属性决策问题的解决提供了新思路,但其在构造知识矩阵中用0代表残缺信息是不合理的.鉴于此,对DS/AHP方法进行了改进,并将改进后的方法拓展到群决策中,研究了专家群体权向量的确定方法.具体地,引入证据距离的概念,通过计算专家证据的综合距离来对专家赋权,体现了群决策中的多数人规则.     

Group decision making model and approach based on interval preference orderings

In group decision making under uncertainty, interval preference orderings as a type of simple uncertain preference structure, can be easily and conveniently used to express the experts’ evaluations over the considered alternatives. In this paper, we investigate group decision making problems with interval preference orderings on alternatives. We start by fusing all individual interval preference orderings given by the experts into the collective interval preference orderings through the uncertain additive weighted averaging operator. Then we establish a nonlinear programming model by minimizing the divergences between the individual uncertain preferences and the group’s opinions, from which we derive an exact formula to determine the experts’ relative importance weights. After that, we calculate the distances of the collective interval preference orderings to the positive and negative ideal solutions, respectively, based on which we use a TOPSIS based approach to rank and select the alternatives. All these results are also reduced to solve group decision making problems where the experts’ evaluations over the alternatives are expressed in exact preference orderings. A numerical analysis of our model and approach is finally carried out using two illustrative examples.     

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.     

Linguistic Discriminative Aggregation in Multicriteria Decision Making

Several new aggregation operators are proposed in the context of multicriteria decision making (MCDM) in the linguistic domain. The proposed operators first infer the discrimination index, based on the extent of variability in the various linguistic evaluations against a criterion. This value is then utilized in the actual aggregation step to discriminate among the alternatives. Besides, the proposed operators also take into account the a priori weights associated with the criteria. The proposed concepts are illustrated through an example in group MCDM.     

Multi-criteria decision-making using interval-valued hesitant fuzzy QUALIFLEX methods based on a likelihood-based comparison approach

QUALIFLEX is a very efficient outranking method to handle multi-criteria decision-making (MCDM) involving cardinal and ordinal preference information. Based on a likelihood-based comparison approach, this paper develops two interval-valued hesitant fuzzy QUALIFLEX outranking methods to handle MCDM problems within the interval-valued hesitant fuzzy context. First, we define the likelihoods of interval-valued hesitant fuzzy preference relations that compare two interval-valued hesitant fuzzy elements (IVHFEs). Then, we propose the concepts of the concordance/discordance index, the weighted concordance/discordance index and the comprehensive concordance/discordance index. Moreover, an interval-valued hesitant fuzzy QUALIFLEX model is developed to solve MCDM problems where the evaluative ratings of the alternatives and the weights of the criteria take the form of IVHFEs. Additionally, this paper propounds another likelihood-based interval-valued hesitant fuzzy QUALIFLEX method to accommodate the IVHFEs’ evaluative ratings of alternatives and non-fuzzy criterion weights with incomplete information. Finally, a numerical example concerning the selection of green suppliers is provided to demonstrate the practicability of the proposed methods, and a comparison analysis is given to illustrate the advantages of the proposed methods.

     

A new method selection approach for fuzzy group multicriteria decision making

Fuzzy multicriteria decision making (MCDM) has been widely used in ranking a finite number of decision alternatives characterized by fuzzy assessments with respect to multiple criteria. In group decision settings, different fuzzy group MCDM methods often produce inconsistent ranking outcomes for the same problem. To address the ranking inconsistency problem in fuzzy group MCDM, this paper develops a new method selection approach for selecting a fuzzy group MCDM method that produces the most preferred group ranking outcome for a given problem. Based on two group averaging methods, three aggregation procedures and three defuzzification methods, 18 fuzzy group MCDM methods are developed as an illustration to solve the general fuzzy MCDM problem that requires cardinal ranking of the decision alternatives. The approach selects the group ranking outcome of a fuzzy MCDM method which has the highest consistency degree with its corresponding ranking outcomes of individual decision makers. An empirical study on the green bus fuel technology selection problem is used to illustrate how the approach works. The approach is applicable to large-scale group multicriteria decision problems where inconsistent ranking outcomes often exist between different fuzzy MCDM methods.     

Comparative analysis of MCDM methods for the assessment of mortality in patients with acute coronary syndrome

Multi-criteria decision-making (MCDM) methods are commonly used in many fields of research, e.g., engineering and manufacturing systems, water resources studies , medicine, and etc. However, there is no effective approach of selecting a MCDM method to problem, which is solved. The formal requirements of each MCDM method are not sufficient because most methods would seem to be appropriate for most problems. Therefore, the main purpose of the paper is a comparison of accuracy selected MCDM methods. Proposed approach is presented on the example of mortality in patients with acute coronary syndrome. Additionally, the paper presents characteristic objects method (COMET) as a potential decision making method for use in medical problems, which accuracy is compared with TOPSIS and AHP. In the experimental study, the average and standard deviation of the root mean square error of evaluations are examined for groups of randomly selected patients, each described by age, blood pressure, and heart rate. Then, the correctness of choosing the patient in the best and worst condition is also examined among randomly selected pairs. As a result of the experimental study, rankings obtained by the COMET method are distinctly more accurate than those obtained by TOPSIS or AHP techniques. The COMET method, in the opposite of others method, is completely free of the rank reversal phenomenon, which is identified as a main source of problems with evaluations accuracy.