A Study on Aggregation of TOPSIS Ideal Solutions for Group Decision-Making

The technique for order preference by similarity to ideal solution (TOPSIS) has become a popular multi-criteria decision making (MCDM) technique, since it has a comprehensible theoretical structure and is able to provide an exact model for decision making. For the use of TOPSIS in group decisions, the common approaches in aggregating individual decision makers’ judgments are the geometric and the arithmetic mean methods, although these are too intuitive and do not consider either preference levels or preference priorities among alternatives for individual decision makers. In this paper, a TOPSIS group decision aggregation model is proposed in which the construction consists of three stages: (1) The weight differences are calculated first as the degrees of preferences among different alternatives for each decision maker; (2) The alternative priorities are then derived, and the highest one can be denoted as the degree to which a decision maker wants his most favorite alternative to be chosen; (3) The group ideal solutions approach in TOPSIS is used for the aggregation of similarities obtained from different decision makers. A comparative analysis is performed, and the proposed aggregation model seems to be more satisfactory than the traditional aggregation model for solving compromise-oriented decision problems.     

Using the Analytic Hierarchy Process as a Two-phase Integrated Decision Approach for Large Nominal Groups

When decision makers who comprise a large nominal group face an unstructured decision problem and no simultaneous interactive communications are available, problem identification and consensus building are difficult, if not impossible. Few tools are available to assist decision makers in this situation. The Analytic Hierarchy Process (AHP) has typically been used to evaluate a set of alternatives after a decision problem has been structured as a hierarchy with various levels of criteria above the alternatives. With a group of decision makers, AHP has been used to evaluate those alternatives either by consensus building or by combining judgments or priorities using the geometric mean to aggregate their preferences. In this paper, we extend the use of AHP to a situation involving a large nominal group of dispersed decision makers where the entire hierarchy is not defined at the outset. In particular, we use the AHP as an integrative approach to identify the priorities of the various criteria and then use those priorities to screen and consolidate a large set of potential alternatives. This results in considering a reduced set of alternatives that will be affected by the more important criteria. The consolidated set of alternatives is evaluated by each individual in the group using AHP, combined using the geometric mean, and the results are synthesized to obtain the overall priorities of the alternatives. The approach is demonstrated and evaluated in a case study to select an alunmi anniversary gift to the U.S. Coast Guard Academy with a large nominal group of decision-makers dispersed throughout the United States.     

An Extended PROMETHE II Multi-Criteria Group Decision Making Technique Based on Intuitionistic Fuzzy Logic for Sustainable Energy Planning

The implementations of Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) category to complex multi-criteria group decision making (MCGDM) scenarios have been included in thousands areas. Outranking methods such as PROMETHEE II are also greatly employed in energy planning application. In MCGDM methods if decision makers (DMs) are not able to treat precise data in order to define their preferences, the intuitionistic fuzzy set (IFS) theory enables them. IFS attributes are connected with the degree of membership and non-membership, and can be used to draw uncertainty in group decision-making situations. In this paper, a new version of the PROMETHEE II method is proposed, aiming at solving MCGDM problems. Linguistic variables are expressed in the membership function and non-membership function of IFS which are used to assess the weights of all criteria and the ratings of each alternative with respect to each criteria. Conditional normalized Euclidean distance measure is adopted to measure deviations between alternatives on intuitionistic fuzzy set. Then, a ranking algorithm is applied to indicate the order of superiority of alternatives. Finally, a practical example is given to an application of sustainable energy planning to verify our proposed method. Additionally, a comparative analysis is done among the proposed PROMETHEE II method and the intuitionistic fuzzy technique for order preference by similarity to ideal solution (IF-TOPSIS) method and elimination and choice translating reality method (IF-ELECTRE).     

Fuzzy Group Decision Making for the Selection of Facility Location

In this paper, fuzzy group decision making based on extension of TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method which was proposed by Chen (Fuzzy Sets Syst, 114:1–9, 2000) is adopted for facility location selection. In this method, the ratings of various alternatives versus various subjective criteria and the weights of all criteria are assessed in linguistic variables represented by fuzzy numbers. By fuzzy numbers, it has been tried to resolve the ambiguity of concepts that are associated with human being’s judgments. To determine the order of the alternatives, closeness coefficient is defined by calculating the distances to the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS). In Chen’s approach, the distance between two fuzzy numbers is calculated with vertex method. But in this study, different distance measurement methods are used and the results are compared. Finally the proposed method has been applied to a facility location selection problem of a textile company in Turkey.     

The Role of the DS/AHP in Identifying Inter-Group Alliances and Majority Rule Within Group Decision Making

DS/AHP is a nascent method of multi-criteria decision-making, based on the Dempster-Shafer theory of evidence and indirectly the Analytic Hierarchy Process. It is concerned with the identification of the levels of preference that decision makers have towards certain decision alternatives (DAs), through preference judgements made over a number of different criteria. The working result from a DS/AHP analysis is the body of evidence (BOE), which includes a series of mass values that represent the exact beliefs in the best DA(s) existing within certain subsets of DAs. This paper considers the role of DS/AHP as an aid to group decision-making, through the utilisation of a distance measure (between BOEs). Here, the distance measure enables the identification of the members of the decision-making group who are in most agreement, with respect to the judgements they have individually made. The utilisation of a single linkage dendrite approach to clustering elucidates an appropriate order to the aggregation of the judgements of the group members. This develops the DS/AHP method as a tool to identify inter-group alliances, as well as introduce a ‘majority rule’ approach to decision-making through consensus building.     

A linguistic decision process in group decision making

Assuming a set of linguistic preferences representing the preferences of the individuals, a linguistic choice process is presented. This is developed using the concept of fuzzy majority for deriving a collective linguistic preference, and the concept of nondominated alternatives for deriving the selected alternatives in the linguistic choice process. The fuzzy majorities are equated with fuzzy linguistic quantifiers. The collective linguistic preference is derived by means of a linguistic ordered weighted averaging operator whose weights are defined using a fuzzy linguistic quantifier. In order to obtain the nondominated alternatives, we present a novel reformulation of Orlovski's nondominance degree under linguistic information.     

Fuzzy Group Decision-Making for Service Innovations in Quality Function Deployment

Since little effort has been devoted to measuring service management from epistemology perspectives, this study develops a scientific framework for its evaluation. Service management is defined as what is perceived by the tourists and decision makers during the process of service generation and delivery processes. This in turn depends on the service conditions experienced during the process and at the accommodation. The study uses fuzzy group decision-making and a Quality Function Deployment method to analyze various service evaluation criteria. It further considers the possibility of “Fuzzy Sets” in making subjective judgments, and applies a Fuzzy-based decision-making method to evaluate service management.     

A Calibrated Group Decision Process

In practice most organisational decisions are made by groups that bring into the problem multiple perspectives, both complementary and contradictory. When having a group of decision makers, usually individuals’ preferences are either led to consensus or are aggregated with the use of some function like the median, the arithmetic or geometric mean. We focus in the second case, where individual’s preferences need to be aggregated. Our approach is based on the fact that when two decision makers are asked to give their preference between a pair of criteria using a specific scale, it is possible that they will give slightly different answers, even when they actually have the same opinion. This difference will not affect the case of a single decision maker, as it will be consistent throughout the whole process. However, it can affect a group decision when the values will be used as an input for the aggregation function. A novel approach is presented that enhances group decision making through a group calibration process. The proposed process adjusts individuals’ preferences based on their answers on a set of standardized questions prior to the aggregation phase. The method focuses The whole concept is applied to the group analytical network process method and it is illustrated through a telecommunications project case. The decision under examination concerns the selection of the right place for deploying a new telecom service of a multinational-based telecommunications company where a group of geographically dispersed decision makers form an ad-hoc virtual team in order to select the location for a new technical support centre.     

Aggregation and Disaggregation of Preferences for Collective Decision-Making

Group decisions are of longstanding interest to researchers from a wide spectrum of disciplines. Group Decision Support Systems (GDSS) can play a vital role in situations where multiple persons are involved, each having their own private perceptions of the context and the decision problem to be tackled. In such an environment the conflict between the members of the planning group is not an unusual situation. Multiple criteria decision aid (MCDA) methods may be a useful tool in coping with such interpersonal conflicts where the aim is to achieve consensus between the group members. This paper combines two well-known multicriteria methods, based on the notion of aggregation of preferences, in order to construct a consensus seeking methodology for collective decision-making.     

A Fuzzy Stochastic Multi-Attribute Group Decision-Making Approach for Selection Problems

The purpose of this paper is to demonstrate how the fuzzy and stochastic approaches as well as multi-attribute group decision-making techniques can be effectively utilized for selection problems in different kinds of uncertainty situations. A group of the decision makers describes a value for an alternative with respect to an attribute by the use of linguistic variables. The rating of each alternative is aggregated, which can be expressed as triangular fuzzy numbers. Then Monte Carlo simulation is applied to generate the performance distribution of alternatives with respect to different attributes in an uncertain environment. Finally, a stochastic compromise ranking technique, known as the VIKOR technique, is developed to evaluate probability distributions for each alternative on each attribute and to prioritize them. The proposed fuzzy stochastic approach is suitable to compromise a solution among the conflicting tangible and intangible attributes under the group decision-making process. In addition, an application of the proposed approach is provided to solve the important risk selection problem in a highway project. The results illustrate its real-life applicability and suitability in discrete group decision-making under uncertainty.     

CONFIDE: A Collective Decision-Making Procedure Using Confidence Estimates of Individual Judgements

An algorithm (termed CONFIDE) is proposed that may capture many of the benefits of group decision making without the necessity of face-to-face interaction. The algorithm allows individual decision makers to differentially weight the contributions from members according to the confidence with which each member holds to their opinions. The CONFIDE algorithm is compared to both face-to-face group decisions and simple averaging of group members opinions on the Lost-at-Sea ranking task. Results indicate that, in terms of decision quality, the CONFIDE algorithm produces solutions equal to that of the face-to-face group decision method and significantly better than the solution achieved by simple averaging of group members responses.     

Coercion,Guidance and Mercifulness: The Different Influences of Ethics Programs on Decision-Making

The development of an ethics program is a method frequently used for organising responsible behaviour within organisations. For such a program, certain preconditions have to be created in the structure, culture and strategy. In this organisational context, managers have to take their decisions in a responsible way. This process of decision-making, embedded in an ethics program, is the main focus of this article. Ethics programs often influence decision-making in a formal way; certain norms and types of behaviour are formalised and controlled within the organisation. Subsequently, individual managers have to infer the meaning of responsible behaviour from the demands laid down in the ethics program. Such a formal ethics program has some important advantages but the dangers of such an approach are often ignored. This article discusses both the advantages and disadvantages of a formal ethics program and adds two alternative ways of stimulating responsible behaviour in the organisation. In a monological approach the reflections of the decision makers on their own values are central in differentiating between right and wrong. In a dialogical approach, the communications between decision makers and other stakeholders involved are the foundations for determining a responsible solution. Because each approach is appropriate for certain issues, a well-chosen combination is justified. Such an ethics program should be strict on certain issues but leave room for reflection and interaction on other issues.     

Deriving Weights from Interval Multiplicative Preference Relations in Group Decision Making

In this article, we investigate group decision making problems with interval multiplicative preference relations (including complete interval multiplicative preference relations and incomplete interval multiplicative preference relations). On the basis of the number of judgments and the consistency degree of each interval multiplicative preference relation, we first give a combined weighting method to derive the weights of decision makers. Then, we establish two linear programming models to derive the weight intervals of alternatives from all individual consistent interval multiplicative preference relations and utilize the continuous ordered weighted averaging operator or the continuous ordered weighted geometric operator to aggregate all the values in each weight interval. In addition, we establish a more general model to check the consistency of all individual interval multiplicative preference relations. In the cases where the optimal objective value of the model is not zero, we can get the optimal weights of alternatives directly, and then utilize these optimal weights and the optimal deviation values derived from the model to construct consistent interval multiplicative preference relations. Furthermore, we discuss some special cases of the established models and illustrate our models with a practical example.     

Multicriteria Portfolio Modeling for the Development of Shared Action Agendas

Organizations and collaborative networks set strategic directions by building agendas of action topics that will be implemented subject to limited resources and other constraints. The development of such agendas typically involves several decision makers and possibly other stakeholders who may have divergent views about how the topics contribute to multiple objectives. The processes of developing these agendas can be supported by methods of multicriteria decision analysis which allow the group members’ preferences to be systematically and transparently synthesized. In this paper, we extend methods of portfolio decision analysis with the aim of guiding the development of agendas in the presence of possibly incomplete information about the group members’ preferences and the impacts of the proposed topics. Specifically, we define performance measures that convey (i) what topics are favored by individual group members and (ii) how acceptable alternative portfolios of topic agendas are to the whole group. The methods are illustrated with data from a real case study for the development of a national research agenda on wood products in Finland.     

Group Decision Making with Dispersion in the Analytic Hierarchy Process

With group judgments in the context of the Analytic Hierarchy Process (AHP) one would hope for broad consensus among the decision makers. However, in practice this will not always be the case, and significant dispersion may exist among the judgments. Too much dispersion violates the principle of Pareto Optimality at the comparison level and/or matrix level, and if this happens, then the group may be homogenous in some comparisons and heterogeneous in others. The question then arises as to what would be an appropriate aggregation scheme when a consensus cannot be reached and the decision makers are either unwilling or unable to revise their judgments. In particular, the traditional aggregation via the geometric mean has been shown to be inappropriate in such situations. In this paper, we propose a new method for aggregating judgments when the raw geometric mean cannot be used. Our work is motivated by a supply chain problem of managing spare parts in the nuclear power generation sector and can be applied whenever the AHP is used with judgments from multiple decision makers. The method makes use of principal components analysis (PCA) to combine the judgments into one aggregated value for each pairwise comparison. We show that this approach is equivalent to using a weighted geometric mean with the weights obtained from the PCA.     

利益相关者财务治理的一致性聚类分析

本文利用聚类分析方法研究利益相关者参与企业财务治理的决策机制,以融资决策为例,将内部融资、债务融资、股权融资三种不同的融资类型作为决策者判断的方案,不同类型融资的具体数值作为三角模糊数,考虑决策者的权重对决策者一致度计算的影响,计算不同决策者之间的一致度距离,进行决策者聚类,依据聚类的结果,计算一致性相同的决策者集合的最终方案集,最后通过实例演示了上述的计算过程。     

A risk-based decision support framework for selection of appropriate safety measure system for underground coal mines

In the context of underground coal mining industry, the increased economic issues regarding implementation of additional safety measure systems, along with growing public awareness to ensure high level of workers safety, have put great pressure on the managers towards finding the best solution to ensure safe as well as economically viable alternative selection. Risk-based decision support system plays an important role in finding such solutions amongst candidate alternatives with respect to multiple decision criteria. Therefore, in this paper, a unified risk-based decision-making methodology has been proposed for selecting an appropriate safety measure system in relation to an underground coal mining industry with respect to multiple risk criteria such as financial risk, operating risk, and maintenance risk. The proposed methodology uses interval-valued fuzzy set theory for modelling vagueness and subjectivity in the estimates of fuzzy risk ratings for making appropriate decision. The methodology is based on the aggregative fuzzy risk analysis and multi-criteria decision making. The selection decisions are made within the context of understanding the total integrated risk that is likely to incur while adapting the particular safety system alternative. Effectiveness of the proposed methodology has been validated through a real-time case study. The result in the context of final priority ranking is seemed fairly consistent.     

Fair and Fast Convergence on Islands of Agreement in Multicriteria Group Decision Making by Logical Navigation

Reasoning on multiple criteria is a key issue in group decision to take into account the multidimensional nature of real-world decision-making problems. In order to reduce the induced information overload, in multicriteria decision analysis, criteria are in general aggregated, in many cases by a simple discriminant function of the form of a weighted sum. It requires to, a priori and completely, elicit preferences of decision makers. That can be quite arbitrary. In everyday life, to reduce information overload people often use a heuristic, called “Take-the-best”: they take criteria in a predefined order, the first criterion which discriminates the alternatives at stake is used to make the decision. Although useful, the heuristic can be biased. This article proposes the Logical Multicriteria Sort process to support multicriteria sorting within islands of agreement. It therefore does not require a complete and consistent a priori set of preferences, but rather supports groups to quickly identify the criteria for which an agreement exists. The process can be seen as a generalization of Take-the-best. It also proposes to consider one criterion at a time but once a criterion has been found discriminating it is recorded, the process is iterated and relevant criteria are logically combined. Hence, the biases of Take-the-best are reduced. The process is supported by a GDSS, based on Logical Information Systems, which gives instantaneous feedbacks of each small decision and keeps tracks of all of the decisions taken so far. The process is incremental, each step involves low information load. It guarantees some fairness because all considered alternatives are systematically analyzed along the selected criteria. A successful case study is reported.     

基于改进多属性群决策的国有企业经营者选择研究

国有企业经营者选择机制与方法的转变是国有企业改革的重点之一,针对经营者选择的研究多集中在定性分析。在经营者能力信号传递研究基础上,引入针对企业自身特点的能力评价指标,通过权重模糊差异对能力评价指标权重进行修正,利用改进多属性群决策方法对候选经营者进行能力评估与选择,并通过一个实例演示该方法的决策过程。     

Group Aggregation Techniques for Analytic Hierarchy Process and Analytic Network Process: A Comparative Analysis

The analytic hierarchy process (AHP) and the analytic network process are important multiple criteria decision making methods for supporting complex, discrete strategic management decision problems. In order to exploit a broader information basis as well as to achieve a sufficient degree of objectivity strategic decision settings are mostly embedded into a multi-personal decision context to which different individuals with expert status contribute. Owing to the fact that there is a vast number of different methods and further internal possibilities (derivation of means) to aggregate the individual expert preferences to a group consensus, the first aim of this paper is to present a comprehensive literature review on various aggregation possibilities. The second aim is the conduction of a transparent comparative analysis of selected approaches and methods (geometric/arithmetic aggregation of individual judgments, geometric/arithmetic aggregation of individual priorities, geometric/arithmetic loss function approach and Group AHP model). Therefore, we use four different evaluation scenarios and point out under which assumptions which solution is suitable. Starting from these results, the aggregation techniques adequate to a specific decision context are provided.