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.     

A new method for multiple criteria group decision making with incomplete weight information under linguistic environment

A new method is proposed to solve multiple criteria group decision making (MCGDM) problems, in which both the criteria values and criteria weights take the form of linguistic information, and the information about linguistic criteria weights is partly known or completely unknown. Firstly, to get reasonable decision result, instead of assigning the same weight to the decision maker (DM) for all criteria, we propose a method to determine the weight of DM with respect to each criterion under linguistic environment by calculating the similarity degree between individual 2-tuple linguistic evaluation value and the mean given by all decision makers (DMs). Secondly, for the situations where the information about the criteria weights is partly known or completely unknown, we establish optimization models to determine the criteria weights by defining 2-tuple linguistic positive ideal solution (TL-PIS), 2-tuple linguistic right negative ideal solution (TL-RNIS) and 2-tuple linguistic left negative ideal solution (TL-LNIS) of the collective 2-tuple linguistic decision matrix. Thirdly, we propose a new method to solve MCGDM problems with partly known or completely unknown linguistic weight information. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method.     

An intuitionistic fuzzy programming method for group decision making with interval-valued fuzzy preference relations

The paper develops a new intuitionistic fuzzy (IF) programming method to solve group decision making (GDM) problems with interval-valued fuzzy preference relations (IVFPRs). An IF programming problem is formulated to derive the priority weights of alternatives in the context of additive consistent IVFPR. In this problem, the additive consistent conditions are viewed as the IF constraints. Considering decision makers’ (DMs’) risk attitudes, three approaches, including the optimistic, pessimistic and neutral approaches, are proposed to solve the constructed IF programming problem. Subsequently, a new consensus index is defined to measure the similarity between DMs according to their individual IVFPRs. Thereby, DMs’ weights are objectively determined using the consensus index. Combining DMs’ weights with the IF program, a corresponding IF programming method is proposed for GDM with IVFPRs. An example of E-Commerce platform selection is analyzed to illustrate the feasibility and effectiveness of the proposed method. Finally, the IF programming method is further extended to the multiplicative consistent IVFPR.     

A Bayesian approach for multiple criteria decision making with applications in Design for Six Sigma

Linking end-customer preferences with variables controlled at a manufacturing plant is a main idea behind popular Design for Six Sigma management techniques. Multiple criteria decision making (MCDM) approaches can be used for such purposes, but in these techniques the decision-maker's (DM) utility function, if modelled explicitly, is considered known with certainty once assessed. Here, a new algorithm is proposed to solve a MCDM problem with applications to Design for Six Sigma based on a Bayesian methodology. At a first stage, it is assumed that there are process responses that are functions of certain controllable factors or regressors. This relation is modelled based on experimental data. At a second stage, the utility function of one or more DMs or customers is described in a statistical model as a function of the process responses, based on surveys. This step considers the uncertainty in the utility function(s) explicitly. The methodology presented then maximizes the probability that the DM's or customer's utility is greater than some given lower bound with respect to the controllable factors of the first stage. Both stages are modelled with Bayesian regression techniques. The advantages of using the Bayesian approach as opposed to traditional methods are highlighted.     

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.     

A study of high-level managerial decision processes, with implications for MCDM research

We study six real-world major strategic decisions and discuss the role that analytic Multiple Criteria Decision Making (MCDM) models could play in helping decision makers structure and solve such problems. We have interviewed successful and well-educated managers who had access to quantitative decision models, but did not use them as part of their decision process. Our approach is a clinical one that takes a close look at the decision processes. We believe that the normative MCDM framework is oversimplified and does not always fit well with complex, real-world organizational decision processes. This may be one reason why decision tools are not used more widely for solving high-level decision problems. We believe that it would be worthwhile to revise some of the MCDM mainstream postulates and practices to make existing models and tools more suitable for practical purposes. The MCDM mainstream research has until today focused on the choice among alternatives. One should realize that MCDM models could also be used in creating alternatives, in assessing the importance of criteria, in providing the decision makers with “post-commitment support”, and as part of a devil's advocate approach.     

IPSSIS: An integrated multicriteria decision support system for equity portfolio construction and selection

A fundamental principle of modern portfolio theory is that comparisons between portfolios are generally made using two criteria, corresponding to the first two moments of return distributions, namely the expected return and portfolio variance. According to this model and according to most of the portfolio models derived from the stochastic dominance approach, the group of portfolios open to comparisons is divided into two parts: on the one hand there are the efficient portfolios (those that are not dominated by any other portfolio in the group), and on the other, those that are dominated. In other words, these models do not solve for one optimal portfolio, but rather solve for an efficient set of portfolios, among which the investor must choose, given his preference system. One criticism over these models, which has often been addressed both by practitioners and academics, is that they fail to embody the objectives of the decision maker (DM), through the various stages of the decision process. Our purpose in this article is to present an integrated and innovative methodological approach for the construction and selection of equity portfolios, which will take into account the inherent multidimensional nature of the problem, while allowing the DM to incorporate his preferences in the decision process. The proposed approach, which grounds its basis on the field of multiple criteria decision making (MCDM) and more specifically on multiobjective mathematical programming (MMP), is implemented in the IPSSIS (Integrated Portfolio Synthesis and Selection Information System) decision support system (DSS). The validity of the proposed approach is tested through an illustrative application in the Athens Stock Exchange (ASE).     

A hybrid model for selection of an outsourcing provider

Outsourcing is a good strategy for firms that need to reduce operating costs and improve competitiveness and it is important that firms scientifically select appropriate outsourcing providers. Some efforts have been made to find systematic ways to deal with outsourcing problems, but these efforts incorrectly assumed that the criteria used in the decision process are independent, which is not true in the real world. In this study, we propose a new hybrid multiple criteria decision-making (MCDM) model, which addresses the dependent relationships between the various criteria. The relations-structure among the criteria is built with the aid of the decision-making trial and evaluation laboratory (DEMATEL) method. Decision-makers tend to hold diverse opinions about their preferences due to incomplete information and knowledge, or inherent conflict between various departments. We further used the fuzzy preference programming and the analytic network process (ANP) to form a model for the selection of partners for outsourcing providers. The proposed model can help practitioners improve their decision making process, especially when criteria are numerous and inter-related. The method is demonstrated using data from a Taiwanese airline.     

A soft multi-criteria decision analysis model with application to the European Union enlargement

This paper proposes a new multi-criteria decision analysis (MCDA) model that uses a series of existing intuitive and analytical methods to systematically capture both objective and subjective beliefs and preferences from a group of decision makers (DMs). A defuzzification method that combines entropy and the theory of displaced ideal synthesizes crisp values from the DMs’ subjective judgments. This approach assists the DMs in their selection process by plotting alternatives in a four quadrant graph and considering their Euclidean distance from the “ideal” choice. A pilot study illustrates the details of the proposed method. The DMs were a group of graduate students from the University of Paderborn in Germany. The pilot study concerned the addition of new members into the European Union (EU), a decision that has profound economic and political effects on both the entering and existing members of the Union. The DMs were required to consider a large number of internal strengths and weaknesses and external opportunities and threats in assessing the decision to enlarge the EU. Although the pilot study was not performed by actual DMs from the EU, it was an excellent platform for testing the proposed model.     

An Experimental Evaluation of Interactive MCDM Methods and the Decision Making Process

Increasingly, it is becoming recognized that interactive solution methods should provide not only a solution to a multiple criteria decision making (MCDM) problem, but also the opportunity for decision makers to learn about their own preferences. In this paper, we describe an experiment that examines three MCDM solution methods and the process of converging on a final solution. Twenty-four management students participated in the experiment and were required to solve two completely different MCDM problems. Within this experimental framework, we examined the use of a two-stage approach to decision making. Both quantitative and qualitative results are presented. Preferences among the different solution methods vary significantly. Several conclusions are drawn concerning the desirable features of interactive MCDM solution methods.     

An interactive sorting approach based on the assignment examples of multiple decision makers with different priorities

Although group decision-making is often adopted by many organizations in today??s highly complicated business environment, the multiple criteria sorting (MCS) problem in the context of group decision-making has not been studied sufficiently. To this end, we propose a new interactive method to assist a group of decision makers (DMs) with different priorities. With the goal of relieving the cognitive effort exerted by DMs, this method uses the assignment examples provided by the DMs to draw the parameters for the group preference model. In the iterative MCS process that we employ, the DMs are supported from two perspectives. When the assignment examples provided by the DMs are inconsistent, a RINCON algorithm is developed to identify all the possible solutions that the DMs can use to resolve the conflicts. When the examples are consistent, the potential and the fittest assignments of each alternative are deduced using linear programming techniques. These are then presented to the DMs to help them provide more information for the decision-making process. Furthermore, the priority of each DM is objectively and subjectively evaluated, and then progressively updated to reflect the decision-making performance of a DM at each iteration. Meanwhile, the priorities are integrated into the linear programming model to deduce the fittest assignment, as well as into the RINCON algorithm. Hence, the assignment examples of the DMs with higher priorities are emphasized in the fittest assignment, and are less likely to be revised for inconsistency. A practical example featuring MBA programs is also presented to demonstrate the proposed method.     

Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment

As a generalized fuzzy number, the hesitant fuzzy element (HFE) has been receiving increased attention and has recently become a popular topic. However, we find that the occurring probabilities of the possible values in the HFE are equal, which is obviously impractical. Consequently, in this paper, we propose a hesitant fuzzy number with probabilities, called the hesitant probabilistic fuzzy number, and construct its score function, deviation function, comparison laws, and its basic operations. It is well known that in the context of a group of decision makers (DMs), one of the basic approaches to built consensus is to aggregate individual evaluations or individual priorities. Thus, to use the hesitant fuzzy numbers for consensus building with a group of DMs, we further propose a method called maximizing score deviation method to obtain the DMs’ weights under the HPFE environment, based on which two extended and four new ordered weighted operators are provided to fuse the HPFE information and build the consensus of the DMs. We also analyze the differences among these ordered weighted operators and provide their application scopes. Finally, a practical case is provided to demonstrate consensus building with a group of DMs under the HPFE environment using the proposed approaches.     

Modeling uncertainty in multi-criteria decision analysis

his paper provides a review of multiple criteria decision analysis (MCDA) for cases where attribute evaluations are uncertain. The main aim is to identify different tools which can be used to represent uncertain evaluations, and to broadly survey the available decision models that can be used to support uncertain decision making. The review includes models using probabilities or probability-like quantities; explicit risk measures such as quantiles and variances; fuzzy numbers, and scenarios. The practical assessment of uncertain outcomes and preferences associated with these outcomes is also discussed.     

Developing a straightforward approach for group decision making based on determining weights of decision makers

Group decision making is an active area of research within multiple attribute decision making. This paper assumes that all the decision makers (DMs) are not equally qualified to contribute equitably to the decision process. The aim of this paper is to develop an approach to determine weights of DMs, in which the decision information on alternatives with respect to attributes, provided by each DM, is represented in the form of interval data. We define the average of all individual decisions as the positive ideal decision (PID), and the maximum separation from PID as the negative ideal decision, which are characterized by a matrix, respectively. The weight of each DM is determined according to the Euclidean distances between the individual decision and ideal decisions. By using the obtained weights of DMs, all individual decisions are aggregated into a collective decision. Then the alternatives is ranked based on the collective decision. Meanwhile, this paper also gives a humanized decision method by using an optimistic coefficient, which is used in adjusting the relative importance between profit and risk. Finally, we give an example to illustrate the developed approach.     

Pseudo-criteria versus linear utility function in stochastic multi-criteria acceptability analysis

Stochastic multi-criteria acceptability analysis (SMAA) is a multi-criteria decision support method for multiple decision-makers (DMs) in discrete problems. SMAA does not require explicit or implicit preference information from the DMs. Instead, the method is based on exploring the weight space in order to describe the valuations that would make each alternative the preferred one. Partial preference information can be represented in the weight space analysis through weight distributions. In this paper we compare two variants of the SMAA method using randomly generated test problems with 2–12 criteria and 4–12 alternatives. In the original SMAA, a utility or value function models the DMs' preference structure, and the inaccuracy or uncertainty of the criteria is represented by probability distributions. In SMAA-3, ELECTRE III-type pseudo-criteria are used instead. Both methods compute for each alternative an acceptability index measuring the variety of different valuations that supports this alternative, and a central weight vector representing the typical valuations resulting in this decision. We seek answers to three questions: (1) how similar are the results provided by the decision models, (2) what kind of systematic differences exists between the models, and (3) how could one select indifference and preference thresholds of the pseudo-criteria model to match a utility model with given probability distributions?     

Mutually dependent multi-criteria decision making

In this paper, a model to estimate the weights of mutually dependent criteria, based on cause-effect assessments of a group of professionals, is developed for problem of multiple criteria decision making (MCDM). Here, both DEMATEL (Decision Making Trial and Evaluation Laboratory) and TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) models are combined and extended to handle fuzzy evaluations where the first is used to set the weights of the interdependent criteria and the second for drawing a decision from a group of professionals who use linguistic ratings in their evaluation. The presented model is characterized by the capability to estimate the criteria weights when the criteria are interrelated. The strict determination of the criteria weights prior to the assessment process is eliminated as they are computed by the DEMATEL part. A classical case-study of optimal sore throat treatment in primary care unit is used to demonstrate the efficiency of the proposed model.     

Dynamic decision making without expected utility: An operational approach

Non-expected utility theories, such as rank dependent utility (RDU) theory, have been proposed as alternative models to EU theory in decision making under risk. These models do not share the separability property of expected utility theory. This implies that, in a decision tree, if the reduction of compound lotteries assumption is made (so that preferences at each decision node reduce to RDU preferences among lotteries) and that preferences at different decision nodes are identical (same utility function and same weighting function), then the preferences are not dynamically consistent; in particular, the sophisticated strategy, i.e., the strategy generated by a standard rolling back of the decision tree, is likely to be dominated w.r.t. stochastic dominance. Dynamic consistency of choices remains feasible, and the decision maker can avoid dominated choices, by adopting a non-consequentialist behavior, with his choices in a subtree possibly depending on what happens in the rest of the tree. We propose a procedure which: (i) although adopting a non-consequentialist behavior, involves a form of rolling back of the decision tree; (ii) selects a non-dominated strategy that realizes a compromise between the decision maker’s discordant goals at the different decision nodes. Relative to the computations involved in the standard expected utility evaluation of a decision problem, the main computational increase is due to the identification of non-dominated strategies by linear programming. A simulation, using the rank dependent utility criterion, confirms the computational tractability of the model.     

A fuzzy-stochastic OWA model for robust multi-criteria decision making

All realistic Multi-Criteria Decision Making (MCDM) problems face various kinds of uncertainty. Since the evaluations of alternatives with respect to the criteria are uncertain they will be assumed to have stochastic nature. To obtain the uncertain optimism degree of the decision maker fuzzy linguistic quantifiers will be used. Then a new approach for fuzzy-stochastic modeling of MCDM problems will be introduced by merging the stochastic and fuzzy approaches into the OWA operator. The results of the new approach, entitled FSOWA, give the expected value and the variance of the combined goodness measure for each alternative. Robust decision depends on the combined goodness measures of alternatives and also on the variations of these measures under uncertainty. In order to combine these two characteristics a composite goodness measure will be defined. The theoretical results will be illustrated in a watershed management problem. By using this measure will give more sensitive decisions to the stakeholders whose optimism degrees are different than that of the decision maker. FSOWA can be used for robust decision making on the competitive alternatives under uncertainty.