Trends in Multiple Criteria Decision Analysis

This chapter introduces the behavior mechanism that integrates the discoveries of neural science, psychology, system science, optimization theory and multiple criteria decision making. It shows how our brain and mind works and describes our behaviors and decision making as dynamic processes of multicriteria decision making in changeable spaces. Unless extraordinary events occur or special effort exerted, the dynamic processes will be stabilized in certain domains, known as habitual domains. Habitual domains and their expansion and enrichment, which play a vital role in upgrading the quality of our decision making and lives, will be explored. In addition, as important consequential derivatives, concepts of competence set analysis, innovation dynamics and effective decision making in changeable spaces will also be introduced.

The classical approach in decision analysis and multiple criteria theory concentrates on subjective ranking, at most including some aspects of intersubjective ranking (ranking understood here in a wide sense, including the selection or a classification of decision options). Intuitive subjective ranking should be distinguished here from rational subjective ranking, based on the data relevant for the decision situation and on an approximation of personal preferences. However, in many practical situations, the decision maker might not want to use personal preferences, but prefers to have some objective ranking. This need of rational objective ranking might have many reasons, some of which are discussed in this chapter. Decision theory avoided the problem of objective ranking partly because of the general doubt in objectivity characteristic for the twentieth century; the related issues are also discussed. While an absolute objectivity is not attainable, the concept of objectivity can be treated as a useful ideal worth striving for; in this sense, we characterize objective ranking as an approach to ranking that is as objective as possible. Between possible multiple criteria approaches, the reference point approach seems to be most suited for rational objective ranking. Some of the basic assumptions and philosophy of reference point approaches are recalled in this chapter. Several approaches to define reference points based on statistical data are outlined. Examples show that such objective ranking can be very useful in many management situations.

We establish the conditions that must be satisfied for the mathematical operations of linear algebra and calculus to be applicable. The mathematical foundations of decision theory and related theories depend on these conditions which have not been correctly identified in the classical literature. Operations Research and Decision Analysis Societies should act to correct fundamental errors in the mathematical foundations of measurement theory, utility theory, game theory, mathematical economics, decision theory, mathematical psychology, and related disciplines.

We consider various frameworks in which preferences can be expressed in a gradual way. The first framework is that of fuzzy preference structures as a generalization of Boolean (two-valued) preference structures. A fuzzy preference structure is a triplet of fuzzy relations expressing strict preference, indifference and incomparability in terms of truth degrees. An important issue is the decomposition of a fuzzy preference relation into such a structure. The main tool for doing so is an indifference generator. The second framework is that of reciprocal relations as a generalization of the three-valued representation of complete Boolean preference relations. Reciprocal relations, also known as probabilistic relations, leave no room for incomparability, express indifference in a Boolean way and express strict preference in terms of intensities. We describe properties of fuzzy preference relations in both frameworks, focusing on transitivity-related properties. For reciprocal relations, we explain the cycle-transitivity framework. As the whole exposition makes extensive use of (logical) connectives, such as conjunctors, quasi-copulas and copulas, we provide an appropriate introduction on the topic.

In this chapter, we discuss some fuzzy sets and fuzzy logic-based methods for multicriteria decision aid. Alternatives are identified with score vectors x ∈ [0, 1] ⁿ , and thus they can be seen as fuzzy sets, too. After discussion of integral-based utility functions, we introduce a transformation of score x into fuzzy quantity U(x). Orderings on fuzzy quantities induce orderings on alternatives. A special attention is paid to defuzzification-based orderings, especially to mean of maxima method. Our approach allows an easy incorporation of importance of criteria. Finally, a fuzzy logic-based construction method to build complete preference structures over set of alternatives is given.

The purpose of this chapter is to examine the existent and potential contribution of argumentation theory to decision aiding, more specifically to multi-criteria decision aiding. On the one hand, decision aiding provides a general framework that can be adapted to different contexts of decision making and a formal theory about preferences. On the other hand, argumentation theory is a growing field of Artificial Intelligence, which is interested in non-monotonic logics. It is the process of collecting arguments in order to justify and explain conclusions. The chapter is decomposed into three successive frames, starting from general considerations regarding decision theory and Artificial Intelligence, moving on to the specific contribution of argumentation to decision-support systems, to finally focus on multi-criteria decision aiding.

This chapter addresses two complementary themes in relation to problem structuring and MCDA. The first and primary theme highlights the nature and importance of problem structuring for MCDA and then reviews suggested ways for how this process may be approached. The integrated use of problem structuring methods (PSMs) and MCDA is one such approach; this potential is explored in greater depth and illustrated by four short case studies. In reflecting on these and other experiences we conclude with a brief discussion of the complementary theme that MCDA can also be viewed as creating a problem structure within which many other standard tools of OR may be applied, and could therefore also be viewed as a PSM.

Within disaggregation–aggregation approach, ordinal regressionaims at inducing parameters of a preference model, for example, parameters of a value function, which represent some holistic preference comparisons of alternatives given by the Decision Maker (DM). Usually, from among many sets of parameters of a preference model representing the preference information given by the DM, only one specific set is selected and used to work out a recommendation. For example, while there exist many value functions representing the holistic preference information given by the DM, only one value function is typically used to recommend the best choice, sorting, or ranking of alternatives. Since the selection of one from among many sets of parameters compatible with the preference information given by the DM is rather arbitrary, robust ordinal regressionproposes taking into account all the sets of parameters compatible with the preference information, in order to give a recommendation in terms of necessary and possible consequences of applying all the compatible preference models on the considered set of alternatives. In this chapter, we present the basic principle of robust ordinal regression, and the main multiple criteria decision methods to which it has been applied. In particular, UTA ^GMS and GRIPmethods are described, dealing with choice and ranking problems, then UTADIS ^GMS , dealing with sorting (ordinal classification) problems. Next, we present robust ordinal regression applied to Choquet integral for choice, sorting, and ranking problems, with the aim of representing interactions between criteria. This is followed by a characterization of robust ordinal regression applied to outranking methods and to multiple criteria group decisions. Finally, we describe an interactive multiobjective optimization methodology based on robust ordinal regression, and an evolutionary multiobjective optimization method, called NEMO, which is also using the principle of robust ordinal regression.

Stochastic multicriteria acceptability analysis (SMAA) is a family of methods for aiding multicriteria group decision making in problems with uncertain, imprecise or partially missing information. These methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one, or that would give a certain rank for a specific alternative. The main results of the analysis are rank acceptability indices, central weight vectors and confidence factors for different alternatives. The rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative, the central weight vectors represent the typical preferences favouring each alternative, and the confidence factors measure whether the criteria measurements are sufficiently accurate for making an informed decision. A general approach for applying SMAA in real-life decision problems is to use it repetitively with more and more accurate information until the information is sufficient for making a decision. Between the analyses, information can be added by making more accurate criteria measurements, or assessing the DMs’ preferences more accurately in terms of various preference parameters.

Collective decision making, the processes of group decision and negotiation, and the differences between them are explained and illustrated. Then the applicability of techniques of multiple criteria decision analysis (MCDA) to problems of group decision and negotiation (GDN) is discussed. A review of systems for Group Decision Support and Negotiation Support then highlights the contributions of MCDA techniques. The roles of decision makers and others in GDN are discussed, and overall progress in GDN is reviewed. Finally, some suggestions for worthwhile future contributions from MCDA are put forward.

By now evolutionary multi-objective optimization (EMO) is an established and a growing field of research and application with numerous texts and edited books, commercial software, freely downloadable codes, a biannual conference series running successfully since 2001, special sessions and workshops held at all major evolutionary computing conferences, and full-time researchers from universities and industries from all around the globe. In this chapter, we discuss the principles of EMO through an illustration of one specific algorithm and an application to an interesting real-world bi-objective optimization problem. Thereafter, we provide a list of recent research and application developments of EMO to paint a picture of some salient advancements in EMO research. Some of these descriptions include hybrid EMO algorithms with mathematical optimization and multiple criterion decision-making procedures, handling of a large number of objectives, handling of uncertainties in decision variables and parameters, solution of different problem-solving tasks better by converting them into multi-objective problems, runtime analysis of EMO algorithms, and others. The development and application of EMO to multi-objective optimization problems and their continued extensions to solve other related problems has elevated the EMO research to a level which may now undoubtedly be termed as an active field of research with a wide range of theoretical and practical research and application opportunities.

This chapter focuses on a review of Geographic Information System-based Multicriteria Decision Analysis (GIS-MCDA). These two distinctive areas of research can benefit from each other. On the one hand, GIS techniques and procedures have an important role to play in analyzing spatial decision problems. Indeed, GIS is often recognized as a spatial decision support system. On the other hand, MCDA provides a rich collection of techniques and procedures for structuring decision problems, designing, evaluating, and prioritizing alternative decisions. At the most rudimentary level, GIS-MCDA can be thought of as a process that transforms and combines geographical (spatial) data and value judgments (the decision maker’s preferences) to obtain information for decision making. It is in the context of the synergetic capabilities of GIS and MCDA that one can see the benefit for advancing theoretical and applied research on GIS-MCDA. The chapter is structured into seven sections. The introductory section outlines the synergetic capabilities of GIS and MCDA. Subsequently, the chapter provides an introduction to the basic concepts of GIS, a historical perspective of GIS-MCDA, and a survey of the GIS-MCDA literature. The following section focuses on the MCDA functions in GIS-based analysis and Multicriteria Spatial Decision Support System (MC-SDSS). The concluding section presents the challenges and prospects for advancing GIS-MCDA.