Multicriteria Decision Making

The object of this chapter is to present an overall view of what Decision-Aiding (DA) is today, or what it seeks to be. The standpoint adopted here is more that of the practitioner than that of the theoretician. Above all, we shall attempt to emphasize what a scientific approach might claim to contribute to illuminating decision-making and how this approach might facilitate the proper functioning of the decision-making process as a whole. It is possible, in one way, to consider that decision-aiding was the natural outgrowth of operational research. This discipline, as it was conceived of and implemented particularly during the 1960s, proved to have a relatively limited field of application. The current conception of DA aims to free itself from these limitations, as will be explained in the first two paragraphs of Section 1.1. This allows us to understand why DA is most often Multicriteria Decision Aiding (MCDA). In the final paragraph of this Section we shall highlight, on these bases, what it is reasonable to expect from DA in actual practice. Section 1.2 presents the conceptual architecture which constitutes the foundation of DA (and, more precisely, MCDA). A glossary (see Appendix) provides definitions for the principle terms used, and furnishes some additional methodological information. The final section is devoted to what the practitioner should expect from using computerized procedures and tools to develop recommendations and/or point the way towards a decision. In order to allow the reader to appreciate the scope and variety of existing applications, we have included in the bibliography a very limited selection of applications which in no way claims to be scientifically representative. This sample of related work points out the diverse number of both countries and sectors of activity which have shown an interest in the methods explored in this book.

This chapter introduces the basic concepts of vector optimization. After the discussion of a simple example from structural engineering partial orderings on ℝ^m are defined and connections to convex cones are investigated. Then we present the definitions of several variants of the efficiency notion: weak, proper, strong and essential efficiency. Relationships between these different concepts are investigated and simple examples illustrate these notions The last section is devoted to the scalarization of vector optimization problems. Based on various concepts of monotonicity basic scalarization results are described and the weighted sum approach is investigated in detail.

Duality is an attractive topic in multi-objective optimization as well as in usual mathematical programming with a single objective function. However, there seems to be no unified approach to dualization in multi-objective optimization. One of the difficulties is in the fact that the efficient solution to multi-objective optimization is not necessarily unique, but in general becomes a set. The definition of infimum (or supremum) of a set with a partial order plays a key role in development of duality theory in multi-objective optimization. In this chapter, these notions will be considered from some geometric viewpoint.

Multicriteria decision aid is above all a human activity in which value judgements of involved actors play a crucial role. Therefore, “how to represent such judgements?” is a key question in MCDM. This chapter is devoted to this subject. Depending on the particular paradigm adopted for preference modelling, different questioning procedures can be conceived which lead to different preference structures. We present a few questioning procedures related to three basic paradigms, together with some preference structures that are useful for MCDM. First, the classical preference-indifference structure is discussed, followed by the introduction of the ideas of “incomparability” and “hesitation”. Finally, we present some complementary questioning procedures particularly relevant for cardinal modelling of value judgements.

The problems of human behavior in decision processes are central in this chapter. The gaps between the requirements of decision methods and the possibilities of human information processing systems are analyzed. The qualitative model describing the decision maker’s behavior is proposed. The model defines the guidelines for the construction of decision methods justified from behavior point of view.

The problem of selecting a method for solving an MCDM problem is dicussed. This problem called meta decision problem can be formulated and solved in different ways. The most common approach is to define it as a problem of choosing one method from a finite set of methods which are evaluated according to several criteria. This leads to a formalization of the meta decision problem as an MCDM problem itself. Scalar evaluations of methods can help to avoid the meta decision problem becoming too complex. The problem of assessing the parameter(s) of an MCDM problem is similar to the meta decision problem above and can be interpreted as the problem to design an MCDM method. This leads to a formalization of the meta decision problem as a scalar parameter optimization problem. Information for solving meta decision problems can be submitted by a decision maker or is given as a data file originating, e.g., from prior decision making processes. Thus a meta decision problem can be solved in an interactive framework or through machine learning.

Stability and sensitivity analysis is both theoretically and practically interesting and important in optimization and decision making. In this chapter we will explain several approaches, though limited, to stability and sensitivity analysis in MCDM.

A review of goal programming formulations and of current applications is presented. Some issues in the use of goal programming are discussed along with current research streams, including interactive goal programming, the use of goal programming to incorporate decision maker preference, and the use of goal programming as a tool to aid in multiple objective decision making.

This chapter presents a summary of reference point methodology in vector optimization and decision support. The methodology has been developed at the International Institute for Applied Systems Analysis (IIASA) since 1980 and found numerous applications, both in IIASA and elsewhere. The chapter presents methodological foundations, basic concepts and notation, reference points and achievement functions, neutral and weighted compromise solutions, issues of modeling for multi-objective analysis, some basic applications of reference point methods and a discussion of a decision process type supported by reference point methodology.

The purpose of this chapter is to present the so-called outranking approach, which was proposed in about 1970 by B. Roy as a complementary approach to multiattribute utility theory. After the description of the motivation and of the basic principles, we present about ten methods, give some comments on the determination of their parameters and illustrate how theoretical results can help to choose a method. The bibliography contains the most known references on the subject.

This chapter focuses on the use in practice of multi-attribute value theory (MAVT). MAVT is a simplification of multi-attribute utility theory (MAUT) in that, unlike MAUT, MAVT does not seek to model the decision maker’s attitude to risk. As a consequence it rests on simpler elicitation procedures which are more widely accepted by practising decision makers. The most significant recent advances in this field relate not to the underlying theory, but to the way in which MAVT can be, and is, used in practice to support decision making. The chapter begins with a brief review of the concepts of value theory. An exemplary decision is then used to convey a sense of how the process of decision making may currently be facilitated through the use of MAVT. The final section reviews recent developments which are beginning to impact on practice. These relate to: the use of problem structuring methods: advances in technology: and organisational developments.

The aim of the chapter is to expose its readers to some basic and generic ideas associated with interior algorithms and develop approaches for using these algorithms to address MOLP problems. In doing so, we discuss basic MOLP questions associated with interior algorithms, develop some specific interior MOLP approaches and illustrated them with examples.

The rough sets theory has been proposed by Z. Pawlak in the early 80’s to deal with inconsistency problems following from information granulation. It operates on an information table composed of a set U of objects (actions) described by a set Q of attributes. Its basic notions are: indiscernibility relation on U, lower and upper approximation of a subset or a partition of U, dependence and reduction of attributes from Q, and decision rules derived from lower approximations and boundaries of subsets identified with decision classes. The original rough sets idea has proved to be particularly useful in the analysis of multiattribute classification problems; however, it was failing when preferential ordering of attributes (criteria) had to be taken into account In order to deal with problems of multicriteria decision making (MCDM), like sorting, choice or ranking, a number of methodological changes to the original rough sets theory were necessary. The main change is the substitution of the indiscernibility relation by a dominance relation (crisp or fuzzy), which permits approximation of ordered sets in multicriteria sorting In order to approximate preference relations in multicriteria choice and ranking problems, another change is necessary: substitution of the information table by a pairwise comparison table, where each row corresponds to a pair of objects described by binary relations on particular criteria. In all those MCDM problems, the new rough set approach ends with a set of decision rules, playing the role of a comprehensive preference model. It is more general than the classic functional or relational model and it is more understandable for the users because of its natural syntax. In order to workout a recommendation in one of the MCDM problems, we propose exploitation procedures of the set of decision rules. Finally, some other recently obtained results are given: rough approximations by means of similarity relations (crisp or fuzzy) and the equivalence of a decision rule preference model with a conjoint measurement model which is neither additive nor transitive.

We survey the different representations, including non-classical logic, issued from artificial intelligence and used in MCDM. On the one hand, we mainly focus on rule-based and object representations, and applications of non-classical logic. On the other hand, we examine the contribution of heuristic search ideas to interactive MCDM.

This chapter describes two stochastic search and optimization techniques, evolutionary algorithms and simulated annealing, both inspired by models of natural processes (evolution and thermodynamics) and considers their role and application in multiple criteria decision making and analysis. The basic single criteria algorithms are first presented in each case and it is then demonstrated with an example problem how these may be modified and set up to deal with multiple design criteria. Whilst the example employed considers the design of a robust control system for a high speed maglev vehicle, the approaches and techniques have a far wider range of application.