Catálogo de publicaciones - libros

Many MCDA models are based on essentially deterministic evaluations of the consequences of each action in terms of each criterion, possibly subjecting final results and recommendations to a degree of sensitivity analysis. In many situations, such an approach may be justified when the primary source of complexity in decision making relates to the multicriteria nature of the problem rather than to the stochastic nature of individual consequences. Nevertheless, situations do arise, especially in strategic planning problems, when risks and uncertainties are as critical as the issue of conflicting management goals. In such situations, more formal modelling of these uncertainties become necessary. In this paper, we start by reviewing the meaning and origin of risk and uncertainty. We recognize both internal uncertainties (related to decision maker values and judgements) and external uncertainties (related to imperfect knowledge concerning consequences of action), but for this paper focus on the latter. Four broad approaches to dealing with external uncertainties are discussed. These are multiattribute utility theory and some extensions; stochastic dominance concepts, primarily in the context of pairwise comparisons of alternatives; the use of surrogate risk measures as additional decision criteria; and the integration of MCDA and scenario planning. To a large extent, the concepts carry through to all schools of MCDA. A number of potential areas for research are identified, while some suggestions for practice are included in the final section.

In this chapter we survey several approaches to derive a recommendation from some preference models for multiple criteria decision aid. Depending on the specificities of the decision problem, the recommendation can be a selection of the best alternatives, a ranking of these alternatives or a sorting. We detail a sorting procedure for the assignment of alternatives to graded classes when the available information is given by interacting points of view and a subset of prototypic alternatives whose assignment is given beforehand. A software dedicated to that approach (TOMASO) is briefly presented. Finally we define the concepts of good and bad choices based on dominant and absorbant kernels in the valued digraph that corresponds to an ordinal valued outranking relation. Aggregation with fuzzy environment, fuzzy choice, ordinal ordered sorting, choquet integral, TOMASO.

We present the methodology of Multiple-Criteria Decision Aiding (MCDA) based on preference modelling in terms of “ if. ⋯, then ⋯” decision rules. The basic assumption of the decision rule approach is that the decision maker (DM) accepts to give preferential information in terms of examples of decisions and looks for simple rules justifying her decisions. An important advantage of this approach is the possibility of handling inconsistencies in the preferential information, resulting from hesitations of the DM. The proposed methodology is based on the elementary, natural and rational principle of dominance. It says that if action is at least as good as action on each criterion from a considered family, then is also comprehensively at least as good as The set of decision rules constituting the preference model is induced from the preferential information using a knowledge discovery technique properly modified, so as to handle the dominance principle. The mathematical basis of the decision rule approach to MCDA is the Dominance-based Rough Set Approach (DRSA) developed by the authors. We present some basic applications of this approach, along with didactic examples whose aim is to show in an easy way how DRSA can be used in various contexts of MCDA.

This chapter aims at a unified presentation of various methods of MCDA based on fuzzy measures (capacity) and fuzzy integrals, essentially the Choquet and Sugeno integral. A first section sets the position of the problem of multicriteria decision making, and describes the various possible scales of measurement (cardinal unipolar and bipolar, and ordinal). Then a whole section is devoted to each case in detail: after introducing necessary concepts, the methodology is described, and the problem of the practical identification of fuzzy measures is given. The important concept of interaction between criteria, central in this chapter, is explained in detail. It is shown how it leads to fuzzy measures. The case of bipolar scales leads to the general model based on bi-capacities, encompassing usual models based on capacities. A general definition of interaction for bipolar scales is introduced. The case of ordinal scales leads to the use of Sugeno integral, and its symmetrized version when one considers symmetric ordinal scales. A practical methodology for the identification of fuzzy measures in this context is given.

Verbal Decision Analysis is a new methodological approach for the construction of decisions methods with multiple criteria. The approach is based on cognitive psychology, applied mathematics, and computer science. Problems of eliciting exact quantitative estimations from the decision makers may be overcome by using preferential information from the decision makers in the ordinal form (e.g., “more preferable”, “less preferable”,⋯). This type of judgments is known to be much more stable and consistent. Ways of how to obtain and use ordinal judgments for multicriteria alternatives’ evaluation are discussed. Decision methods ZAPROS, and ORCLASS based on the approach are briefly described.

We provide an introduction to the use of interactive methods in multiple objective programming. We focus on discussing the principles to implement those methods. Our purpose is not to review existing procedures, but some examples are picked to illustrate the main ideas behind those procedures. Furthermore, we discuss two available software systems developed to implement interactive methods. Abstract

We present our view of the state of the art in multiobjective programming. After an introduction we formulate the multiobjective program (MOP) and define the most important solution concepts. We then summarize the properties of efficient and nondominated sets. In Section 4 optimality conditions are reviewed. The main part of the chapter consists of Sections 5 and 6 that deal with solution techniques for MOPs and approximation of efficient and nondominated sets. In Section 7 we discuss specially-structured problems including linear and discrete MOPs as well as selected nonlinear MOPs. In Section 8 we present our perspective on future research directions.

In this paper, we treat multiple objective programming problems with fuzzy coefficients. We introduce the approaches based on possibility and necessity measures. Our aim in this paper is to describe the treatments of the problem rather than the solution method for the problem. We describe the modality constrained programming approach, the modality goal programming approach and modal efficiency approach. In the first approach, we discuss treatments of fuzziness in the programming problems. The extensions of a fuzzy relation to the relation between fuzzy numbers are developed in order to treat generalized constraints. In the second approach, we show that two kinds of differences between a fuzzy objective function value and a fuzzy target are conceivable under the fuzziness. We describe the distinction of their applications in programming problems. In the third approach, we describe how the efficiency can be extended to multiple objective programming problems with fuzzy coefficients. Necessary and sufficient conditions for a feasible solution to satisfy the extended efficiency are discussed. Finally some concluding remarks are given.

In this chapter, we provide a broad overview of the most representative multicriteria location problems as well as of the most relevant achievements in this field, indicating the relationship between them whenever possible. We consider a large number of references which have been classified in three sections depending on the type of decision space where the analyzed models are stated. Therefore, we distinguish between continuous, network, and discrete multicriteria location problems.

Over the past decades the complexity of financial decisions has increased rapidly, thus highlighting the importance of developing and implementing sophisticated and efficient quantitative analysis techniques for supporting and aiding financial decision making. Multicriteria decision aid (MCDA), an advanced branch of operations research, provides financial decision makers and analysts with a wide range of methodologies well-suited for the complexity of modern financial decision making. The aim of this chapter is to provide an in-depth presentation of the contributions of MCDA in finance focusing on the methods used, applications, computation, and directions for future research.