New Perspectives in Multiple Criteria Decision Making

We give an overview of some new trends in preference modeling, utility representation, and choice rationalization. Several recent contributions on these topics point in the same direction: the use of multiple tools—may they be binary relations, utility functions, or rationales explaining a choice behavior—in place of a single one, in order to more faithfully model economic phenomena. In this stream of research, the two traditional tenets of economic rationality, completeness and transitivity, are partially (and naturally) given up. Here we describe some recent approaches of this kind, namely: (1) utility representations having multiple orderings as a codomain, (2) multi-utility and modal utility representations, (3) a finer classifications of preference structures and forms of choice rationalizability by means of generalized Ferrers properties, (4) a descriptive characterization of all semiorders in terms of shifted types of lexicographic products, (5) bi-preference structures, and, in particular, necessary and possible preferences, (6) simultaneous and sequential multi-rationalizations of choices, and (7) multiple, iterated, and hierarchical resolutions of choice spaces. As multiple criteria decision analysis provides broader models to better fit reality, so does a multi-approach to preference, utility, and choice. The overall goal of this survey is to suggest the naturalness of this general setting, as well as its advantages over the classical mono-approach.

Analytic Hierarchy Process (AHP) is a popular and long used multi-criteria decision analysis method. Despite this fact, there are still space for new research in all its methodological steps. These include problem structuring, pairwise comparisons, priorities derivation, consistency and reduction techniques of pairwise comparisons. Moreover, future research agenda can also be found in the extensions of AHP: Analytic Network Process (for dealing with interactions) and AHPSort (for sorting problems). Finally, we discuss visualisation techniques for the Analytic Hierarchy Process.

PROMETHEE is a well-known multicriteria outranking method. If it was primarily developed for (complete or partial) ranking purposes, recent extensions have been proposed in sorting and clustering contexts. Among them, the methods called PROMETHEE TRI and PROMETHEE CLUSTER were first presented in 2004. Unfortunately, these suffered from some drawbacks that we highlight in this contribution. To overcome these problems, authors have developed other extensions such as FlowSort, PCLUST, etc. The purpose of this paper is to provide a summary of some of these contributions, to highlight their existing links and list several remaining research questions. From a global perspective, we will show that the boundaries between ranking, sorting and clustering are blurred.

In multicriteria decision aiding, preference disaggregation analysis involves the inference of preferential information from holistic judgments that the decision maker provides. This area of research has attracted strong interest and various methodologies have been proposed over the past three decades for different types of decision problems and multicriteria models. This chapter overviews the developments and perspective in this field, covering established techniques as well as the state-of-the-art developments and future prospects.

In this chapter, we summarize some new results and trends in aggregation theory, thus contributing to the domain of normed utility functions. In particular, we discuss k-additive and k-maxitive aggregation functions and also present some construction methods. Penalty- and deviation-based approaches can be seen as implicitly given construction methods. For non-symmetric (weighted) aggregation functions, four symmetrization methods based on the optimization are introduced. All discussed results and construction methods are exemplified.

We consider general MCDA models with discrete attributes. These models are shown to be equivalent to a multichoice game and we put some emphasis on discrete Generalized Independence Models (GAI), especially those which are 2-additive, that is, limited to terms of at most two attributes. The chapter studies the interpretation of these models. For general MCDA models, we study how to define a meaningful importance index, and propose mainly two kinds on importance indices: the signed and the absolute importance indices. For 2-additive GAI models, we study the issue of the decomposition, which is not unique in general. We show that for a monotone 2-additive GAI model, it is always possible to obtain a decomposition where each term is monotone. This has important consequences on the tractability and interpretability of the model.

This chapter provides a state-of-the-art account of the use of Sugeno integrals in decision evaluation, when it is difficult to use meaningful figures of merit when assessing the worth of a decision and when only a finite scale of, e.g., linguistic categories, can be used. Here, Sugeno integrals are thought of as idempotent lattice polynomial functions on a finite bounded chain, which makes it possible to assign importance weights to groups of criteria or states. Algebraic and behavioral characterizations of the Sugeno integral are presented and discussed, including the special cases of weighted minima and maxima. Extensions of this framework are also surveyed, namely: lexicographic refinements that increase the discrimination power of this approach; the use of local utility functions in order to cope with criteria having distinct rating scales; and the generalization of the criteria weighting scheme at work in Sugeno integrals. Another kind of extension considered is when ratings belong to a bipolar scale where good and bad figures are explicitly present, thus giving rise to the symmetric Sugeno integral or to the separate evaluation of pros and cons. Moreover, it is pointed out that Sugeno integrals encode decision rules and that this bridge leads to methods for extracting knowledge from qualitative data. The results of empirical studies of the latter are also presented and discussed, accordingly.

This chapter starts by providing a categorization of current goal programming literature by type of variant used. Subsequently, goal programming is presented as a secondary model of a general p-metric distance function primary model. This orientation allows us to link goal programming with several fields like the determination of social choice functions or the interpretation and implementation of the Simonian concepts of bounded rationality and “satisficing”. To undertake the latter task, this epistemic framework is understood as a Laudian “Research Tradition” instead of the usual understanding as a scientific theory. Finally, potential future developments to expand the use and flexibility of goal programming as well as to explore possible logical connections of goal programming with other decision-making areas are highlighted.

In this paper, goal programming problems with interactive fuzzy coefficients are treated. Two types of targets can be expressed by fuzzy sets in goal programming problems with fuzzy coefficients. One is the ambiguous target whose true value is not known precisely and the other is the target distribution to which the fuzzy set of objective function values is brought close. Corresponding to the difference of targets, we use two kinds of deviations naturally obtained from the extension principle. On the other hand, to treat the interaction among fuzzy coefficients, we introduce oblique fuzzy vectors (OFVs). An OFV can be obtained from the expert knowledge about the behavior of coefficients as well as from the principal component analysis of the stored coefficient data. It is shown that linear functions with OFVs can be obtained easily. The goal programming problems are formulated based on the necessity measure maximization model. It is shown that the reduced programming problems can be solved by a bisection method together with a simplex method. Moreover, it is shown that the constraints of the reduced programming problems have special structures such as a dual block angular structure and a bordered angular structure so that some decomposition methods are applicable.

Bilevel programs model hierarchical non-cooperative decision processes with two decision makers, the leader and the follower, who control different sets of variables and have their own objective functions with interdependent constraints. Bilevel programs are very difficult to solve and even the linear case is NP-hard. In this chapter, a novel view on the main concepts in multiobjective and semivectorial bilevel problems is offered, including new types of solutions that are relevant for decision support. Optimistic and pessimistic leader’s perspectives are explored; the extreme optimistic/deceiving and pessimistic/rewarding solutions in semivectorial problems and the optimistic Pareto fronts in multiobjective problems are defined and illustrated. Traditional and emerging application fields are reviewed. Potential difficulties and pitfalls associated with computing solutions to bilevel models with multiple objectives are outlined, shaping possible research avenues.

Public administrations need to assess policy options before their implementation; often there is some uncertainty if cost-benefit analysis (CBA) or multi-criteria evaluation (MCE) should be used. This Chapter aims at showing that MCE may help economics at overcoming some of its current difficulties in the empirical assessment of public policy options; thus MCE has to be placed in the future of welfare economics with no doubt. To corroborate this conclusion, a structured comparison of the main distinguishing features of CBA and MCE is carried out according to the following ten comparison criteria: efficiency, fairness, democratic basis, effectiveness, problem structuring, alternatives taken into account, policy consequences, comprehensiveness, transparency and mathematical aggregation rule.

This chapter covers the combined use of Multi-Criteria Decision Analysis (MCDA) and Life-Cycle Assessment methodologies. It first reviews environmental Life-Cycle Assessment (LCA), introduces the main challenges and perspectives, including how to extend LCA towards Life Cycle Sustainability Assessment (LCSA), and discusses how LCAs might be useful for the MCDA practitioner. Then, it discusses how MCDA can complement LCA. Challenges and perspectives are presented concerning LCSA, relative versus absolute evaluation, criteria weighting, and criteria selection.

When the Municipality of Turin first decided to invest in social innovation, a public program and a network of partners were created, and a procedure to support social innovation start-ups was developed, and applied for the first time in 2014. After selection and funding of several young social entrepreneur projects, the Municipality activated a monitoring process. Different methodological approaches, including cognitive mapping, actor network analysis and multicriteria analysis, have been combined to analyse the behaviour of these start-ups and to evaluate whether they would address the social needs of their specific fields, and develop business projects as part of an inclusive and sustainable economy. Each element of this analysis has been proposed and discussed in relation to the monitoring and decision processes. The adopted multi-methodology and its results are here presented as a proposal for new models, metrics and methods for the social economy.

The application of multiobjective models and methods in a vast range of problems in the energy sector has been a consolidated practice in the last four decades. The need to consider explicitly multiple axes of evaluation of the merits of solutions in decision processes, generally involving large investments as well as social and environmental impacts, has led to the recognition of the potential benefits of multiobjective optimization approaches. Trends such as the increasing share of renewable sources in the energy generation matrix, the evolution towards smart grids involving the deployment of information and communication technologies, the dissemination of electric mobility and the consumer empowerment by means of the utilization of demand-side resources introduce challenging problems for which the capability of multiobjective models and methods to explore and provide assistance in the appraisal of well-balanced solutions is of utmost importance. This chapter aims to offer a broad view of some of the most challenging problems concerning the application of multiobjective optimization models and methods in the energy sector, with focus on electricity smart grids, outlining promising research avenues in problems of planning and operational nature.

Climate change mitigation policy requires reducing dependence on fossil fuels and transition to low carbon energy production in district heating (DH). We study here inclusion of two kinds of renewable energy to a CHP based DH system in Finland: solar heat and ground source heat. In addition, we apply heat storages to balance the gap between production and fluctuating demand. The optimal operation of the extended systems is determined by a simulation and optimization model to minimize the operating costs. We evaluate the different possible extensions in terms of multiple economic, technical and environmental criteria using Stochastic Multicriteria Acceptability Analysis (SMAA). The results show that under Finnish conditions, ground source heat is more favourable than solar heat for DH.

The performance evaluation and comparison of routing models in telecommunication networks, normally imply the necessity of evaluating them through multidimensional, potentially conflicting, often incommensurate criteria, frequently involving imprecise information regarding the relative importance of the various network performance criteria. As we will show, this is particularly relevant for flow-oriented, decentralized routing optimization methods, having in mind their inherent limitations. Therefore, we formulate a decision problem focused on the comparison and selection of flow-oriented routing models, evaluated through multiple global network performance measures. A proposal of a multi-criteria/multi-attribute approach for tackling this decision problem, based on the VIP (Variable Interdependent Parameter) software, will be described. The adequacy of the features of the multi-attribute decision analysis model, which uses additive aggregation of criteria with variable interdependent importance parameters, coping with imprecise information, will be discussed. A detailed formulation of the application of the proposed approach to a specific problem involving the choice of a point-to-point routing method in a modern transport telecom network, from a set of height routing models, by considering their performance evaluated in terms of nine global network performance measures, will be presented. Moreover, the extension of the decision analysis model, based on the VIP decision support tool, for dealing with this problem, in the case of face-to-face cooperative group decision, will be addressed. A case study concerning the application of this approach to the aforementioned decision problem, in a setting involving three decision makers, including a facilitator, will be presented. Finally, some conclusions, both from a methodological and practical nature, founded on the application study, will be put forward, highlighting the interest of this type of approach in this important area of telecom-network design.