Model choice in multicriteria decision aid

The purpose of this paper is to illustrate, using a real case study, one of the points stressed in the “Manifesto of the new Multi Criteria Decision Aid (MCDA) era” (Bouyssou et al., 1993) regarding the application of the basic theory of MCDA procedures. Although the great diversity of MCDA procedures may be seen as a strong point, it can be a weakness, and a systematic analysis of decision procedures if one method makes more sense than another for a specific problem is necessary. The problem of selecting the most appropriate (MCDA) technique for a particular application is in itself a MCDA problem since the decision making criteria used for the selection are different and conflicting in nature. In this paper three selection models are implemented to assist the system analyst, when confronted with a multi-objective decision problem, to select the most appropriate MCDA technique for application to the problem of optimal ranking of water development projects in an arid country. These models are developed by Deason (1984), Gershon (1981), and Tecle (1988). Results indicated that PROMETHEE was the most preferred method for this problem.     

Determining new possible weight values in PROMETHEE: a procedure based on data envelopment analysis

Operational research (OR) offers efficient tools to support managers in strategic decision-making processes. Data envelopment analysis (DEA) and multiple criteria decision aid (MCDA) are two important research areas in OR. These two domains are both based on the evaluation of “objects” according to multiple “points of views”. Within the MCDA framework, choosing appropriate weights for the different criteria often arises as a problem itself for decision makers. As a consequence, researchers have developed original methodologies to help them during this elicitation phase. In this work, we aim to investigate how DEA can be used to propose weights in the context of the PROMETHEE II method. More precisely, we suggest an extension of the so-called “decision maker brain” used in the GAIA plane (also known as PROMETHEE VI) based on DEA. The underlying idea is based on the computation of weights in PROMETHEE (GAIA brain) which are compatible with the DEA analysis. We end this paper with a numerical example.     

The SMAA-PROMETHEE method

PROMETHEE methods are widely used in Multiple Criteria Decision Aiding (MCDA) to deal with real world decision making problems. In this paper, we propose to apply the Stochastic Multicriteria Acceptability Analysis (SMAA) to the family of PROMETHEE methods in order to explore the whole set of parameters compatible with some preference information provided by the Decision Maker (DM). The application of the presented methodology is described in a didactic example.     

Modelling of linguistic variables in multicriteria energy policy support

The climate change and the increasing complexity of the energy sector along with the prerequisite for sustainability have broadened the energy policy shaping field by bringing out new challenges. Decision support tools and methods, such as Multicriteria Decision Aid (MCDA), are necessary for energy policy, in the pursuit of appropriate approaches necessary to support the restructuring of the energy sector, concerning patterns of energy extraction, generation, transformation and use, from unsustainable to sustainable forms of development. Papers devoted to the investigation of MCDA models using linguistic variables for energy policy support seem to be not available in the international literature. The scope of this paper is to explore different linguistic representation and computational models in MCDA that are or can be applied to energy policy support and to establish a clear linkage between them. This paper argues that MCDA methodologies with direct computation on linguistic variables can support energy policy frameworks, bridging the gap between energy policy makers thinking, reasoning, representation and computing. Finally, current trends, open questions and prospects in this topic are pointed out.     

Technology selection: application of the PROMETHEE in determining preferences—a real case of nanotechnology in Iran

PROMETHEE (Preference Ranking Organization METHod for Enrichment) is a family of outranking methods. In this paper, we explore its application to technology selection by first providing a generic comparison of PROMETHEE with other ranking methods. We start our investigation by comparing the strengths and weaknesses of PROMETHEE to prevalently used methods in technology selection, such as Analytic Hierarchical Process (AHP), technology selection framework and Fuzzy Analytic Hierarchical Process (FAHP with Fuzzy Delphi). We then explain how PROMETHEE can be applied to a particular technology selection application by detailing the steps for selecting among various nanotechnology application fields. Lastly, we compare PROMETHEE to other methods in this context and explain the advantages and constraints of its use.     

Ethics and decision

Real World situations can be faced by qualitative and by quantitative approaches, by perceptions and by measurements, by feelings and by models. In this paper we first compare the management of Natural Real World situations and the management of Human Real World situations. Although there are strong similarities, there are also major differences. “GOD” is keeping the laws of Nature unchanged and therefore it is not to be included in the models of Physics, while the “MIND” of the Decision-maker has to be taken into account in Operational Research (OR). Decision-making for Human processes requires also to take into account three poles of influence: the Rational, the Subjective and the Ethical one. Most of the basic models of OR are only considering the Rational Pole. No freedom is left to the Decision-maker, no Ethical aspects are considered. It is shown that, if well adapted, the Multicriteria Decision Aid (MCDA) PROMETHEE–GAIA procedure can provide well-balanced solutions between Rationality, Subjectivity and Ethics. Both the Mind of the Decision-maker and the “Ethical Conscience” of Mankind can be represented and included in the model.     

A note on the use of PROMETHEE multicriteria methods

The PROMETHEE methods are rather popular in the world of outranking methods. One of the reasons for this popularity is the existence of the very userfriendly software, called PROMCALC-PROMethee CALCulation. More and more practitioners are using PROMCALC to handle their multiple criteria problems. However, not all users are aware of the consequences of the model assumptions made in PROMETHEE methods. A short overview of some drawbacks of PROMETHEE methods that users must know and avoid are described in this paper.     

A general decomposition approach for multi-criteria decision trees

In this paper, we address the dynamic and multi-criteria decision-making problems under uncertainty, generally represented by multi-criteria decision trees. Decision-making consists of choosing, at each period, a decision that maximizes the decision-maker outcomes. These outcomes should often be measured against a set of heterogeneous and conflicting criteria. Generating the set of non-dominated solutions is a common approach considered in the literature to solve the multi-criteria decision trees, but it becomes very challenging for large problems. We propose a new approach to solve multi-criteria decision trees without generating the set of all non-dominated solutions, which should reduce the computation time and the cardinality of the solution set. In particular, the proposed approach combines the advantages of decomposition with the application of multi-criteria decision aid (MCDA) methods at each decision node. A generalization of the Bellman’s principle of decomposition to the multi-criteria context is put forward. A decomposition theorem is therefore proposed. Under the sufficient conditions stated by the theorem, the principle of decomposition will generate the set of best compromise strategies. Seven MCDA methods are then characterized (lexicographic, weighted sum, multi-attribute value theory, TOPSIS, ELECTRE III, and PROMETHEE II) against the conditions of the theorem of decomposition and against other properties (neutrality, anonymous, fidelity, dominance, independency), in order to confirm or infirm their applicability with the proposed decomposition principle. Moreover, the relationship between independency and temporal consistence is discussed as well as the effects of incomparableness, rank reversals, and use of thresholds. Two conjectures resulted from this characterization.     

A data model for algorithmic multiple criteria decision analysis

Various software tools implementing multiple criteria decision analysis (MCDA) methods have appeared over the last decades. Although MCDA methods share common features, most of the implementing software have been developed independently from scratch. Majority of the tools have a proprietary storage format and exchanging data among software is cumbersome. Common data exchange standard would be useful for an analyst wanting to apply different methods on the same problem. The Decision Deck project has proposed to build components implementing MCDA methods in a reusable and interchangeable manner. A key element in this scheme is the XMCDA standard, a proposal that aims to standardize an XML encoding of common structures appearing in MCDA models, such as criteria and performance evaluations. Although XMCDA allows to present most data structures for MCDA models, it almost completely lacks data integrity checks. In this paper we present a new comprehensive data model for MCDA problems, implemented as an XML schema. The data model includes types that are sufficient to represent multi-attribute value/utility models, ELECTRE III/TRI models, and their stochastic extensions, and AHP. We also discuss use of the data model in algorithmic MCDA.     

Formalizing and solving the problem of clustering in MCDA

The topic of clustering has been widely studied in the field of Data Analysis, where it is defined as an unsupervised process of grouping objects together based on notions of similarity. Clustering in the field of Multi-Criteria Decision Aid (MCDA) has seen a few adaptations of methods from Data Analysis, most of them however using concepts native to that field, such as the notions of similarity and distance measures. As in MCDA we model the preferences of a decision maker over a set of decision alternatives, we can find more diverse ways of comparing them than in Data Analysis. As a result, these alternatives may also be arranged into different potential structures. In this paper we wish to formally define the problem of clustering in MCDA using notions that are native to this field alone, and highlight the different structures which we may try to uncover through this process. Following this we propose a method for finding these structures. As in any clustering problem, finding the optimal result in an exact manner is impractical, and so we propose a stochastic heuristic approach, which we validate through tests on a large set of artificially generated benchmarks.     

A synergy of multicriteria techniques to assess additive value models

The assessment of additive value functions in Multicriteria Decision Aid (MCDA) has to face issues of legitimacy and technical difficulties when real decision makers are involved. This paper presents a synergy of three complementary techniques to assess additive models on the whole criteria space. The synergy includes a revised MACBETH technique, the standard MAUT trade-off analysis and UTA-based methods for the assessment of both the marginal value functions and the weighting factors. The paper uses a set of original robustness measures and rules associated with revised MACBETH and UTA in order to manage multiple linear programming solutions and to extract robust conclusions from them. Finally, to illustrate the methods’ synergy, an application example is presented, dealing with the planning of metro extension lines.     

Project prioritization under policy restrictions. A combination of MCDA with 0–1 programming

Multiple Criteria Decision Aid methods are increasingly used in financial decision making in order to capture the multifaceted character of modern enterprises activated in a complex and versatile market environment. This paper presents a multiple criteria approach for the selection of firms applying for financial support from public funds. Besides the budget constraint, the specific decision situation imposes the consideration of additional policy constraints that prevent from directly exploiting rankings provided by a multiple criteria method. In such a case the problem solution is to find a set of alternatives satisfying the constraints and at the same time maximizing a measure of global performance. The proposed procedure relies on the PROMETHEE V method which belongs to the well-known PROMETHEE family of multiple criteria outranking methods and is combined with an integer programming formulation capable to effectively deal with the problem’s combinatorial character. This method is modified in order to avoid any bias in the selection of the optimal set that may arrive because of the apparent contradiction between the rate of resources consumption and the coefficients of the alternatives in the additive objective function.     

Approximating Unknown Mappings: An Experimental Evaluation

Different methodologies have been introduced in recent years with the aim of approximating unknown functions. Basically, these methodologies are general frameworks for representing non-linear mappings from several input variables to several output variables. Research into this problem occurs in applied mathematics (multivariate function approximation), statistics (nonparametric multiple regression) and computer science (neural networks). However, since these methodologies have been proposed in different fields, most of the previous papers treat them in isolation, ignoring contributions in the other areas. In this paper we consider five well known approaches for function approximation. Specifically we target polynomial approximation, general additive models (Gam), local regression (Loess), multivariate additive regression splines (Mars) and artificial neural networks (Ann).Neural networks can be viewed as models of real systems, built by tuning parameters known as weights. In training the net, the problem is to find the weights that optimize its performance (i.e. to minimize the error over the training set). Although the most popular method for Ann training is back propagation, other optimization methods based on metaheuristics have recently been adapted to this problem, outperforming classical approaches. In this paper we propose a short term memory tabu search method, coupled with path relinking and BFGS (a gradient-based local NLP solver) to provide high quality solutions to this problem. The experimentation with 15 functions previously reported shows that a feed-forward neural network with one hidden layer, trained with our procedure, can compete with the best-known approximating methods. The experimental results also show the effectiveness of a new mechanism to avoid overfitting in neural network training.     

Analytic hierarchy process: An overview of applications

This article presents a literature review of the applications of Analytic Hierarchy Process (AHP). AHP is a multiple criteria decision-making tool that has been used in almost all the applications related with decision-making. Out of many different applications of AHP, this article covers a select few, which could be of wide interest to the researchers and practitioners. The article critically analyses some of the papers published in international journals of high repute, and gives a brief idea about many of the referred publications. Papers are categorized according to the identified themes, and on the basis of the areas of applications. The references have also been grouped region-wise and year-wise in order to track the growth of AHP applications. To help readers extract quick and meaningful information, the references are summarized in various tabular formats and charts.A total of 150 application papers are referred to in this paper, 27 of them are critically analyzed. It is hoped that this work will provide a ready reference on AHP, and act as an informative summary kit for the researchers and practitioners for their future work.     

PROMETHEE: an extension through fuzzy mathematical programming

PROMETHEE multi-criteria methods are based on fuzzy evaluations of the differences between pairs of alternatives for each criterion. PROMETHEE II associates a crisp number to each action. PROMETHEE III associates an interval to each action and two actions are considered indifferent when they are very close to each other. PROMETHEE V applies Integer Linear Programming in order to select the subset of alternatives that maximizes the sum of PROMETHEE II scorings, subject to a set of constraints. In order to make the model more realistic, this paper proposes that some constraints are soft and some coefficients are estimated by fuzzy numbers. Fuzzy Integer Linear Programming is applied, using the PROMETHEE III scorings as objective function coefficients, in order to find the subsets of non-outranked alternatives that best satisfy the soft constraints. The new model is more realistic and fits better the fuzzy philosophy of PROMETHEE. The method is illustrated with an example.     

Using a multi-criteria decision aid methodology to implement sustainable development principles within an organization

The implementation of Sustainable Development (SD) within an Organization is a difficult task. This is due to the fact that it is difficult to deal with conflicting and incommensurable aspects such as environmental, economic and social dimensions. In this paper we have used a Multi-Criteria Decision Aid (MCDA) methodology to cope with these difficulties. MCDA methodology offers the opportunity to avoid monetary valuation of the different dimensions of the SD. These dimensions are not substitutable for one another and all have a role to play. There is an abundance of possible aggregation procedures in MCDA methodology. In this paper we have proposed an innovative method to choose a suitable aggregation procedure for SD problems. Real life case studies of the implementation of an outranking approach (i.e., ELECTRE) and of a mono-criterion synthesis approach (i.e., MAUT approaches based on the Choquet integral) were done to respectively rank 22 SD strategic actions within an expertise Institute and rank 20 practical operational actions to control energy consumption of the Institute’s buildings.     

Extending the use of scenario planning and MCDA for the evaluation of strategic options

Multi-criteria decision analysis (MCDA) is well equipped to deal with conflicting, qualitative objectives when evaluating strategic options. Scenario planning provides a framework for confronting uncertainty, which MCDA lacks. Integration of these methods offers various advantages, yet its effective application in evaluating strategic options would benefit from scenarios that reflect a larger number of wide-ranging scenarios developed in a time-efficient manner, as well as incorporation of MCDA measures that inform within and across scenario comparison of options. The main contribution of this paper is to illustrate how a more diverse set of scenarios could be developed quickly, and to investigate how regret could be used to facilitate comparison of options. First, the reasons for these two areas of development are elaborated with respect to existing techniques. The impacts of applying the proposed method in practice are then assessed through a case study involving food security in Trinidad and Tobago. The paper concludes with a discussion of findings and areas for further research.     

An interval version of PROMETHEE for the comparison of building products' design with ill-defined data on environmental quality

Life Cycle Assessment (LCA) is a powerful technique used to calculate total input and output flows of materials and energy from and to the environment during every step of a product life. A measure of a product Environmental Quality (EQ) can then be derived and help in the selection and in the design of more environmentally friendly design alternatives. EQ is a multicriteria measurement. In the construction field, LCA flows cannot be known with precision without loss of realism. Hence intervals have been introduced to model them. Thus, different designs are characterized by interval multicriteria measures. Manipulation of such environmental performances calls for a MCDA method which (1) does not allow for trade-offs between criteria, (2) preserves as much information as possible and (3) is simple enough to be understood by non-specialist users. PROMETHEE was identified as a suitable method according to the previous criteria, but it is not able to handle interval performances so far. We discuss the necessary changes to devise an interval version, called “PROMETHEE I”.     

Nonparametric estimation of operational value-at-risk (OpVaR)

This paper introduces nonparametric methods for estimating 99.9% operational value-at-risk (OpVaR) and its confidence interval (CI), and demonstrates their applications to US business losses. An attractive feature of these new methods is that there is no need to estimate either the entire heavy-tailed loss distribution or the tail region of the distribution. Furthermore, we provide algorithms that facilitate applied researchers and practitioners in risk management area to implement the sophisticated empirical likelihood ratio (ELR) based methodologies to construct the CI of the true underlying 99.9% OpVaR. In a simulation study, we find that the weighted ELR (WELR) CI estimator is more reliable than the ELR CI estimator. The empirical results show that the nonparametric OpVaR estimates are consistently larger than those of other comparable methods, which provide adequate regulatory capitals, particularly during crises. The findings have implications for regulators, and effective and efficient risk financing.     

Comparing multicriteria methods in the context of environmental problems

The present paper gives an analysis of the use of ELECTRE III, PROMETHEE I, II, and SMART decision-aids in the context of four different real applications to environmental problems in Finland. These methods are widely used decision-aids in the real planning processes. The purpose of this study is to define the differences of these methods and the results obtained with them, and in this way also to consider their applicability in aiding environmental decision-making. Furthermore, a comparison of the methods based on a set of randomly generated problems is carried out. The choice in practice will not be easy; PROMETHEE does not differ much from SMART with linear value functions, and in many cases this holds for ELECTRE III, too. However, in a particular problem the `best alternatives' obtained with these methods may differ greatly. Therefore, the conclusion is that it is better to use several methods for the same problem when possible; when not, we recommend the use of ELECTRE III.