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.     

An effective Markov based approach for calculating the Limit Matrix in the analytic network process

Analytic network process is a multiple criteria decision analysis (MCDA) method that aids decision makers to choose among a number of possible alternatives or prioritize the criteria for making a decision in terms of importance. It handles both qualitative and quantitative criteria, that are compared in pairs, in order to forge a best compromise answer according to the different criteria and influences involved. The method has been widely applied and the literature review reveals a rising trend of ANP-related articles. The ‘power’ matrix method, a procedure necessary for the stability of the decision system, is one of the critical calculations in the mathematical part of the method. The present study proposes an alternative mathematical approach that is based on Markov chain processes and the well-known Gauss-Jordan elimination. The new approach obtains practically the same results as the power matrix method, requires slightly less time and number of calculations and handles effectively cyclic supermatrices, optimizing thus the whole procedure.     

MCDA and preference disaggregation in group decision support systems

Within the frame of decision aid literature, group decision making has drawn the attention of researchers from a wide spectrum of disciplines. Group Decision Support Systems (GDSS) can play a critical role, in decision situations with multiple individuals, each having his/her own private point of view on the handling of the decision problem. In such an environment, the conflict between the members of the group is not a seldom situation. Multiple criteria decision aid (MCDA) methods can be proven as invaluable tools in handling such interpersonal conflicts where the aim is to achieve consensus between the group members or at least reduce the amount of conflict among participating individuals. This paper reviews some of the past approaches in the multiple criteria–multiple decision makers context.     

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.     

An MCDA approach for the selection of bike projects based on structuring and appraising activities

This paper presents an MCDA approach for the structuring and appraising activities of a large and complex decision problem. More specifically, the paper makes use of the three-step structuring process for decision analysis proposed by von Winterfeldt and Edwards: (1) identifying the problem; (2) selecting an appropriate analytic approach; and (3) developing a detailed analytic structure. For illustration of the approach a case study dealing with the assessment task of prioritising and selecting initiatives and projects from a public pool with limited funds is examined throughout the paper. The process is embedded in a Decision Support System (DSS) making use of the REMBRANDT technique for pair wise comparisons to determine project rankings. A procedure for limiting the number of pair wise comparisons to be made in the process is in this connection presented. Finally, strengths and weaknesses in the approach are discussed and conclusions are made.     

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.     

Structuring an MCDA model using SSM: A case study in energy efficiency

This work presents the use of a problem structuring method, Soft Systems Methodology (SSM), to structure a Multi-Criteria Decision Analysis (MCDA) model, aimed at appraising energy efficiency initiatives. SSM was useful to help defining clearly the decision problem context and the main actors involved, as well as to unveil the relevant objectives for each stakeholder. Keeney’s Value Focused Thinking approach was then used to refine and structure the list of objectives according to the perspective of the main evaluators identified. In addition to describing this particular case study, this paper aims at providing some general guidelines on how SSM may facilitate the emergence of objectives for MCDA models.     

Stochastic Programming with Multivariate Second Order Stochastic Dominance Constraints with Applications in Portfolio Optimization

In this paper we study optimization problems with multivariate stochastic dominance constraints where the underlying functions are not necessarily linear. These problems are important in multicriterion decision making, since each component of vectors can be interpreted as the uncertain outcome of a given criterion. We propose a penalization scheme for the multivariate second order stochastic dominance constraints. We solve the penalized problem by the level function methods, and a modified cutting plane method and compare them to the cutting surface method proposed in the literature. The proposed numerical schemes are applied to a generic budget allocation problem and a real world portfolio optimization problem.     

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.     

Solving electronic spreadsheet models by interactive multicriterion optimization: a budgeting illustration

In previous papers a connection between general spreadsheet models and interactive multicriterion optimization has been discussed. The purpose of the present paper is to provide proof of the concept with a detailed example. The main idea is that interactive multicriterion optimization can be viewed as a new way of interacting with spreadsheet models. It offers advantages over the two prevailing ones, namely what-if and goal-seeking. A simplified budgeting example is given to clarify this connection. Directions of improvement are assumed to be provided by the decision maker using one of the several existing methods. One improvement iteration is illustrated and analyzed following the method of Loganathan and Sherali.     

Spatial multicriteria decision support for robust land-use suitability: The case of landfill site selection in Northeastern Greece

Multicriteria spatial decision support systems (MC-SDSS) have emerged as an integration of geographical information systems (GIS) and multiple criteria decision aid (MCDA) methods for incorporating conflicting objectives and decision makers’ preferences into spatial decision models. In this paper, we present spatial UTASTAR (S-UTASTAR), a raster-based MC-SDSS for land-use suitability analysis. The multicriteria component of the system is based on the UTA-type disaggregation-aggregation approach. S-UTASTAR is applied in a raster-based case study concerning land-use suitability analysis to identify appropriate municipal solid waste landfill (MSW) sites in Northeast Greece. Moreover, robustness analysis tools are implemented to guarantee robust decision support results. More specifically, during the aggregation phase, the Stochastic Multiobjective Acceptability Analysis (SMAA) is used to indicate the frequency at which a site achieves the best ranking positions within a large set of alternative landfill sites.     

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.     

模糊环境下的一种多准则决策方法

本文利用模糊集理论以及层次分析法（AHP）原理，建立了一种在模糊环境下对方案进行择优或排序的多准则决策方法。     

A robust additive consistency-based method for decision making with triangular fuzzy reciprocal preference relations

To express uncertain information in decision making, triangular fuzzy reciprocal preference relations (TFRPRs) might be adopted by decision makers. Considering consistency of this type of preference relations, this paper defines a new additive consistency concept, which can be seen as an extension of that for reciprocal preference relations. Then, a simple method to calculate the triangular fuzzy priority weight vector is introduced. When TFRPRs are inconsistent, a linear goal programming framework to derive the completely additive consistent TFRPRs is provided. Meanwhile, an improved linear goal programming model is constructed to estimate the missing values in an incomplete TFRPR that can address the situation where ignored objects exist. After that, an algorithm for decision making with TFRPRs is presented. Finally, numerical examples and comparison analysis are offered.     

Modeling uncertainty in multi-criteria decision analysis

his paper provides a review of multiple criteria decision analysis (MCDA) for cases where attribute evaluations are uncertain. The main aim is to identify different tools which can be used to represent uncertain evaluations, and to broadly survey the available decision models that can be used to support uncertain decision making. The review includes models using probabilities or probability-like quantities; explicit risk measures such as quantiles and variances; fuzzy numbers, and scenarios. The practical assessment of uncertain outcomes and preferences associated with these outcomes is also discussed.     

Handling imprecise evaluations in multiple criteria decision aiding and robust ordinal regression by <Emphasis Type="Italic">n</Emphasis>-point intervals

We consider imprecise evaluation of alternatives in multiple criteria ranking problems. The imprecise evaluations are represented by n-point intervals which are defined by the largest interval of possible evaluations and by its subintervals sequentially nested one in another. This sequence of subintervals is associated with an increasing sequence of plausibility, such that the plausibility of a subinterval is greater than the plausibility of the subinterval containing it. We explain the intuition that stands behind this proposal, and we show the advantage of n-point intervals compared to other methods dealing with imprecise evaluations. Although n-point intervals can be applied in any multiple criteria decision aiding (MCDA) method, in this paper, we focus on their application in robust ordinal regression which, unlike other MCDA methods, takes into account all compatible instances of an adopted preference model, which reproduce an indirect preference information provided by the decision maker. An illustrative example shows how the method can be applied in practice.     

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.     

Preference disaggregation and statistical learning for multicriteria decision support: A review

Disaggregation methods have become popular in multicriteria decision aiding (MCDA) for eliciting preferential information and constructing decision models from decision examples. From a statistical point of view, data mining and machine learning are also involved with similar problems, mainly with regard to identifying patterns and extracting knowledge from data. Recent research has also focused on the introduction of specific domain knowledge in machine learning algorithms. Thus, the connections between disaggregation methods in MCDA and traditional machine learning tools are becoming stronger. In this paper the relationships between the two fields are explored. The differences and similarities between the two approaches are identified, and a review is given regarding the integration of the two fields.     

Behavioural decision theory for multi-criteria decision analysis: a guided tour

Multi-criteria decision analysis (MCDA) involves asking decision makers difficult questions, and can leave them thinking that their judgements are not as coherent as they might have thought. This experience can be distressing and may even lead to rejection of the analysis. The psychology of preference sheds light both on how people naturally make choices without decision analytic assistance, and on how people think about the MCDA elicitation questions. As such, it can help the analyst to respond helpfully to difficulties which decision makers may face. In this paper, we review research from Behavioural Decision Theory relevant to MCDA. Our review follows the MCDA process, discussing research relevant to the structuring, value elicitation, and weighting phases of the analysis, outlining relevant and important findings, and open questions for research and practice.