The outranking approach and the foundations of electre methods
TL;DR: The main features of real-world problems for which the outranking approach is appropriate and the concept of outranking relations are described and the definition of such out ranking relations is given for the main ELECTRE methods.
Abstract: In the first part of this paper, we describe the main features of real-world problems for which the outranking approach is appropriate and we present the concept of outranking relations. The second part is devoted to basic ideas and concepts used for building outranking relations. The definition of such outranking relations is given for the main ELECTRE methods in Part 3. The final part of the paper is devoted to some practical considerations.
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TL;DR: In this article, a new method, called best-worst method (BWM) is proposed to solve multi-criteria decision-making (MCDM) problems, in which a number of alternatives are evaluated with respect to different criteria in order to select the best alternative(s).
Abstract: In this paper, a new method, called best-worst method (BWM) is proposed to solve multi-criteria decision-making (MCDM) problems. In an MCDM problem, a number of alternatives are evaluated with respect to a number of criteria in order to select the best alternative(s). According to BWM, the best (e.g. most desirable, most important) and the worst (e.g. least desirable, least important) criteria are identified first by the decision-maker. Pairwise comparisons are then conducted between each of these two criteria (best and worst) and the other criteria. A maximin problem is then formulated and solved to determine the weights of different criteria. The weights of the alternatives with respect to different criteria are obtained using the same process. The final scores of the alternatives are derived by aggregating the weights from different sets of criteria and alternatives, based on which the best alternative is selected. A consistency ratio is proposed for the BWM to check the reliability of the comparisons. To illustrate the proposed method and evaluate its performance, we used some numerical examples and a real-word decision-making problem (mobile phone selection). For the purpose of comparison, we chose AHP (analytic hierarchy process), which is also a pairwise comparison-based method. Statistical results show that BWM performs significantly better than AHP with respect to the consistency ratio, and the other evaluation criteria: minimum violation, total deviation, and conformity. The salient features of the proposed method, compared to the existing MCDM methods, are: (1) it requires less comparison data; (2) it leads to more consistent comparisons, which means that it produces more reliable results.
2,214 citations
TL;DR: The original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation, but is failing when preference-orders of attribute domains (criteria) are to be taken into account and it cannot handle inconsistencies following from violation of the dominance principle.
1,544 citations
Cites background or methods from "The outranking approach and the fou..."
...The relational model has its most widely known representation in the form of an outranking relation (Roy, 1991) and a fuzzy relation (Fodor and Roubens, 1994)....
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...x does not outrank y (denoted by xScy or x; y 2 Sc), where x; y 2 B, and S [ Sc B, where ``x outranks y'' means ``x is at least as good as y'' Roy (1985); observe that the binary relation S is re ̄exive, but neither necessarily transitive nor complete (Roy, 1991; Bouyssou, 1996)....
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...Rough approximation by means of dominance relations Let Sq be an outranking relation Roy (1985) on U with reference to criterion q 2 C, such that xSqy means ``x is at least as good as y with respect to criterion q''....
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...…where x; y 2 B, 2. x does not outrank y (denoted by xScy or x; y 2 Sc), where x; y 2 B, and S [ Sc B, where ``x outranks y'' means ``x is at least as good as y'' Roy (1985); observe that the binary relation S is re¯exive, but neither necessarily transitive nor complete (Roy, 1991; Bouyssou, 1996)....
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TL;DR: This paper applies support vector machines (SVMs) to the bankruptcy prediction problem in an attempt to suggest a new model with better explanatory power and stability, and shows that SVM outperforms the other methods.
Abstract: Bankruptcy prediction has drawn a lot of research interests in previous literature, and recent studies have shown that machine learning techniques achieved better performance than traditional statistical ones. This paper applies support vector machines (SVMs) to the bankruptcy prediction problem in an attempt to suggest a new model with better explanatory power and stability. To serve this purpose, we use a grid-search technique using 5-fold cross-validation to find out the optimal parameter values of kernel function of SVM. In addition, to evaluate the prediction accuracy of SVM, we compare its performance with those of multiple discriminant analysis (MDA), logistic regression analysis (Logit), and three-layer fully connected back-propagation neural networks (BPNs). The experiment results show that SVM outperforms the other methods.
797 citations
Additional excerpts
...…& Papayan nakis, 1992; Dimitras, Zanakis, & Zopounidis, 1996; Emel et al., 2003; Falbo, 1991; Frydman, Altman, & Kao, 1985; Jo & Han, 1996; Lee, Sung, & Chang, 1999; Martin, 1997; Reichert, Cho, & Wagner, 1983; Roy, 1991; Tam & Kiang, 1992; Troutt et al., 1996; Zopounidis & Doumpos, 1998)....
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TL;DR: A conceptual framework for articulating tentative guidelines to choose an appropriate MCDA method is drawn and the results of the comparison of well known multicriterion aggregation procedures (MCAP) on the basis of these guidelines are presented.
786 citations
References
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01 Jan 1985
TL;DR: Analytic Hierarchy Process (AHP) as mentioned in this paper is a systematic procedure for representing the elements of any problem hierarchically, which organizes the basic rationality by breaking down a problem into its smaller constituent parts and then guides decision makers through a series of pairwise comparison judgments to express the relative strength or intensity of impact of the elements in the hierarchy.
Abstract: This chapter provides an overview of Analytic Hierarchy Process (AHP), which is a systematic procedure for representing the elements of any problem hierarchically. It organizes the basic rationality by breaking down a problem into its smaller constituent parts and then guides decision makers through a series of pair-wise comparison judgments to express the relative strength or intensity of impact of the elements in the hierarchy. These judgments are then translated to numbers. The AHP includes procedures and principles used to synthesize the many judgments to derive priorities among criteria and subsequently for alternative solutions. It is useful to note that the numbers thus obtained are ratio scale estimates and correspond to so-called hard numbers. Problem solving is a process of setting priorities in steps. One step decides on the most important elements of a problem, another on how best to repair, replace, test, and evaluate the elements, and another on how to implement the solution and measure performance.
16,547 citations
Book•
01 Jan 1976TL;DR: In this article, a confused decision maker, who wishes to make a reasonable and responsible choice among alternatives, can systematically probe his true feelings in order to make those critically important, vexing trade-offs between incommensurable objectives.
Abstract: Many of the complex problems faced by decision makers involve multiple conflicting objectives. This book describes how a confused decision maker, who wishes to make a reasonable and responsible choice among alternatives, can systematically probe his true feelings in order to make those critically important, vexing trade-offs between incommensurable objectives. The theory is illustrated by many real concrete examples taken from a host of disciplinary settings. The standard approach in decision theory or decision analysis specifies a simplified single objective like monetary return to maximise. By generalising from the single objective case to the multiple objective case, this book considerably widens the range of applicability of decision analysis.
8,895 citations
01 Jan 1979
TL;DR: In this article, the authors studied the transitivity of preference through a new approach to consistency, which need not always strictly hold for the results to be acceptable, and not all alternatives need to be directly comparable.
Abstract: : The Analytic Hierarchy Process serves as a framework for people to structure their own problems and provide their own judgements based on knowledge, reason or feelings, to derive a set of priorities for activities to which they, for example, wish to allocate effort or resources. In this process transitivity of preference is studied through a new approach to consistency - which need not always strictly hold for the results to be acceptable. Also since hierarchic structures may not be complete, not all alternatives need to be directly comparable. It is necessary to construct a pairwise comparison matrix of the relative contribution or impact of each element on each governing objective or criterion in the adjacent upper level. In such a matrix of the elements by the elements, the elements are compared in a pairwise manner with respect to a criterion in the next level. In comparing the i,j elements, people prefer to give a judgement which indicates the dominance as an integer. Thus, if the dominance does not occur in the i,j position while comparing the ith element with the jth element then it is given in the j,i position as a ji and its reciprocal is automatically assigned to aij.
1,385 citations
01 Jan 1968
1,036 citations
Posted Content•
729 citations