Sensitivity analysis for the ELECTRE multicriteria method

In this paper, we develop sensitivity ranges for parameters used in the ELECTRE I multicriteria decision method. Parameters studied include criteria weights as well as significance thresholds. For these parameters, intervals are determined in which parameter changes will not affect the set of non-outranked alternatives. The approach developed is illustrated by a numerical example and possible applications are discussed.

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Zusammenfassung In dieser Arbeit wird ein Ansatz zur Sensitivitätsanalyse für das Multikriteria-Entscheidungsverfahren ELECTRE I vorgestellt. Für die Gewichte der Kriterien sowie die im Verfahren verwendeten Signifikanzschwellen werden jeweils Intervalle konstruiert, innerhalb derer Parameteränderungen keine Änderungen im Ergebnis des Verfahrens bewirken. Die entwickelte Sensitivitätsanalyse wird anhand eines Beispiels illustriert und mögliche Anwendungen des Konzeptes werden aufgezeigt.

     

Business failure prediction using the UTADIS multicriteria analysis method

Business failure prediction is one of the most essential problems in the field of financial management. The research on developing quantitative business failure prediction models has been focused on building discriminant models to distinguish among failed and non-failed firms. Several researchers in this field have proposed multivariate statistical discrimination techniques. This paper explores the applicability of multicriteria analysis to predict business failure. Four preference disaggregation methods, namely the UTADIS method and three of its variants, are compared to three well-known multivariate statistical and econometric techniques, namely discriminant analysis, logit and probit analyses. A basic (learning) sample and a holdout (testing) sample are used to perform the comparison. Through this comparison, the relative performance of all the aforementioned methods is investigated regarding their discriminating and predicting ability.     

Solving large-scale multicriteria problems by the decomposition method

The problem of constructing a set of effective vector estimates under a large number of partial performance criteria is examined.     

An approximate solution of linear multicriteria control problems through the multicriteria simplex method

This paper deals with multicriteria, linear, continuous optimal control problems through the application of the multicriteria simplex method. Since the system is linear, the state variables at a given time can be expressed in terms of definite integrals. Upon using standard numerical integration formulas, the definite integrals are approximately expressed by means of weighted sums of the integrands. Then, after introducing some suitable auxiliary variables, approximate linear multicriteria programming problems are formulated. Illustrative numerical examples are provided to indicate the efficiency of the proposed method.The author is indebted to Professor Y. Sawaragi of Kyoto University for his constant encouragement. The author also wishes to thank T. Suwa for his cooperation in preparing the programming for the digital computer.     

Some considerations concerning the presentations of universal algebras

The aim of this work is to present some proposals of a general definition of a presentation for universal algebras and some basic conclusions originating from this definition. Next, we formulate Tietze's theorem for varieties of universal algebras in a form which is a generalization of the method used in [4] for groups.The author is greatful to the referee for his helpful suggestions which influenced the version of this paper.Presented by G. Grätzer.     

Decision making in multiobjective optimization aided by the multicriteria tournament decision method

This paper proposes a new method for multicriteria analysis, named Multicriteria Tournament Decision (MTD). It provides the ranking of alternatives from best to worst, according to the preferences of a human decision-maker (DM). It has some positive aspects such as: it has a simple algorithm with intuitive appeal; it involves few input parameters (just the importance weight of each criterion).The helpfulness of MTD is demonstrated by using it to select the final solution of multiobjective optimization problems in an a posteriori decision making approach. Having at hand a discrete approximation of the Pareto front (provided by a multiobjective evolutionary search algorithm), the choice of the preferred Pareto-optimal solution is performed using MTD.A simple method, named Gain Analysis method (GAM), for verifying the existence of a better solution (a solution associated to higher marginal rates of return) than the one originally chosen by the DM, is also introduced here. The usefulness of MTD and GAM methods is confirmed by the suitable results shown in this paper.     

Decision making in multiobjective optimization aided by the multicriteria tournament decision method

This paper proposes a new method for multicriteria analysis, named Multicriteria Tournament Decision (MTD). It provides the ranking of alternatives from best to worst, according to the preferences of a human decision-maker (DM). It has some positive aspects such as: it has a simple algorithm with intuitive appeal; it involves few input parameters (just the importance weight of each criterion).The helpfulness of MTD is demonstrated by using it to select the final solution of multiobjective optimization problems in an a posteriori decision making approach. Having at hand a discrete approximation of the Pareto front (provided by a multiobjective evolutionary search algorithm), the choice of the preferred Pareto-optimal solution is performed using MTD.A simple method, named Gain Analysis method (GAM), for verifying the existence of a better solution (a solution associated to higher marginal rates of return) than the one originally chosen by the DM, is also introduced here. The usefulness of MTD and GAM methods is confirmed by the suitable results shown in this paper.     

Some considerations concerning the optimal calculation of stage-discharge functions

Different methods of the computation of curves describing the relation between stage and discharge of a river profile are discussed. Using several measurements of passed years one tries to compute such curves as close to reality as possible.     

Comparative analysis of UTA multicriteria methods

This paper reviews the main variants of the utility additive (UTA) multicriteria method, and systematically compares their predictive performance on two sets of data. It analyses both those cases where the model provides a ranking with errors and those without errors. First, it shows that the reference projects should be chosen carefully in order to elicit as much information as possible from the decision maker: a set of projects satisfying a fractional factorial plan is recommended. Second, it discusses the use of alternative post-optimality methods for solving the problem of multiple solutions and their different predictive performances. Third, it presents the results of simulations based on utility functions involving interdependence between criteria, and shows that UTA handles this problem effectively by an adjustment of its coefficients. Finally, the influence of the model's parameters on the predictive performance is also investigated.     

Postoptimal analysis of the multicriteria combinatorial median location problem

We consider a multicriteria variant of the well-known combinatorial minisum facility location problem (median problem) with Pareto and lexicographic optimality principles. Necessary and sufficient conditions of a solution stability to the initial data perturbations in such problems are formulated in terms of binary relations. Numerical examples are given.     

Some general considerations concerning the destabilizing effect in nonconservative systems

Zusammenfassung Es wird ein lineares System mitN Freiheitsgraden untersucht, beansprucht durch eine Gruppe nichtkonservativer Kräfte, welche linear von den verallgemeinerten Koordinaten abhängen. Mehrere Sätze bezüglich die labilisierende Wirkung von kleinen Kräften, die von den verallgemeinerten Geschwindigkeiten abhängen, werden aufgestellt. Diese Kräfte können von der Dämpfung oder von gyroskopischen Einflüssen herrühren.

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This research was supported by the National Aeronautics and Space Administration under Grant NsG 605.     

Stochastic multicriteria acceptability analysis using the data envelopment model

Data envelopment analysis (DEA) and stochastic multicriteria acceptability analysis (SMAA-2) are methods for evaluating alternatives based on multiple criteria. While DEA is mainly an ex-post tool used for classifying alternatives into efficient and inefficient ones, SMAA-2 is an ex-ante tool for supporting multiple criteria decision-making. Both methods use a kind of value function where the importance of criteria is modeled using weights. Unlike many other methods, neither DEA nor SMAA-2 requires decision-makers’ weights as input. Instead, these so-called non-parametric methods explore the weight space in order to identify weights favorable for each alternative. This paper introduces the SMAA-D method, which is a combination of DEA and SMAA-2. SMAA-D can be characterized as an extension of DEA to handle uncertain or imprecise data to provide stochastic efficiency measures. Alternatively, the combined method can be seen as a variant of SMAA-2 with a DEA-type value function.     

A teaching system using fuzzy subsets and multicriteria analysis

Learning management in the field of didactics demands an evaluation of knowledge and aptitudes which is as precise as possible. The treatment of subjective data will be facilitated by the ‘fuzzy subset theory ‘, a new theory particularly interesting for those connected with the social sciences. Objective data will be dealt with by multicriteria analysis, more precisely, by simultaneously using the Iphigenia method and the hierarchical analysis method.

This will permit us to effect a single partition in a group of students, that is to say, to distribute them into some number of disjointed aggregates.

To each aggregate, we associate a state function characterized by a vector having a component for each evaluated aptitude. If the evaluations succeed each other, each individual will be guided across the different delineated learning steps with maximum efficiency.     

An application of the TODIM method to the multicriteria rental evaluation of residential properties

This article presents an evaluation study of residential properties carried out together with real estate agents in the city of Volta Redonda, Brazil. The study aimed to define a reference value for the rents of these properties using the TODIM method of Multicriteria Decision Aiding. By applying this method to the ordering of properties with different characteristics, a ranking of all the properties was obtained and, as a result of this, diverse ranges of rental values for the properties under analysis. The study was complemented by an analysis of the sensitivity of the numerical results obtained.     

Extensions of the multicriteria analysis with pairwise comparison under a fuzzy environment

Multicriteria decision-making (MCDM) problems often involve a complex decision process in which multiple requirements and fuzzy conditions have to be taken into consideration simultaneously. The existing approaches for solving this problem in a fuzzy environment are complex. Combining the concepts of grey relation and pairwise comparison, a new fuzzy MCDM method is proposed. First, the fuzzy analytic hierarchy process (AHP) is used to construct fuzzy weights of all criteria. Then, linguistic terms characterized by L–R triangular fuzzy numbers are used to denote the evaluation values of all alternatives versus subjective and objective criteria. Finally, the aggregation fuzzy assessments of different alternatives are ranked to determine the best selection. Furthermore, this paper uses a numerical example of location selection to demonstrate the applicability of the proposed method. The study results show that this method is an effective means for tackling MCDM problems in a fuzzy environment.     

Application of the ellipsoid method in an interactive procedure for multicriteria linear programming

The research reported in this paper is concerned with an application of the ellipsoid algorithm in the interactive multicriteria linear programming step method (STEM) byBenayoun et al. [1971]. Due to this application we eliminate some drawbacks of the original version of STEM and, moreover, we avoid extra computations connected with sensitivity analysis in every iteration. Specifically, we use the ellipsoid algorithm to minimize the Euclidean norm in the criterion space instead of the Chebyshev norm, which ensures that every solution submitted to the decision maker is efficient. As follows from a computational experiment, in comparison with the application of the simplex method, the proposed modification of STEM shows a smaller increase of the computational effort when the number of criteria increases. However, the absolute computation time becomes worse for problems of larger size.

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Zusammenfassung In dieser Arbeit wird über eine Anwendungsmöglichkeit der Khachiyan-Shor-Algorithmus (Ellipsoid-Algorithmus) im Rahmen des STEM-Verfahrens zur interaktiven Lösung linearer Vektoroptimierungsmodelle berichtet. Auf diese Weise können einige spezifische Nachteile des STEM-Verfahrens in seiner Originalversion vermieden werden. Durch die Verwendung der Euklidischen Norm anstelle der beim STEM-Verfahren üblichen Tschebyscheff-Norm wird garantiert, daß dem Entscheidungsträger nur effiziente Lösungen vorgeschlagen werden. Die numerischen Erfahrungen zeigen, daß der Lösungsaufwand der hier vorgeschlagenen Modifikation des STEM-Verfahrens mit steigender Anzahl von Zielfunktionen weniger stark zunimmt als bei der üblichen Version. Dies gilt jedoch nicht hinsichtlich der allgemeinen Problemgröße.