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  • 1
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    ISSN: 0020-7373
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Computer Science
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1129-6569
    Keywords: Rough set theory ; knowledge analysis ; information system ; indiscemibility relation among objects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Riassunto Nella teoria degli insiemi apprissimati, la relazione di indiscemibilità trao oggetti costituisce il punto di partenza della definizione della coppia di insiemi, chiamati rispettivamente approssimazione superiore ed inferiore, che caratterizzano ciascun insieme. Se gli oggetti sono descritti mediante atributi di natura quantitativa, occorre suddividere il dominio di ciascuno di questi in sottointervalli, mediante l'introduzione di opportuni confini. Per analizzare l'effetto dell'arbitrarietà della scelta di tali valori, si introducono delle soglie additive e si considerano le zone di sovrapposizione di tali sottointervalli, definendo opportunamente relazioni di indiscemibilità forte e debole. Siggene ralizzano quindi i concetti di approssimazione superiore ed infereiore, gli indicaartori della qualità dell'approssimazione e le regole decisionali stesse, fornendone un'esemplificazione applicativa.
    Notes: Abstract Rough set theory is a formal tool for analysis of knowledge gained by experience. The knowledge is represented by a data set organized in a table called information system. Rows of the table correspond to objects and columns to attributes. The idea of the rough set consists in approximation of a set of objects by a pair of sets called lower and upper approximation. The definition of the approximations follows from an indiscernibility relation between objects. Objects are described by attributyes of qualitative or quantitative nature. In the case of quantitative atrributes, the indiscrenibility relation has been defined after partition of the real scale into a finite number of intervals. The bounds of the intervals are more or less arbitrary and may influence the result of the rough set analysis. In order to capture this influence, we consider overlapped intervals and introduce for them a strict and a weak indiscernibility relation. Then, we generalize the lower and upper approximations, the measures of the quality of approximation and the concept of decision rules.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: 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.
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1432-5217
    Keywords: scheduling ; production ; resource constraints ; flexible manufacturing systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Abstract Some variations are presented for the preemptive scheduling problem on unrelated processors, one shows how nonrenewable resources with a time-varying supply may be taken into account in an extension of the two-phase method; phase 1 consists in solving an LP problem and phase 2 is the construction of the schedule; such a construction reduces to the determination of integral vectors in polyhedra defined by totally unimodular matrices. In special cases, this is simply a compatible flow problem.
    Notes: Zusammenfassung Es werden Variationen für Reihenfolgeprobleme mit Unterbrechungen betrachtet bei denen die Aufgaben mit unterschiedlicher Bearbeitungszeit auf den einzelnen Maschinen gelöst werden können. Insbesondere wird ein Problem mit nichterneuerbaren Resourcen und zeitabhängigen Nachfragen behandelt und es wird gezeigt, daß dieses Problem durch eine Erweiterung der 2-Phasenmethode gelöst werden kann. In Phase 1 wird ein LP gelöst, während in Phase 2 ein zugehöriger Schedule konstruiert wird. Diese Konstruktion erfolgt durch die Bestimmung ganzzahliger Vektoren, die Ecken eines Polyeders entsprechen, der durch eine vollständig unimodulare Matrix definiert wird. In Spezialfällen reduziert sich dies auf Flußprobleme.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of global optimization 12 (1998), S. 157-174 
    ISSN: 1573-2916
    Keywords: Multiple criteria decision aid ; sorting problem ; ELECTRE TRI method ; parameters' elicitation ; inference procedure ; optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given a finite set of alternatives, the sorting problem consists in the assignment of each alternative to one of the pre-defined categories. In this paper, we are interested in multiple criteria sorting problems and, more precisely, in the existing method ELECTRE TRI. This method requires the elicitation of parameters (weights, thresholds, category limits,...) in order to construct the Decision Maker's (DM) preference model. A direct elicitation of these parameters being rather difficult, we proceed to solve this problem in a way that requires from the DM much less cognitive effort. We elicit these parameters indirectly using holistic information given by the DM through assignment examples. We propose an interactive approach that infers the parameters of an ELECTRE TRI model from assignment examples. The determination of an ELECTRE TRI model that best restitutes the assignment examples is formulated through an optimization problem. The interactive aspect of this approach lies in the possibility given to the DM to revise his/her assignment examples and/or to give additional information before the optimization phase restarts.
    Type of Medium: Electronic Resource
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