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Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty

  • Book
  • © 1990

Overview

Editors:
  1. Roman Slowinski

    1. Technical University of Poznan, Poznan, Poland

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    You can also search for this editor in PubMed   Google Scholar

  2. Jacques Teghem

    1. Faculté Polytechnique de Mons, Mons, Belgium

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Theory and Decision Library D: (TDLD, volume 6)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-viii
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  4. The Fuzzy Approach

    1. Front Matter

      Pages 189-189
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    2. Interactive Decision Making for Multiobjective Programming Problems with Fuzzy Parameters

      • Masatoshi Sakawa, Hitoshi Yano
      Pages 191-228

    3. A Possibilistic Approach for Multiobjective Programming Problems. Efficiency of Solutions

      • M. Delgado, J. L. Verdegay, M. A. Vila
      Pages 229-248

    4. ’FLIP’: An Interactive Method for Multiobjective Linear Programming with Fuzzy Coefficients

      • R. SłowińSki
      Pages 249-262

    5. Application of the ’FLIP’ Method to Farm Structure Optimization under Uncertainty

      • P. Czyżak
      Pages 263-278

    6. Fulpal — An Interactive Method for Solving (Multiobjective) Fuzzy Linear Programming Problems

      • H. Rommelfanger
      Pages 279-299

    7. Multiple Objective Linear Programming Problems in the Presence of Fuzzy Coefficients

      • M. K. Luhandjula, Masatoshi Sakawa
      Pages 301-320

    8. Inequality Constraints between Fuzzy Numbers and Their Use in Mathematical Programming

      • Marc Roubens
      Pages 321-330
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Keywords

About this book

Operations Research is a field whose major contribution has been to propose a rigorous fonnulation of often ill-defmed problems pertaining to the organization or the design of large scale systems, such as resource allocation problems, scheduling and the like. While this effort did help a lot in understanding the nature of these problems, the mathematical models have proved only partially satisfactory due to the difficulty in gathering precise data, and in formulating objective functions that reflect the multi-faceted notion of optimal solution according to human experts. In this respect linear programming is a typical example of impressive achievement of Operations Research, that in its detenninistic fonn is not always adapted to real world decision-making : everything must be expressed in tenns of linear constraints ; yet the coefficients that appear in these constraints may not be so well-defined, either because their value depends upon other parameters (not accounted for in the model) or because they cannot be precisely assessed, and only qualitative estimates of these coefficients are available. Similarly the best solution to a linear programming problem may be more a matter of compromise between various criteria rather than just minimizing or maximizing a linear objective function. Lastly the constraints, expressed by equalities or inequalities between linear expressions, are often softer in reality that what their mathematical expression might let us believe, and infeasibility as detected by the linear programming techniques can often been coped with by making trade-offs with the real world.

Editors and Affiliations

  • Technical University of Poznan, Poznan, Poland

    Roman Slowinski

  • Faculté Polytechnique de Mons, Mons, Belgium

    Jacques Teghem

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