Optimization Models Using Fuzzy Sets and Possibility Theory

1. Front Matter

   Pages i-xii

   PDF

2. Introductory Sections

   1. Front Matter

      Pages 1-1

      PDF

   2. New Paradigms in Systems Engineering: From “Hard” to “Soft” Approaches

      • Brian R. Gaines

      Pages 3-12

   3. Introduction to Fuzzy Sets and Possibility Theory

      • Mario Fedrizzi

      Pages 13-26

   4. Introduction to Decision Making under Various Kinds of Uncertainty

      • Thomas Whalen

      Pages 27-49

   5. Fuzzy Optimization and Mathematical Programming: A Brief Introduction and Survey

      • Janusz Kacprzyk, Sergei A. Orlovski

      Pages 50-72

3. Advances in Fuzzy Decision Making, Fuzzy Optimization, and Fuzzy Mathematical Programming

   1. Front Matter

      Pages 73-73

      PDF

   2. Fuzzy Preferences and Choice

      1. Fuzzy Preferences in an Optimization Perspective

         • Marc Roubens, Philippe Vincke

         Pages 77-90

      2. Preference and Choice in a Fuzzy Environment

         • Serge Ovchinnikov

         Pages 91-98

      3. Fuzzy Choice

         • V. B. Kuz’min, S. I. Travkin

         Pages 99-109

      4. Preferences Deduced from Fuzzy Questions

         • Bernadette Bouchon

         Pages 110-120

   3. Aspects of Fuzzy Decision Making and Optimization

      1. Optimal Alternative Selection in The Face of Evidential Knowledge

         • Ronald R. Yager

         Pages 123-140

      2. Analysis of Fuzzy Evidence in Decision Making Models

         • V. I. Glushkov, A. N. Borisov

         Pages 141-153

      3. Fuzzy Inclusions and Fuzzy Dichotomous Decision Procedures

         • L. M. Kitainik

         Pages 154-170

      4. Combinatorial Search with Fuzzy Estimates

         • Didier Dubois, Henri Farreny, Henri Prade

         Pages 171-185

      5. Linear Regression Analysis by Possibilistic Models

         • H. Tanaka, J. Watada, K. Asai

         Pages 186-199

   4. Fuzzy Multicriteria Decision Making, Optimization, and Mathematical Programming: Analysis, Solution Procedures, and Interactive Approaches

      1. A Fuzzy Multicriteria Decision Making Model

         • Vladimir E. Zhukovin

         Pages 203-215

      2. Fuzzy Programming — A New Model of Optimization

         • Feng Yingjun

         Pages 216-225

      3. Fuzzy Programming and the Multicriteria Decision Problem

         • J. J. Buckley

         Pages 226-244

      4. Hierarchical Programming With Fuzzy Objectives and Constraints

         • Yee Leung

         Pages 245-257

Optimization is of central concern to a number of discip­ lines. Operations Research and Decision Theory are often consi­ dered to be identical with optimizationo But also in other areas such as engineering design, regional policy, logistics and many others, the search for optimal solutions is one of the prime goals. The methods and models which have been used over the last decades in these areas have primarily been "hard" or "crisp", i. e. the solutions were considered to be either fea­ sible or unfeasible, either above a certain aspiration level or below. This dichotomous structure of methods very often forced the modeller to approximate real problem situations of the more-or-less type by yes-or-no-type models, the solutions of which might turn out not to be the solutions to the real prob­ lems. This is particularly true if the problem under considera­ tion includes vaguely defined relationships, human evaluations, uncertainty due to inconsistent or incomplete evidence, if na­ tural language has to be modelled or if state variables can only be described approximately. Until recently, everything which was not known with cer­ tainty, i. e. which was not known to be either true or false or which was not known to either happen with certainty or to be impossible to occur, was modelled by means of probabilitieso This holds in particular for uncertainties concerning the oc­ currence of events.

• calculus
• decision making
• decision support
• fuzzy sets
• linear optimization
• mathematical programming
• nonlinear optimization
• optimization
• regression
• regression analysis

• Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

  J. Kacprzyk

• International Institute for Applied Systems Analysis, Laxenburg, Austria

  S. A. Orlovski

Policies and ethics