Optimization Models Using Fuzzy Sets and Possibility Theory

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.

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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.

Contenu
Introductory Sections.- New Paradigms in Systems Engineering: From Hard to Soft Approaches.- to Fuzzy Sets and Possibility Theory.- to Decision Making under Various Kinds of Uncertainty.- Fuzzy Optimization and Mathematical Programming: A Brief Introduction and Survey.- Advances in Fuzzy Decision Making, Fuzzy Optimization, and Fuzzy Mathematical Programming.- Fuzzy Preferences in an Optimization Perspective.- Preference and Choice in a Fuzzy Environment.- Fuzzy Choice.- Preferences Deduced from Fuzzy Questions.- Optimal Alternative Selection in The Face of Evidential Knowledge.- Analysis of Fuzzy Evidence in Decision Making Models.- Fuzzy Inclusions and Fuzzy Dichotomous Decision Procedures.- Combinatorial Search with Fuzzy Estimates.- Linear Regression Analysis by Possibilistic Models.- A Fuzzy Multicriteria Decision Making Model.- Fuzzy Programming A New Model of Optimization.- Fuzzy Programming and the Multicriteria Decision Problem.- Hierarchical Programming With Fuzzy Objectives and Constraints.- An Interactive Satisficing Method For Multiobjective Nonlinear Programming Problems With Fuzzy Parameters.- Interactive Polyoptimization for Fuzzy Mathematical Programming.- A Concept of Rule-Based Decision Support Systems.- Fuzzy Optimization in Networks.- On Fuzzy Location Models.- Fuzzy Transportation Problems: A General Analysis.- Fuzzy Parameters in Optimal Allocation of Resources.- Applications.- Analysis of Water Use and Needs in Agriculture Through a Fuzzy Programming Model.- An Interactive Method for Multiobjective Linear Programming with Fuzzy Parameters and Its Application to Water Supply Planning.- Fuzzy Evaluation of Pareto Points and its Application to Hydrocracking Processes.- Optimal Classifier Design Using Fuzzy k-Nearest Neighbor Rules.-Grey Decision Making and its Use for The Determination of Irrigation Strategies.