Fuzzy mathematical programming: methods and applications
In the last 25 years, the fuzzy set theory has been applied in many disciplines such as operations research, management science, control theory,artificial intelligence/expert system, etc. In this volume, methods and applications of fuzzy mathematical programming and possibilistic mathematical programming are first systematically and thoroughly reviewed and classified. This state-of-the-art survey provides readers with a capsule look into the existing methods, and their characteristics and applicability to analysis of fuzzy and possibilistic programming problems. To realize practical fuzzy modelling, we present solutions for real-world problems including production/manufacturing, transportation, assignment, game, environmental management, resource allocation, project investment, banking/finance, and agricultural economics. To improve flexibility and robustness of fuzzy mathematical programming techniques, we also present our expert decision-making support system IFLP which considers and solves all possibilities of a specific domain of (fuzzy) linear programming problems. Basic fuzzy set theories, membership functions, fuzzy decisions, operators and fuzzy arithmetic are introduced with simple numerical examples in aneasy-to-read and easy-to-follow manner. An updated bibliographical listing of 60 books, monographs or conference proceedings, and about 300 selected papers, reports or theses is presented in the end of this study.
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FUZZY MATHEMATICAL PROGRAMMING
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a-level approach assumed Ax)i Azznj Chanas's computational concept Consider the following crisp linear programming cx s.t. Ax)j decision maker decision problem defined degree of membership discussed equivalent example following auxiliary fuzzy constraints fuzzy linear programming fuzzy mathematical programming Fuzzy Multiple fuzzy numbers fuzzy objective fuzzy resources fuzzy set theory fuzzy subset given go to Step goal b0 Hwang imprecise coefficients inequality interactive fuzzy linear interest rate John is tall linear membership functions linear programming problem long-term securities man-weeks mathematical programming problems max cx s.t. Max Operator max-min operator maximizing minimal non-linear programming objective function obtain the following operations research optimal solution parameters parametric programming possibilistic linear programming preference-based membership functions probability theory problem of Equation production profit proposed Sets and Systems shooter shown in Figure solution of Equation solve Equation stochastic programming techniques truth value variables Verdegay Werners's WSDM Zadeh Zimmermann