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Fuzzy Geometric Programming

✍ Scribed by Bing-Yuan Cao (auth.)


Publisher
Springer US
Year
2002
Tongue
English
Leaves
280
Series
Applied Optimization 76
Edition
1
Category
Library

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✦ Synopsis


Fuzzy geometric programming was originated by the author in the ProceedΒ­ ing of the second IFSA conferences, 1987(Tokyo) 14 years ago. Later, the paper was invited for formal publication in the International Journal of Fuzzy Sets and Systems. From then on, more and more papers have been written by scholars all over the world who have been interested in its research. So this programming method has been acknowledged by experts and has gradually formed a new branch of fuzzy mathematics. lnspired by Zadeh's fuzzy sets theory, fuzzy geometric programming emerges from the combination of fuzzy sets theory with geometric programming, where models are built in the fuzzy posynomial and the reverse geometric programΒ­ ming. The present book is intended to discuss fuzziness of objective function and constraint conditions, a variety of fuzzy numbers in coefficients and variΒ­ ables and problems about multi-objective fuzzy geometric programming. It establishes and rounds out an entire theory system, showing that there exist conditions of fuzzy optimal or most satisfactory solutions in fuzzy geometric ptogramming, and it develops some effective algorithms. In order to introduce this new branch, the book aims at the exposition of three points: encompassing ideas and conception, theory and methods, and diffusion and application. lt lays more emphasis on the second point than the first one, and less on the third. Besides, it introduces some knowledge of classical geometric programming and of fuzzy sets theory and application examples of fuzzy geometric programming in electric power systems as weil.

✦ Table of Contents


Front Matter....Pages i-xix
Mathematical Preliminaries....Pages 1-22
Fuzzy Posynomial Geometric Programming....Pages 23-63
Fuzzy Strongly Dual Results for Fuzzy PGP....Pages 65-94
Initial Study of Fuzzy Reverse PGP....Pages 95-114
Geometric Programming with Fuzzy Coefficients....Pages 115-148
Programming with Fuzzy Variables....Pages 149-180
Fuzzy Multi-Objective Programming....Pages 181-214
Application of Fuzzy Geometric Programming....Pages 215-234
Antinomy and Fuzzy GP Research Directions....Pages 235-254
Bibliography....Pages 255-261
Back Matter....Pages 263-267

✦ Subjects


Mathematical Logic and Foundations; Optimization; Complexity; Operation Research/Decision Theory


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