Fuzzy Geometric Programming (Applied Optimization, 76)

Fuzzy geometric programming was originated by the author in the Proceed­ 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 program­ ming. The present book is intended to discuss fuzziness of objective function and constraint conditions, a variety of fuzzy numbers in coefficients and vari­ 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. The Book Gives Readers A Thorough Understanding Of Fuzzy Geometric Programming, A Field That Was Originated By The Author. It Is Organized Into Two Parts: Theory And Applications. The Former Aims At Development Of Issues Including Fuzzy Posynomial Geometric Programming And Its Dual Form, A Fuzzy Reverse Posynomial Geometric Programming And Its Dual Form And A Geometric Programming Model With Fuzzy Coefficients And Fuzzy Variables. The Latter Is Intended To Discuss Problems In Applications, Including Antinomy In Fuzzy Geometric Programming, As Well As Practical Examples From The Power Of Industry And The Administration Of Postal Services. Audience: Researchers, Doctoral And Post-doctoral Students Working In Fuzzy Mathematics, Applied Mathematics, Engineering, Operations Research, And Economics. List Of Figures -- List Of Tables -- Preface.-acknowledgements -- Introduction Of Author -- 1. Mathematical Preliminaries -- 2. Fuzzy Posynomial Geometric Programming -- 3. Fuzzy Strongly Dual Results For Fuzzy Pgp -- 4. Initial Study Of Fuzzy Reverse Pgp -- 5. Geometric Programming With Fuzzy Coefficients -- 6. Programming With Fuzzy Variables -- 7. Fuzzy Multi-objective Programming -- 8. Application Of Fuzzy Geometric Programming -- 9. Antinomy And Fuzzy Gp Research Directions -- Bibliography -- Index. By Bing-yuan Cao. 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