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Author
Ramik Jaroslav (Silesian University Karvina)
Title
Duality in Fuzzy Multiple Objective Linear Programming with Possibility and Necessity Relations
Source
Multiple Criteria Decision Making / University of Economics in Katowice, 2006, vol. 1, s. 201-224, tab., bibliogr. 13 poz.
Keyword
Programowanie liniowe, Zbiory rozmyte
Linear programming, Fuzzy sets
Note
Korespondencja z redakcją: numeracja wpisana za zgodą redakcji (wynika z ciągłości wydawniczej serii MCDM) - brak numeracji na stronie tytułowej
Abstract
W artykule przedstawiono problemy klasy wieloobiektowego programowania liniowego rozmytego (FMOLP) z rozmytymi współczynnikami opartymi na związkach rozmytych. Zostały określone pojęcia realnych oraz (α,β) - maksymalnych i minimalnych rozwiązań. Klasa problemów precyzyjnego (klasycznego) wieloobiektowego programowania liniowego (MOLP) może być włączona do klasy FMOLP. Ponadto dla problemów FMOLP zostało przedstawione nowe pojęcie dwoistości oraz wyprowadzono słabe i mocne twierdzenia dwoistości. Pojęcia i rezultaty przedstawione w artykule są zilustrowane i omówione o prostym przykładzie liczbowym. (AT)

In the paper a class of fuzzy multiple objective linear programming (FMOLP) problems with fuzzy coefficients based on fuzzy relations is introduced. The concepts of feasible and (α,β) - maximal and minimal solutions are defined. The class of crisp (classical) multiple objective linear programming (MOLP) problems can be embedded into the class of FMOLP. Moreover, for FMOLP problems a new concept of duality is introduced and the weak and strong duality theorems are derived. The concepts and results introduced in the paper are illustrated and discussed on a simple numerical example.
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The Library of Warsaw School of Economics
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Bibliography
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ISSN
2084-1531
Language
eng
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