Duality in Fuzzy Linear Programming: Some New Concepts and Results

Authors:
Jaroslav Ramík
Affiliations:
Department of Mathematical Methods in Economics, Faculty of Business Administration, Silesian University, Karviná, Czech Republic 733 40
Venue:
Fuzzy Optimization and Decision Making
Year:
2005

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Abstract

A class of fuzzy linear programming (FLP) problems based on fuzzy relations is introduced, the concepts of feasible and α -efficient solutions are defined. The class of crisp (classical) LP problems and interval LP problems can be embedded into the class of FLP ones. Moreover, for FLP problems a new concept of duality is introduced and the weak and strong duality theorems are derived. The previous results are applied to the special case of interval LP and compared to the existing literature.