Duality in fuzzy linear programming with possibility and necessity relations

Authors:
Jaroslav Ramík
Affiliations:
Faculty of Economics, VSB - Technical University Ostrava, Czech Republic and Faculty of Business Administration, Department of Mathematical Methods in Economics, Silesian University, Karviná, ...
Venue:
Fuzzy Sets and Systems
Year:
2006

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Abstract

A class of fuzzy linear programming (FLP) problems with fuzzy coefficients based on fuzzy relations is introduced, the concepts of feasible and (@a,@b)-maximal and minimal solutions are defined. The class of crisp (classical) 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 introduced concepts and results are illustrated and discussed on a simple numerical example.