Fuzzy linear programming and applications

Heinrich Rommelfanger

Institute of Statistics and Mathematics, J.W. Goethe

University of Frankfurt am Main, D-60054 Frankfurt am Main, Germany

FS 09

Abstract

This paper presents a survey on methods for solving fuzzy linear programs. First LP models with soft constraints are discussed.

Then LP problems in which coefficients of constraints and/or of the objective function may be fuzzy are outlined. Pivotal questions are the interpretation of the inequality relation in fuzzy constraints and the meaning of fuzzy objectives.

In addition to the commonly applied extended addition, based on the min-operator and used for the aggregation of the left-hand sides of fuzzy constraints and fuzzy objectives, a more flexible procedure, based on Yager's parametrized t-norm Tp, is presented.

Finally practical applications of fuzzy linear programs are listed,

Keywords:

Fuzzy sets; Mathematical Programming; Extended addition of fuzzy intervals; Compromise solution; Inequality relation in fuzzy conslraints