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This paper presents a new method for solving linear programming papers with fuzzy parameters in the objective function. To determine a compromise solution the authors do not reduce the set of infinitely many objective functions to a single "compromise objective function" as done in classical deterministic or stochastic procedures. Here the problem is only reduced to a few extreme objective functions. The information contained in the membership functions can be used to any extent by a method called "alpha -level related pair formation". Moreover, if different level sets are considered the stability of the optimal solution can be tested.

@article{rommelfanger_linear_1989, title = {Linear programming with fuzzy objectives}, volume = {29}, url = {http://dx.doi.org/10.1016/0165-0114(89)90134-6}, doi = {10.1016/0165-0114(89)90134-6}, abstract = {This paper presents a new method for solving linear programming papers with fuzzy parameters in the objective function. To determine a compromise solution the authors do not reduce the set of infinitely many objective functions to a single "compromise objective function" as done in classical deterministic or stochastic procedures. Here the problem is only reduced to a few extreme objective functions. The information contained in the membership functions can be used to any extent by a method called "alpha -level related pair formation". Moreover, if different level sets are considered the stability of the optimal solution can be tested.}, number = {1}, journal = {Fuzzy Sets Syst.}, author = {Rommelfanger,, H. and Hanuscheck,, R. and Wolf,, J.}, year = {1989}, pages = {31--48} }

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