Abstract
This paper presents a method for solving (multicriteria) linear programs, where the right-hand sides as well as the coefficients in the constraints and/or the objective function(s) may be fuzzy. This approach is based on a new interpretation of the inequality-relation “\( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{ \leqq } \)”. Here a fuzzy constraint is replaced by a crisp inequality and a fuzzy objective function (utility function).
This interpretation coincides with the well-known concepts in crisp inequalities and in soft constraints.
The decision procedure is modelled as an interactive man-machine process, called FULPAL (Fuzzy linear programming based on aspiration levels), which can be controlled by aspiration levels. This general method includes the procedure for solving LP-problems with soft constraints, proposed by ZIMMERMANN [1978],[ROMMELFANGER 1983], [WERNERS 1984] a.o.
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Rommelfanger, H. (1990). Fulpal — An Interactive Method for Solving (Multiobjective) Fuzzy Linear Programming Problems. In: Slowinski, R., Teghem, J. (eds) Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty. Theory and Decision Library, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2111-5_14
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DOI: https://doi.org/10.1007/978-94-009-2111-5_14
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