Empiric Solutions to Full Fuzzy Linear Programming Problems Using the Generalized min Operator

Solving optimization problems in a fuzzy environment is an area widely addressed in the recent literature. De-fuzzification of data, construction of crisp more or less equivalent problems, unification of multiple objectives, and solving a single crisp optimization problem are the general descriptions of many procedures that approach fuzzy optimization problems. Such procedures are misleading (since relevant information is lost through de-fuzzyfication and aggregation of more objectives into a single one), but they are still dominant in the literature due to their simplicity. In this paper, we address the full fuzzy linear programming problem, and provide solutions in full accordance with the extension principle. The main contribution of this paper is in modeling the conjunction of the fuzzy sets using the product operator instead of min within the definition of the solution concept. Our theoretical findings show that using a generalized min operator within the extension principle assures thinner shapes to the derived fuzzy solutions compared to those available in the literature. Thinner shapes are always desirable, since such solutions provide the decision maker with more significant information.

Automated summary

Solving optimization problems in a fuzzy environment is a widely discussed topic in recent literature. Most existing methods in this field are misleading due to the loss of relevant information through de-fuzzification and aggregation. In this paper, a new solution method is proposed using the product operator instead of min to model the conjunction of fuzzy sets. Theoretical findings suggest that this method can generate thinner fuzzy solutions, providing decision makers with more significant information.