Extension-principle-based Solution Algorithm to Full LR-fuzzy Linear Programming Problems

In the literature one can find various methods for solving full fuzzy linear programming problems. Very few of them fully comply to the extension principle, even though it is known that errors or misinterpretations might arise by ignoring or superficially utilizing it. In the current study we extend an existing solution approach based on the extension principle to derive fuzzy-set optimal results to full fuzzy linear programming problems with LR fuzzy parameters. Our approach is a twofold extension of a procedure from the literature: (i) it employs LR membership functions in the optimization models that derive fuzzy-set optimal objective values; and (ii) it introduces new optimization models for deriving fuzzy-set optimal solution values in accordance to the extension principle and product operator. The developed approach derives more realistic results than those found in the literature, since it works in full accordance to the extension principle. Moreover, the employment of the product operator makes the derived fuzzy-set results more thinner, thus more appropriate from a practical point of view.

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1. Main Track: Short Papers

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2. Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).