Authors: Stanojević, Bogdana 
Nǎdǎban, Sorin
Affiliations: Computer Science 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Empiric Solutions to Full Fuzzy Linear Programming Problems Using the Generalized “min” Operator
Journal: Mathematics
Volume: 11
Issue: 23
First page: 4864
Issue Date: 2023
Rank: ~M21a
ISSN: 2227-7390
DOI: 10.3390/math11234864
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.
Keywords: full fuzzy linear programming | fuzzy numbers | extension principle | generalized product | Monte Carlo simulation
Publisher: MDPI

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