Correctness of Fuzzy Inference Systems Based on f -Inclusion

Carolina Díaz-Montarroso, Nicolás Madrid () and Eloísa Ramírez-Poussa
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Carolina Díaz-Montarroso: Department of Mathematics, University of Cádiz, C. Republica Saharaui, 11510 Puerto Real, Spain
Nicolás Madrid: Department of Mathematics, University of Cádiz, C. Republica Saharaui, 11510 Puerto Real, Spain
Eloísa Ramírez-Poussa: Department of Mathematics, University of Cádiz, C. Republica Saharaui, 11510 Puerto Real, Spain

Mathematics, 2025, vol. 13, issue 11, 1-35

Abstract: Recent work has shown that the f -index of inclusion can serve as a foundation for modeling Generalized Modus Ponens. In this paper, we develop a novel fuzzy inference system based on this inference rule. To establish its soundness, we connect it to a Fuzzy Description Logic LU enriched with fuzzy modifiers (also known as fuzzy hedges). This logic background provides to the approach a strength absent in most fuzzy inference systems in the literature, which allows us to formally prove a series of results that culminate in a final correctness theorem for the proposed fuzzy inference system. This paper also presents a running example aimed at showing the potential applicability of the proposal.

Keywords: fuzzy logic; f -index of inclusion; fuzzy inference system; fuzzy description logic; inclusion measures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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