Correctness of Fuzzy Inference Systems Based on <i>f</i>-Inclusion

Recent work has shown that the <i>f</i>-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 <in...

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Bibliographic Details
Main Authors: Carolina Díaz-Montarroso, Nicolás Madrid, Eloísa Ramírez-Poussa
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/11/1897
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Summary:Recent work has shown that the <i>f</i>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">LU</mi></semantics></math></inline-formula> 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.
ISSN:2227-7390