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Correctness of Fuzzy Inference Systems Based on f -Inclusion

Author

Listed:
  • 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)

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.

Suggested Citation

  • Carolina Díaz-Montarroso & Nicolás Madrid & Eloísa Ramírez-Poussa, 2025. "Correctness of Fuzzy Inference Systems Based on f -Inclusion," Mathematics, MDPI, vol. 13(11), pages 1-35, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1897-:d:1672787
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