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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MDPI AG
2025-06-01
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| author | Carolina Díaz-Montarroso Nicolás Madrid Eloísa Ramírez-Poussa |
| author_facet | Carolina Díaz-Montarroso Nicolás Madrid Eloísa Ramírez-Poussa |
| author_sort | Carolina Díaz-Montarroso |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-072f921e40ba4f2d937f5a4b4262de01 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-072f921e40ba4f2d937f5a4b4262de012025-08-20T03:11:19ZengMDPI AGMathematics2227-73902025-06-011311189710.3390/math13111897Correctness of Fuzzy Inference Systems Based on <i>f</i>-InclusionCarolina Díaz-Montarroso0Nicolás Madrid1Eloísa Ramírez-Poussa2Department of Mathematics, University of Cádiz, C. Republica Saharaui, 11510 Puerto Real, SpainDepartment of Mathematics, University of Cádiz, C. Republica Saharaui, 11510 Puerto Real, SpainDepartment of Mathematics, University of Cádiz, C. Republica Saharaui, 11510 Puerto Real, SpainRecent 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.https://www.mdpi.com/2227-7390/13/11/1897fuzzy logic<i>f</i>-index of inclusionfuzzy inference systemfuzzy description logicinclusion measures |
| spellingShingle | Carolina Díaz-Montarroso Nicolás Madrid Eloísa Ramírez-Poussa Correctness of Fuzzy Inference Systems Based on <i>f</i>-Inclusion Mathematics fuzzy logic <i>f</i>-index of inclusion fuzzy inference system fuzzy description logic inclusion measures |
| title | Correctness of Fuzzy Inference Systems Based on <i>f</i>-Inclusion |
| title_full | Correctness of Fuzzy Inference Systems Based on <i>f</i>-Inclusion |
| title_fullStr | Correctness of Fuzzy Inference Systems Based on <i>f</i>-Inclusion |
| title_full_unstemmed | Correctness of Fuzzy Inference Systems Based on <i>f</i>-Inclusion |
| title_short | Correctness of Fuzzy Inference Systems Based on <i>f</i>-Inclusion |
| title_sort | correctness of fuzzy inference systems based on i f i inclusion |
| topic | fuzzy logic <i>f</i>-index of inclusion fuzzy inference system fuzzy description logic inclusion measures |
| url | https://www.mdpi.com/2227-7390/13/11/1897 |
| work_keys_str_mv | AT carolinadiazmontarroso correctnessoffuzzyinferencesystemsbasedonifiinclusion AT nicolasmadrid correctnessoffuzzyinferencesystemsbasedonifiinclusion AT eloisaramirezpoussa correctnessoffuzzyinferencesystemsbasedonifiinclusion |