The -index of inclusion as optimal adjoint pair for fuzzy modus ponens

 

Abstract

We continue studying the properties of the f-index of inclusion and show that, given a fixed pair of fuzzy sets, their f-index of inclusion can be linked to a fuzzy conjunction which is part of an adjoint pair. We also show that, when this pair is used as the underlying structure to provide a fuzzy interpretation of the modus ponens inference rule, it provides the maximum possible truth-value in the conclusion among all those values obtained by fuzzy modus ponens using any other possible adjoint pair.

Citation

Please, cite this work as:

[MO23] N. Madrid and M. Ojeda-Aciego. “The f-index of inclusion as optimal adjoint pair for fuzzy modus ponens”. In: Fuzzy Sets Syst. 466 (2023), p. 108474. DOI: 10.1016/J.FSS.2023.01.009. URL: https://doi.org/10.1016/j.fss.2023.01.009.

BibTeX

@Article{Madrid2023,
     author = {Nicol{’a}s Madrid and Manuel Ojeda-Aciego},
     journal = {Fuzzy Sets Syst.},
     title = {The -index of inclusion as optimal adjoint pair for fuzzy modus ponens},
     year = {2023},
     pages = {108474},
     volume = {466},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/journals/fss/MadridO23.bib},
     doi = {10.1016/J.FSS.2023.01.009},
     timestamp = {Tue, 12 Sep 2023 01:00:00 +0200},
     url = {https://doi.org/10.1016/j.fss.2023.01.009},
}

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7

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7 Total citations

6 Recent citations

6.98 Field Citation Ratio

n/a Relative Citation Ratio

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• CrossRef - Citation Indexes: 1
• Scopus - Citation Indexes: 7

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Cites

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Papers citing this work

The following is a non-exhaustive list of papers that cite this work:

[1] C. Díaz-Montarroso, N. Madrid, and E. Ramírez-Poussa. “Towards a Generalized Modus Ponens Based on the $$\varphi$$-Index of Inclusion”. In: Conceptual Knowledge Structures. Springer Nature Switzerland, 2024, p. 36–48. ISBN: 9783031678684. DOI: 10.1007/978-3-031-67868-4_3. URL: http://dx.doi.org/10.1007/978-3-031-67868-4_3.

[2] J. Dombi and T. Jónás. “Approximate reasoning based on the preference implication”. In: Fuzzy Sets and Systems 499 (Jan. 2025), p. 109187. ISSN: 0165-0114. DOI: 10.1016/j.fss.2024.109187. URL: http://dx.doi.org/10.1016/j.fss.2024.109187.

[3] T. Flaminio, L. Godo, N. Madrid, et al. “A Logic to Reason About f-Indices of Inclusion over Ł$$_n$$”. In: Fuzzy Logic and Technology, and Aggregation Operators. Springer Nature Switzerland, 2023, p. 530–539. ISBN: 9783031399657. DOI: 10.1007/978-3-031-39965-7_44. URL: http://dx.doi.org/10.1007/978-3-031-39965-7_44.

[4] N. Madrid, M. Ojeda‐Aciego, and E. Ramírez‐Poussa. “On the φ$$\varphi$$‐Index of Inclusion: Studying the Structure Generated by a Subset of Indexes”. In: Mathematical Methods in the Applied Sciences (Feb. 2025). ISSN: 1099-1476. DOI: 10.1002/mma.10833. URL: http://dx.doi.org/10.1002/mma.10833.

[5] N. Madrid and E. Ramírez-Poussa. “Analysis of the $$\varphi$$-Index of Inclusion Restricted to a Set of Indexes”. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Springer Nature Switzerland, 2024, p. 3–11. ISBN: 9783031740039. DOI: 10.1007/978-3-031-74003-9_1. URL: http://dx.doi.org/10.1007/978-3-031-74003-9_1.