Approaching the square of opposition in terms of the -indexes of inclusion and contradiction

 

Abstract

We continue our research line on the analysis of the properties of the f-indexes of inclusion and contradiction; in this paper, specifically, we show that both notions can be related by means of the, conveniently reformulated, Aristotelian square of opposition. We firstly show that the extreme cases of the f-indexes of inclusion and contradiction coincide with the vertexes of the Aristotelian square of opposition in the crisp case; then, we allocate the rest of f-indexes in the diagonals of the extreme cases and we prove that the Contradiction, Contrariety, Subcontrariety, Subalternation and Superalternation relations also hold between the f-indexes of inclusion and contradiction.

Citation

Please, cite this work as:

[MO24] N. Madrid and M. Ojeda-Aciego. “Approaching the square of opposition in terms of the f-indexes of inclusion and contradiction”. In: Fuzzy Sets Syst. 476 (2024), p. 108769. DOI: 10.1016/J.FSS.2023.108769. URL: https://doi.org/10.1016/j.fss.2023.108769.

BibTeX

@Article{Madrid2024,
     author = {Nicol{’a}s Madrid and Manuel Ojeda-Aciego},
     journal = {Fuzzy Sets Syst.},
     title = {Approaching the square of opposition in terms of the -indexes of inclusion and contradiction},
     year = {2024},
     pages = {108769},
     volume = {476},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/journals/fss/MadridO24.bib},
     doi = {10.1016/J.FSS.2023.108769},
     timestamp = {Sat, 08 Jun 2024 01:00:00 +0200},
     url = {https://doi.org/10.1016/j.fss.2023.108769},
}

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5 Recent citations

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Papers citing this work

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

[1] 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.

[2] 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.

[3] 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.