On Contradiction and Inclusion Using Functional Degrees

 

Abstract

The notion of inclusion is a cornerstone in set theory and therefore, its generalization in fuzzy set theory is of great interest.The degree of f-inclusion is one generalization of such a notion that differs from others existing in the literature because the degree of inclusion is considered as a mapping instead of a value in the unit interval.On the other hand, the degree of f-weakcontradiction was introduced to represent the contradiction between two fuzzy sets via a mapping and its definition has many similarities with the f-degree of inclusion.This suggests the existence of relations between both f-degrees.Specifically, following this line, we analyze the relationship between the f-degree of inclusion and the f-degree of contradiction via the complement of fuzzy sets and Galois connections.

Citation

Please, cite this work as:

[MO20] N. Madrid and M. Ojeda-Aciego. “On Contradiction and Inclusion Using Functional Degrees”. In: Int. J. Comput. Intell. Syst. 13.1 (2020), pp. 464-471. DOI: 10.2991/IJCIS.D.200409.001. URL: https://doi.org/10.2991/ijcis.d.200409.001.

NoteBibTeX

@Article{Madrid2020a,
     author = {Nicol{’a}s Madrid and Manuel Ojeda-Aciego},
     journal = {Int. J. Comput. Intell. Syst.},
     title = {On Contradiction and Inclusion Using Functional Degrees},
     year = {2020},
     number = {1},
     pages = {464–471},
     volume = {13},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/journals/ijcisys/MadridO20.bib},
     doi = {10.2991/IJCIS.D.200409.001},
     timestamp = {Mon, 03 Jan 2022 00:00:00 +0100},
     url = {https://doi.org/10.2991/ijcis.d.200409.001},
}

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On Contradiction and Inclusion Using Functional Degrees

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Papers citing this work

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

[1] N. Madrid and M. Ojeda-Aciego. “The f-index of inclusion as optimal adjoint pair for fuzzy modus ponens”. In: Fuzzy Sets and Systems 466 (Aug. 2023), p. 108474. ISSN: 0165-0114. DOI: 10.1016/j.fss.2023.01.009. URL: http://dx.doi.org/10.1016/j.fss.2023.01.009.

[2] J. Medina, J. Moreno-García, E. Ramírez-Poussa, et al. “Mathematics and Computational Intelligence Synergies for Emerging Challenges”. In: International Journal of Computational Intelligence Systems 14.1 (2021), p. 818. ISSN: 1875-6883. DOI: 10.2991/ijcis.d.210121.001. URL: http://dx.doi.org/10.2991/ijcis.d.210121.001.