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.
Bibliometric data
The following data has been extracted from resources such as OpenAlex, Dimensions, PlumX or Altmetric.
Cites
The following graph plots the number of cites received by this work from its publication, on a yearly basis.
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.