March 2020
Journal paper accepted
13/03/20/10:32 Filed in: Journal paper
N. Madrid, M. Ojeda. On contradiction and inclusion using functional degrees. International Journal of Computational Intelligence Systems 13(1):464-471, 2020.
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-weak-contradiction 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 analyse the relationship between the f-degree of inclusion and the f-degree of contradiction via the complement of fuzzy sets and Galois connections.
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-weak-contradiction 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 analyse the relationship between the f-degree of inclusion and the f-degree of contradiction via the complement of fuzzy sets and Galois connections.