Conference papers accepted: CMMSE, CONCEPTS
18/05/24/12:28 Filed in: Conference papers
N. Madrid, M. Ojeda-Aciego. New results on f-indexes of inclusion: composition as a fuzzy conjunction. Intl Conf on Computational and Mathematical Methods in Science and Engineering (CMMSE), Rota, 2024.
ABSTRACT We show that composition behaves like a fuzzy conjunction on the set of indexes of inclusion. By restricting the latter set to a join-subsemilattice of indexes we can find a representation theorem for monoids on the unit interval in terms of the composition and subsets of indexes. Furthermore, we show that composition (as a fuzzy conjunction) admits two residuated implications, hence forming an adjoint triple.
D. López-Rodríguez, M. Ojeda-Hernández. Rearrangement of fuzzy formal contexts for reducing cost of algorithms. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT In this paper, the effect of reordering the attributes prior to computing the concept lattice in formal contexts is explored. Several criteria are given in order to choose an ordering and then some experimental results are provided, first comparing the state-of-the-art algorithms in the crisp case and then examining the results of reordering the attributes in fuzzy formal contexts.
O. Krídlo, D. López-Rodríguez, L. Antoni, P. Eliaš, S. Krajči, and M. Ojeda-Aciego. Connecting concept lattices with bonds between L-fuzzy formal contexts by external information. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT We have delved into the interpretation of two novel methods for selecting appropriate bonds between L-fuzzy formal contexts, based on the use of the rigorous and benevolent concept-forming operators. The strategy presented therein for the construction of the rigorous and the benevolent bonds is knowledge-driven: the presence of external information about the strength of the connection about the attribute sets, given by an operator p: A_1 x A_2 -> L, induces both types of bond. Therefore, these new methods overcome the difficulty of bond interpretation by taking advantage of the incorporation of knowledge into the problem. In that paper, we formally verified that the bonds built using this strategy produce results coherent with the piece of external information used.
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco and M. Ojeda-Hernández. Fuzzy relational Galois connections between fuzzy transitive digraphs. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT In this work, we present an adequate notion of fuzzy relational Galois connection with both components now being fuzzy relations between two universes each endowed with binary transitive fuzzy relations. We focus on the specific setting in which the underlying algebra of truth values is a complete Heyting algebra.
C. Díaz-Montarroso, N. Madrid, E. Ramírez-Poussa. Towards a generalized modus ponens based on the f-index of inclusion. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT This paper proposes a generalized modus ponens and a generalized modus tollens based on the f-index of inclusion. Moreover, we analyze the properties of generalized modus ponens and generalized modus tollens according to the axioms proposed by Baldwin and Pilsworth.
ABSTRACT We show that composition behaves like a fuzzy conjunction on the set of indexes of inclusion. By restricting the latter set to a join-subsemilattice of indexes we can find a representation theorem for monoids on the unit interval in terms of the composition and subsets of indexes. Furthermore, we show that composition (as a fuzzy conjunction) admits two residuated implications, hence forming an adjoint triple.
D. López-Rodríguez, M. Ojeda-Hernández. Rearrangement of fuzzy formal contexts for reducing cost of algorithms. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT In this paper, the effect of reordering the attributes prior to computing the concept lattice in formal contexts is explored. Several criteria are given in order to choose an ordering and then some experimental results are provided, first comparing the state-of-the-art algorithms in the crisp case and then examining the results of reordering the attributes in fuzzy formal contexts.
O. Krídlo, D. López-Rodríguez, L. Antoni, P. Eliaš, S. Krajči, and M. Ojeda-Aciego. Connecting concept lattices with bonds between L-fuzzy formal contexts by external information. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT We have delved into the interpretation of two novel methods for selecting appropriate bonds between L-fuzzy formal contexts, based on the use of the rigorous and benevolent concept-forming operators. The strategy presented therein for the construction of the rigorous and the benevolent bonds is knowledge-driven: the presence of external information about the strength of the connection about the attribute sets, given by an operator p: A_1 x A_2 -> L, induces both types of bond. Therefore, these new methods overcome the difficulty of bond interpretation by taking advantage of the incorporation of knowledge into the problem. In that paper, we formally verified that the bonds built using this strategy produce results coherent with the piece of external information used.
I.P. Cabrera, P. Cordero, E. Muñoz-Velasco and M. Ojeda-Hernández. Fuzzy relational Galois connections between fuzzy transitive digraphs. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT In this work, we present an adequate notion of fuzzy relational Galois connection with both components now being fuzzy relations between two universes each endowed with binary transitive fuzzy relations. We focus on the specific setting in which the underlying algebra of truth values is a complete Heyting algebra.
C. Díaz-Montarroso, N. Madrid, E. Ramírez-Poussa. Towards a generalized modus ponens based on the f-index of inclusion. International Joint Conference on Conceptual Knowledge Structures (CONCEPTS), Cádiz, 2024.
ABSTRACT This paper proposes a generalized modus ponens and a generalized modus tollens based on the f-index of inclusion. Moreover, we analyze the properties of generalized modus ponens and generalized modus tollens according to the axioms proposed by Baldwin and Pilsworth.