February 2025
Journal paper accepted: IJAR
25/02/25/10:31 Filed in: Journal paper
Francisco Pérez-Gámez, Carlos Bejines. An exploration of weak Heyting algebras: Characterization and properties. International Journal of Approximate Reasoning, 179: Article 109365, 2025.
ABSTRACT This paper explores weak Heyting algebras, an extension of complete Heyting algebras, focusing on characterizing this concept and identifying essential properties in terms of implication operators. The main emphasis is on unraveling the defining features and significance of the novel weak Heyting algebras. We further classify these structures within the context of a complete lattice and extend our findings to the Cartesian product. We facilitate comprehensive comparisons among these structures, by contributing to the broader understanding of weak Heyting algebras in mathematical research.
ABSTRACT This paper explores weak Heyting algebras, an extension of complete Heyting algebras, focusing on characterizing this concept and identifying essential properties in terms of implication operators. The main emphasis is on unraveling the defining features and significance of the novel weak Heyting algebras. We further classify these structures within the context of a complete lattice and extend our findings to the Cartesian product. We facilitate comprehensive comparisons among these structures, by contributing to the broader understanding of weak Heyting algebras in mathematical research.
Journal paper accepted: MMAS
05/02/25/13:34 Filed in: Journal paper
N. Madrid and M. Ojeda-Aciego. On the φ-index of inclusion: studying the structure generated by a subset of indexes. Mathematical Methods in the Applied Sciences, 2025.
ABSTRACT The φ-index of inclusion has proven to be a suitable generalization of the inclusion in the fuzzy setting. In this paper, the properties of the φ-index of inclusion, when its definition is restricted to a subset of indexes, are analyzed. The theoretical results obtained in this work are necessary in order to develop fuzzy inference systems based on the φ-index of inclusion.
ABSTRACT The φ-index of inclusion has proven to be a suitable generalization of the inclusion in the fuzzy setting. In this paper, the properties of the φ-index of inclusion, when its definition is restricted to a subset of indexes, are analyzed. The theoretical results obtained in this work are necessary in order to develop fuzzy inference systems based on the φ-index of inclusion.