On Semi-Vector Spaces and Semi-Algebras with Applications in Fuzzy Automata
La Guardia, Giuliano G.
Universidade Estadual de Ponta Grossa
Chagas, Jocemar Q.
Universidade Estadual de Ponta Grossa
Lenzi, Ervin K.
Universidade Estadual de Ponta Grossa
Pires, Leonardo
Universidade Estadual de Ponta Grossa
Bedregal, Benjamin
Fed Univ Rio Grande Norte UFRN
Journal
Axioms
ISSN
2075-1680
Open Access
gold
Volume
13
In this paper, we expand the theory of semi-vector spaces and semi-algebras, both over the semi-field of nonnegative real numbers R0+. More precisely, we prove several new results concerning these theories. We introduce to the literature the concept of eigenvalues and eigenvectors of a semi-linear operator, describing how to compute them. The topological properties of semi-vector spaces, such as completeness and separability, are also investigated here. New families of semi-vector spaces derived from the semi-metric, semi-norm and semi-inner product, among others, are exhibited. Furthermore, we show several new results concerning semi-algebras. After this theoretical approach, we apply such a theory in fuzzy automata. More precisely, we describe the semi-algebra of A-fuzzy regular languages and we apply the theory of fuzzy automata for counting patterns in DNA sequences.