On Semi-Vector Spaces and Semi-Algebras with Applications in Fuzzy Automata
Giuliano G. La Guardia,
Jocemar Q. Chagas,
Ervin K. Lenzi,
Leonardo Pires,
Nicolás Zumelzu,
Benjamín Bedregal
Affiliations
Giuliano G. La Guardia
Department of Mathematics and Statistics, State University of Ponta Grossa, (UEPG), Avenida General Carlos Cavalcanti N° 4748, Ponta Grossa 84030-900, Paraná, Brazil
Jocemar Q. Chagas
Department of Mathematics and Statistics, State University of Ponta Grossa, (UEPG), Avenida General Carlos Cavalcanti N° 4748, Ponta Grossa 84030-900, Paraná, Brazil
Ervin K. Lenzi
Department of Physics, State University of Ponta Grossa, Avenida General Carlos Cavalcanti N° 4748, Ponta Grossa 84030-900, Paraná, Brazil
Leonardo Pires
Department of Mathematics and Statistics, State University of Ponta Grossa, (UEPG), Avenida General Carlos Cavalcanti N° 4748, Ponta Grossa 84030-900, Paraná, Brazil
Nicolás Zumelzu
Department of Mathematics and Physics, University of Magallanes (UMAG), Avenida Bulnes N° 01855, Punta Arenas 6200000, Chile
Benjamín Bedregal
Department of Informatics and Applied Mathematics, Federal University of Rio Grande do Norte (UFRN), Campus Universitário Lagoa Nova, Natal 59078-900, Río Grande do Norte, Brazil
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.
