التفاصيل البيبلوغرافية
| العنوان: |
On Semi-Vector Spaces and Semi-Algebras with Applications in Fuzzy Automata. |
| المؤلفون: |
La Guardia, Giuliano G., Chagas, Jocemar Q., Lenzi, Ervin K., Pires, Leonardo, Zumelzu, Nicolás, Bedregal, Benjamín |
| المصدر: |
Axioms (2075-1680); May2024, Vol. 13 Issue 5, p308, 28p |
| مصطلحات موضوعية: |
REAL numbers, TOPOLOGICAL property, DNA sequencing, EIGENVECTORS, EIGENVALUES, VECTOR algebra |
| مستخلص: |
In this paper, we expand the theory of semi-vector spaces and semi-algebras, both over the semi-field of nonnegative real numbers R 0 + . 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. [ABSTRACT FROM AUTHOR] |
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