2021/11/17 by Giuliano G. La Guardia, Jocemar Q. Chagas, La Guardia, Giuliano G. +5
Computer Science · Decision Sciences · Mathematics · #FOS: Mathematics #Fuzzy Logic and Control Systems #Fuzzy Systems and Optimization #Fuzzy and Soft Set Theory #General Mathematics (math.GM)
paper · pdf · doi:10.48550/arxiv.2111.11206
openalex publication_date 2021/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well-known that the theories of semi-vector spaces and semi-algebras -- which were not much studied over time -- are utilized/applied in Fuzzy Set Theory in order to obtain extensions of the concept of fuzzy numbers as well as to provide new mathematical tools to investigate properties and new results on fuzzy systems. In this paper we investigate the theory of semi-vector spaces over the semi-field of nonnegative real numbers \mathbb R0+. We prove several results concerning semi-vector spaces and semi-linear transformations. Moreover, we introduce in the literature the concept of eigenvalues and eigenvectors of a semi-linear operator, describing in some cases how to compute them. Topological properties of semi-vector spaces such as completeness and separability are also investigated. New families of semi-vector spaces derived from semi-metric, semi-norm, semi-inner product, among others are exhibited. Additionally, some results on semi-algebras are presented.