A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces

Juan Luis García Guirao, Mobashir Iqbal, Zia Bashir and Tabasam Rashid
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Juan Luis García Guirao: Departamento de Matemática Aplicada y Estadástica, Universidad Politácnica de Cartagena, Hospital de Marina, 30203 Murcia, Spain
Mobashir Iqbal: Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
Zia Bashir: Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
Tabasam Rashid: Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan

Mathematics, 2021, vol. 9, issue 13, 1-14

Abstract: This paper aims to study fuzzy order bounded linear operators between two fuzzy Riesz spaces. Two lattice operations are defined to make the set of all bounded linear operators as a fuzzy Riesz space when the codomain is fuzzy Dedekind complete. As a special case, separation property in fuzzy order dual is studied. Furthermore, we studied fuzzy norms compatible with fuzzy ordering (fuzzy norm Riesz space) and discussed the relation between the fuzzy order dual and topological dual of a locally convex solid fuzzy Riesz space.

Keywords: fuzzy order bounded operators; fuzzy order dual spaces; fuzzy norm riesz spaces; locally convex-solid fuzzy riesz spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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