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

Author

Listed:
  • Juan Luis García Guirao

    (Departamento de Matemática Aplicada y Estadástica, Universidad Politácnica de Cartagena, Hospital de Marina, 30203 Murcia, Spain
    Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddha 21589, Saudi Arabia)

  • 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)

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.

Suggested Citation

  • Juan Luis García Guirao & Mobashir Iqbal & Zia Bashir & Tabasam Rashid, 2021. "A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces," Mathematics, MDPI, vol. 9(13), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1512-:d:583938
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