The degree of (L, M)-fuzzy σ-algebra and its related mappings

Article type: Research Article

Authors: Ghareeb, A.^{a; b} | Khalil, O.H.^{c; d; *} | Omran, Saleh^a

Affiliations: [a] Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt | [b] Department of Mathematics, Faculty of Science, Al-Baha University, Al-Baha, Saudi Arabia | [c] Department of Mathematics, College of Science, Majmaah University, Al-Majmaah, 11952, Saudi Arabia | [d] Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

Correspondence: [*] Corresponding author. O.H. Khalil. E-mail: [email protected].

Abstract:  The aim of this paper is mainly to study the (L, M)-fuzzy measurability in view of degree. Firstly, we generalize the notion of (L, M)-fuzzy σ-algebra by defining the degree of an (L, M)-fuzzy σ-algebra with respect to a mapping σ : LX ⟶ M. Such kind of degrees is proved to satisfy some axioms of (L, M)-fuzzy σ-algebra. Additionally, we define and study some special degrees such as the degree of (L, M)-fuzzy measurable mapping, (L, M)-fuzzy measurable-to-measurable mapping, isomorphic mapping and quotient mapping with respect to mappings between two (L, M)-fuzzy measurable spaces in details. Finally, we give characterizations of these degrees and investigate the relationships between them.

Keywords: (L, M)-fuzzy σ-algebra, (L, M)-fuzzy measurable mapping, (L, M)-fuzzy measurable-to-measurable mapping, isomorphism mapping, quotient mapping

DOI: 10.3233/JIFS-191117

Journal: Journal of Intelligent & Fuzzy Systems, vol. 38, no. 3, pp. 3141-3150, 2020