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A Special Class of Multi-Fuzzy Algebra Over Multi-Fuzzy Field

Author(s):K.Shaju1, Sabu Sebastian2, P.Priyanka3, C.Haseena4, I.Gafoor5 and S.J.Sangeeth6

Affiliation: 1Research Scholar,Department of Mathematical Sciences,Kannur University,Kerala,India E-mail: shaju.kollaroth@gmail.com 2Professor, Department of Mathematics, Nirmalagiri College, Kerala,India E-mail:sabukannur@gmail.com 3,4,5,6Research Scholar,Department of Mathematical Sciences,Kannur University,Kerala,India

Page No: 14-25

Volume issue & Publishing Year: Volume 2 Issue 10,Oct-2025

Journal: International Journal of Advanced Multidisciplinary Application.(IJAMA)

ISSN NO: 3048-9350

DOI: https://doi.org/10.5281/zenodo.17527866

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Abstract:
The concept of multi-fuzzy algebra extends the traditional notions of fuzzy algebra by introducing multi-dimensional membership functions, allowing for a more nuanced representation of uncertainty and vagueness in algebraic structures. This paper explores the properties and algebraic structures of multi-fuzzy algebras over multi-fuzzy field, generalizing the framework of fuzzy vector spaces and fuzzy fields. We introduce a novel approach using a bridge function h to define multi-fuzzy algebras when the dimensions of the multi-fuzzy set on an algebra A and the multi-fuzzy field differ. The paper investigates the influence of this bridge function on the algebraic properties of these spaces and provides a comprehensive analysis of their structure. Key results include the characterization of multi-fuzzy algebras, their intersections, and their behaviour under linear transformations

Keywords: Multi-fuzzy vector spaces, Multi-fuzzy field, Multi-fuzzy Algebra, Space of Multi-fuzzy Algebra over Multi-fuzzy field with respect to a bridge function

Reference:

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