On a Two-Fold Algebra Based on the Standard Fuzzy Number Theoretical System

Mohammad Abobala

Tishreen University, Department of Mathematics, Latakia, Syria

Abstract

This paper is dedicated to studying the algebraic structure generated from the fusion of two-fold algebras with the standard fuzzy number theoretical system, where the novel fuzzy algebraic structure will be defined with a well-defined binary operation, and then its substructures will be studied concerning the corresponding operation such as hyper/under ideals, and two-fold fuzzy homomorphisms. Also, many examples will be illustrated to clarify the validity of our work.

Keywords: two-fold algebra; fuzzy number theoretical system; two-fold fuzzy algebra; two-fold fuzzy homomorphism.