The Properties of Two-Fold Algebra Based on the n-standard Fuzzy Number Theoretical System

Raed Hatamleh^*, Ayman Hazaymeh

Department of Mathematics, Faculty of Science and Information Technology, Jadara University, P.O. Box 733, Irbid 21110, Jordan

Emails: raed@jadara.edu.jo; aymanha@jadara.edu.jo  

Abstract

In this paper, we study the two-fold algebra based on the n-standard fuzzy number theoretical system as a special type of two-fold fuzzy algebras, where we study the elementary properties of the algebraic operations defined over this system. Also, we prove many results that describe the relations between two-fold substructures and sub-algebras defined by fuzzy number theoretical systems. On the other hand, we provide many different examples to explain our results.

Keywords: n-standard fuzzy number theoretical system; two-fold algebra; sub-algebra; fuzzy number theory.