Square root of fuzzy QS-ideals on QS-algebras

Samy M.  Mostafa; Mostafa A.  Hassan; Fatema F.  Kareem

doi:10.24996/ijs.2026.67.1.25

Authors

Samy M. Mostafa Department of Mathematics, college of Education, Ain Shams University, Roxy, Cairo
Mostafa A. Hassan Department of Mathematics, college of Education, Ain Shams University, Roxy, Cairo
Fatema F. Kareem Department of Mathematics, Ibn-Al-Haitham college of Education, University of Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2026.67.1.25

Keywords:

QS-algebras, QS-ideal, fuzzy QS-ideal, the image of SRF-QS-ideals, the product of SRF-QS-ideals

Abstract

In real-life problems, we use square roots in natural distributions such as (the probability density function), distances and lengths in the Pythagorean theorem, and quadratic formulas in (the height of falling objects), radius of circles, harmonic movements (pendulum and springs), and standard deviation in statistics. We have observed that using fuzzy sets in real-life problems is more convenient than ordinary sets. Therefore, they are important in algebraic structures. As a result, more effort has been made to study square root structures in fuzzy sets.

This paper introduces the notion of square roots fuzzy of QS-ideals on QS-algebras and some important characteristics. Some illustrative examples have been provided which prove that every SRF-BCK-ideal is an SRF QS-ideal. Also, the image and the inverse image of SRF-QS-ideals are discussed. Finally, the product of SRF-QS-ideals on QS-algebra is defined and some important properties have been proved.