A scientific study was conducted at the Faculty of science at the University of Basra, prepared by the teaching professor Dr. Shukr Mahmoud Khalil entitled "The new category of fuzzy algebra systems with its applications about transformations and near-ideal cliques bipolar fuzzy pattern—Ru, which was published in the Journal Afrika Matematika, which is a sober scientific journal within the publishing house Springer indexed within Clarivate and Scopus and has an impact factor0. 9