Albayrak, BarişDiasamidze, I. YashaAydin, Neşet2025-01-272025-01-2720131314-3395https://doi.org/10.12732/ijpam.v86i1.13https://hdl.handle.net/20.500.12428/12919In this paper let Q = {T1, T2, T3, T 4, T5, T6, T7, T8} be a subsemilattice of X-semilattice of unions D where T1 ? T 2 ? T3 ? T5 ? T6 ? T8, T1 ? T2 ? T3 ? T5 ? T7 ? T8, T1 ? T2 ? T4 ? T5 ? T6 ? T8, T1 ? T2 ? T4 ? T5 ? T7 ? T8, T1 ? ?, T4\T3 ? ?, T3\T4 ? ?, T6\T7 ? ?, T7\T 6 ? ?, T3 ? T4 = T5, T6 ? T7 = T8, then we characterize the class each element of which is isomorphic to Q by means of the characteristic family of sets, the characteristic mapping and the generate set of Q. Moreover, we calculate the number of regular elements of BX(D) for a finite set X. © 2013 Academic Publications, Ltd.eninfo:eu-repo/semantics/openAccessBinary relation; Regular elements; SemigroupsArticle86119921610.12732/ijpam.v86i1.132-s2.0-84880283112N/A