Shahrood University of Technology Journal of Algebraic Systems 2345-5128 14 1 2026 01 01 TRUE-FALSE STRUCTURES AND ITS APPLICATION IN GROUPS AND BCK/BCI-ALGEBRAS 1 28 3125 10.22044/jas.2024.13268.1736 EN Mohammad Mohseni Takallo Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran. Rajab Ali Borzooei Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran. Young Bae Jun Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea. Journal Article 2023 06 16 By utilizing the concept of interval-valued fuzzy sets, a novel structure called True-False structures is introduced. Its application in groups and BCK/BCI-algebras is discussed. The introduction of (limited) T &F -subgroups and (limited) T &F -subalgebras is carried out, along with an investigation of various associated properties. Characterizations of (limited) T&F- subgroups and (limited) T&F-subalgebras are provided, and it is demonstrated that the in- tersection of two T &F -subgroups (respectively, T &F -subalgebras) also forms a T &F -subgroup (respectively, T &F -subalgebra). Additionally, the union and intersection of two T &F -subgroups (respectively, T&F-subalgebras) are explored. https://jas.shahroodut.ac.ir/article_3125_49f233c7eea22ed5f6fdfdcdb5951dc0.pdf