TRUE-FALSE STRUCTURES AND ITS APPLICATION IN GROUPS AND BCK/BCI-ALGEBRAS; ساختارهای درست نادرست و کاربرد آن در گروه ها و BCK/BCI - جبرها

Abstract

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 intersection of two T&Fsubgroups (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. © 2025 Elsevier B.V., All rights reserved.