On Sub-implicative (α, Β)-fuzzy Ideals of Bch-algebras

The theory of fuzzy sets, which was initiated by Zadeh in his seminal paper [33] in 1965, was applied to generalize some of the basic concepts of algebra. The fuzzy algebraic structures play a vital role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, logic, set theory, real analysis, measure theory etc. Chang applied it to the topological spaces in [5]. Das and Rosenfeld applied it to the fundamental theory of fuzzy groups in [9, 27]. In [15], Hong et al. applied the concept to BCH-algebras and studied fuzzy dot subalgebras of BCH-algebras. Jun, give characterizations of BCI/BCH-algebras in [17]. In 2001, Jun et al. discussed on imaginable T-fuzzy subalgebras and imaginable T-fuzzy closed ideals in BCH-algebras [18]. Kim [22] studied intuitionistic (T, S)-normed fuzzy closed ideals of BCH-algebras. In [20], Jun et al. discussed N-structures applied to closed ideals in BCHalgebras. Jun and Park investigated filters of BCH-algebras based on bipolarvalued fuzzy sets in [19]. In [10], Dudek and Rousseau, give the idea of settheoretic relations and BCH-algebras with trivial structure. In [21], Kazanci et al. studied soft set and soft BCH-algebras. Yin initiated the concepts of fuzzy dot ideals and fuzzy dot H-ideals of BCH-algebras in [32]. In [31], Saeid et al. discussed fuzzy n-fold ideals in BCH-algebras. The concept of a BCH-algebra was initiated by Hu and Li in [13] and gave examples of proper BCH-algebras [14]. Some classifications of BCH-algebras were studied by Dudek [11] and Ahmad [1]. They also have studied several