(anti) fuzzy ideals of sheffer stroke bck-algebras

the aim of this study is to introduce (anti) fuzzy ideals of a sheffer stroke bck-algebra. after describing an anti fuzzy subalgebra and an anti fuzzy (sub-implicative) ideal of a sheffer stroke bck-algebra, the relationships of these structures are demonstrated. also, a t-level cut and a complement of a fuzzy subset are defined and some properties are investigated. an implicative sheffer stroke bck-algebra is defined and it is proved that a fuzzy subset of an implicative sheffer stroke bck-algebra is an anti fuzzy ideal if and only if it is an anti fuzzy sub-implicative ideal of this algebraic structure. a fuzzy congruence and a fuzzy quotient set of a sheffer stroke bck-algebra are studied in details and it is shown that there is a bijection between the set of fuzzy ideals and the set of fuzzy congruences on this algebraic structure. finally, cartesian product of fuzzy subsets of a sheffer stroke bck-algebra is determined and it is expressed that the cartesian product of two anti fuzzy ideals of this algebraic structure is anti fuzzy ideal.