Characterizations of semigroups by their linear Diophantine anti-fuzzy bi-ideals Характеризація напівгруп за їхніми лінійними діофантовими антинечіткими бі-ідеалами

The purpose of this paper is to introduce linear Diophantine anti-fuzzification of algebraic structures. In this regard, we define linear Diophantine anti-fuzzy (LDAF) substructures of a semigroup and discuss some of its properties. Moreover, we characterize semigroups in terms of LDAF-ideals and LDAF-bi-ideals. Finally, we apply the linear Diophantine anti-fuzzification to groups and find a relationship between LDAF-subgroups of a group and its LDF-subgroups.