Hybrid Structure for Fantastic and Integral Filters in EQ-algebras

The main objective of this paper is to introduce hybrid fantastic and hybrid integral (pre)filters in EQ-algebras. Several characterizations of these hybrid (pre)filters are investigated, and it is shown that the quotient algebras induced by hybrid (integral) fantastic filters in good EQ-algebras form (integral) involutive EQ-algebras. Furthermore, the concept of divisible EQ-algebras is introduced, along with some related properties. Hybrid fantastic (pre)filters in divisible residuated EQ-algebras are also examined. Finally, the relationship between integral prefilters and other types of (pre)filters, such as implicative and fantastic (pre)filters in EQ-algebras, is explored.