Preideals in EQ-algebras

EQ-algebras were introduced by Novak (2006) as an algebraic structure of truth values for fuzzy-type theory (FFT). Novák and De Baets (2009) various kinds such good, residuated, IEQ-algebras. In this paper, we define the notion (pre)ideal in bounded (BEQ-algebras) investigate some properties. Then, introduce a congruence relation on good BEQ-algebras using ideals, then, solve open problem Paad (2019). Moreover, show that IEQ-algebras, there is one-to-one correspondence between relations set ideals. following, characterize generated preideal BEQ-algebras, this, prove family all preideals BEQ-algebra complete lattice. prelinear IEQ-algebras distributive lattice becomes Heyting algebra. Finally, can construct MV-algebra from IEQ-algebra.