A Representation Theorem for 𝑘 × 𝑗-rough Heyting Algebras
Federico Almiñana and Gustavo Pelaitay
𝑘-rough Heyting algebras were introduced by Eric San Juan in 2008 as an algebraic formalism for reasoning on finite increasing sequences over Boolean algebras in general and on generalizations of rough set concepts in particular. In 2020, we defined and studied the variety of 𝑘 × 𝑗-rough Heyting algebras. These algebras constitute an extension of Heyting algebras and in j = 2 case they coincide with 𝑘-rough Heyting algebras. In this note, we give a functional representation theorem and we determine a necessary and sufficient condition under which such embedded is onto.
Keywords: Heyting algebras, 𝑘-rough Heyting algebras, 𝑘 × 𝑗-rough Heyting algebras, 3-valued Łukasiewicz–Moisil algebras