HH∗−intuitionistic heyting valued Ω-algebra and homomorphism

Abstract

Intuitionistic Logic was introduced by L. E. J. Brouwer in[1] and Heyting algebra was defined by A. Heyting to formalize the Brouwer’s intuitionistic logic[4]. The concept of Heyting algebra has been accepted as the basis for intuitionistic propositional logic. Heyting algebras have had applications in different areas. The coHeyting algebra is the same lattice with dual operation of Heyting algebra[5]. Also, co-Heyting algebras have several applications in different areas. In this paper, we introduced the new concept HH∗− Intuitionistic Heyting Valued Ω-Algebra. The purpose of introducing this new concept is to expand the field of researchers’ area using both membership degree and non-membership degree. This allows us to get more sensitive results.The HH∗− Intuitionistic Heyting valued set, HH∗− Intuitionistic Heyting valued relation, HH∗− Intuitionistic Heyting valued Ω-algebra and the homomorphism over HH∗− Intuitionistic Heyting valued Ω-algebra were defined.

Keywords

• heyting valued algebra
• co-heyting valued algebra
• omega algebra
• intuitionistic logic