On intuitionistic Q-fuzzy subalgebras/ideals/deductive systems in Hilbert algebras

Abstract

This study introduces the concepts of intuitionistic Q-fuzzy subalgebras, ideals, and deductive systems in the setting of Hilbert algebras and investigates their fundamental properties and interrelations. The theoretical results are supported by concrete examples and are structured in a way that facilitates understanding of the algebraic-logical framework underlying fuzzy logic extensions. By presenting clear definitions, illustrative cases, and step-by-step reasoning, the paper serves not only as a contribution to the field of abstract algebra but also as a useful learning resource for upper secondary science students beginning to engage with research. The work encourages early exploration of mathematical structures, fosters critical and creative thinking, and promotes accessibility of advanced topics through collaboration across academic levels and institutions.