General Framework for Intuitionistic Values and Related Fuzzy Sets Based on Automorphisms

Abstract This paper introduces a novel framework for understanding intuitionistic values and fuzzy sets through the automorphism of the unit interval [0, 1]. By generalizing the concepts of classical intuitionistic sets using strong negations generated by these automorphisms, we define the φ-intuitionistic values and explore their arithmetic, establishing a comprehensive set of operations based mainly on additive generators of t-(co)norms and their properties. This approach provides greater flexibility to the modelling with these sets.