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.
Ďubek et al. (Wed,) studied this question.