Extending intuitionistic operations, orderings, and entropy measures on generalized fuzzy orthopartitions

Generalized fuzzy orthopartitions extend the traditional concept of partitions to include both fuzziness and uncertainty. A generalized fuzzy orthopartition is a collection of intuitionistic fuzzy sets representing equivalence classes and satisfying a specific pair of axioms, which capture the idea that the classes must be disjoint and cover the initial universe. The aim of this article is twofold. Firstly, we aggregate and order generalized fuzzy orthopartitions by extending intuitionistic operations and relations. Secondly, we introduce and study entropy measures on generalized fuzzy orthopartitions by employing entropies on intuitionistic fuzzy sets already existing in the literature.