Picture fuzzy multifunctions and modal topological structures

This paper introduces the notion of picture fuzzy modal topological multifunctions. These structures are grounded on novel picture fuzzy topological operators for closure and interior types, thereby utilizing the two standard picture fuzzy modal operators $ \square $ and $ \Diamond $. The paper discusses several fundamental properties of picture fuzzy multifunctions. Many types of structures are introduced, and some types of continuous multifunctions between picture fuzzy topological structures are discussed. The results indicate that some properties considered satisfactory in the intuitionistic fuzzy modal topological structures, as defined by Atanassov in 2022, are not fulfilled.