Picture Fuzzy Modal Ideal Multifunctions

This paper introduces the notion of a picture fuzzy modal topological structures (PFMTSs) via ideal. These structures are grounded on novel picture fuzzy topological operators for closure and interior types, utilizing the two standard picture fuzzy modal operators $\square $ and $\Diamond $. The paper discusses several fundamental properties of picture fuzzy multifunctions PFMs via ideals. The results indicate that some properties considered satisfactory in the intuitionistic fuzzy modal topological structures, as defined by Atanassov in 2022, are not fulfilled. Also, we introduce many types of continuous multifunctions between picture fuzzy ideal topological spaces