This paper introduces the notion of a temporal picture fuzzy modal topological structure (TPFMTS). These structures are based on novel temporal picture fuzzy topological operators as common modal topological operators standing for the closure and interior operators. The paper discusses several fundamental properties of these new TPFMTSs. The constructed temporal picture fuzzy modal topological operators establish that some properties that were considered satisfactory in the temporal intuitionistic fuzzy modal topological structures, as defined by Atanassov in 2023, are not fulfilled. Also, we introduce the concepts of $TP{F}^u$ and $TP{F}^l$-continuous and almost continuous multifunctions. Several properties and characterizations of the presented continuous multifunctions and their types of continuity are established. Some examples are given to explain the correct implications between these notions.

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 $◻$ and $◊$. 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.

In this paper, we extend the concept of fuzzy rough sets to graphs by introducing the notion of "fuzzy graph ideals". This novel approach enables the construction of rough fuzzy digraphs, termed "fuzzy graph ideal approximation spaces", along with associated methods of formation. We define new fuzzy lower and upper graphs based on any two fuzzy binary relations on the vertex and edge sets of a directed graph thereby utilizing the concept of fuzzy graph ideals. Additionally, we explore fuzzy interior and fuzzy closure graphs within rough fuzzy graphs, and examine properties such as fuzzy graph connectedness through the application of these new operators. These developments offer valuable tools to address uncertain decision-making problems, with potential practical applications in various domains. Particularly, we provide an algorithm to solve decision-making problems regarding the identification of the best location in a department to set a mobile phone Jammer.