| Summary: | This paper comprises the introduction of weighted mean products of fuzzy graph structures (<italic>FGSs</italic>) to construct weighted mean fuzzy graph structures (<italic>WMFGSs</italic>) with the help of optimization parameter, and establish some novel results after validating with examples, accordingly. The notions of regular and <inline-formula> <tex-math notation="LaTeX">$m\mu _{k}$ </tex-math></inline-formula>-regular <italic>FGSs</italic> are described, where <inline-formula> <tex-math notation="LaTeX">$m\in$ </tex-math></inline-formula>]0, 1] represents the degree of all vertices in <inline-formula> <tex-math notation="LaTeX">$\widetilde {G}$ </tex-math></inline-formula> under mapping <inline-formula> <tex-math notation="LaTeX">$\mu _{k}$ </tex-math></inline-formula>, and develop certain properties of regular <italic>WMFGSs</italic>. In addition, we create a flowchart to present common application procedures of fuzzy graphical frameworks to classify the advanced city out of some important Pakistani cities subject to certain parameters.
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