<p>The well-known topic of crisp graph planarity is contrasted with the more new and thoroughly studied field of planarity inside a fuzzy framework. In cubic fuzzy domain, cubic multisets with interval and fuzzy number to capture vagueness. Cubic fuzzy graphs (CuFGs) are structures which use cubic multisets to represent membership of vertices and edges. The interval represents a continuous process, whereas the point defines a specific process. Thus, cubic fuzzy graphs perform better than both interval valued graphs and fuzzy graphs as they indicate the level of participation of vertices and edges enabling management of uncertainty and ambiguity in interval valued fuzzy graphs (IvFG) and fuzzy graphs (FGs). The properties and characteristics of cubic fuzzy outerplanar graphs is investigated in this article, diving into a variety of fascinating elements of these topics. Cubic fuzzy graphs (CuFGs) can be created by removing individual vertices or edges from cubic fuzzy outerplanar subgraphs (CuFOSs). The study also includes examples of maximal and maximum cubic fuzzy outerplanar subgraphs obtained by removing both vertices and edges. Furthermore, the definition of cubic fuzzy dual graphs (CuFDGs), which are formed from cubic fuzzy outerplanar graphs (CuFGs) is presented and underlying relationship among these is explored. A practical application of this work is found in human face shape recognition, where cubic fuzzy graphs (CuFGs) offer a powerful framework for modeling facial geometry. It is observed that by accommodating uncertainty in facial feature positions and relationships, CuFGs enable more accurate recognition in complex biometric identification tasks.</p>