Spherical Linear Diophantine Fuzzy Graphs: Unleashing the Power of Fuzzy Logic for Uncertainty Modeling and Real-World Applications

The theory of spherical linear Diophantine fuzzy sets (SLDFS) boasts several advantages over existing fuzzy set (FS) theories such as Picture fuzzy sets (PFS), spherical fuzzy sets (SFS), and T-spherical fuzzy sets (T-SFS). Notably, SLDFS offers a significantly larger portrayal space for acceptable triplets, enabling it to encompass a wider range of ambiguous and uncertain knowledge data sets. This paper delves into the regularity of spherical linear Diophantine fuzzy graphs (SLDFGs), establishing their fundamental concepts. We provide a geometrical interpretation of SLDFGs within a spherical context and define the operations of complement, union, and join, accompanied by illustrative examples. Additionally, we introduce the novel concept of a spherical linear Diophantine isomorphic fuzzy graph and showcase its application through a social network scenario. Furthermore, we explore how this amplified depiction space can be utilized for the study of various graph theoretical topics.