{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T19:14:28Z","timestamp":1740165268250,"version":"3.37.3"},"reference-count":52,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,27]],"date-time":"2024-02-27T00:00:00Z","timestamp":1708992000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"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.<\/jats:p>","DOI":"10.3390\/axioms13030153","type":"journal-article","created":{"date-parts":[[2024,2,27]],"date-time":"2024-02-27T08:35:48Z","timestamp":1709022948000},"page":"153","source":"Crossref","is-referenced-by-count":0,"title":["Spherical Linear Diophantine Fuzzy Graphs: Unleashing the Power of Fuzzy Logic for Uncertainty Modeling and Real-World Applications"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1390-2049","authenticated-orcid":false,"given":"Mani","family":"Parimala","sequence":"first","affiliation":[{"name":"Department of Mathematics, Bannari Amman Institute of Technology, Sathyamangalam 638401, Tamil Nadu, India"}]},{"given":"Saeid","family":"Jafari","sequence":"additional","affiliation":[{"name":"Mathematical and Physical Science Foundation, Sidevej 5, 4200 Slagelse, Denmark"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,27]]},"reference":[{"key":"ref_1","first-page":"338","article-title":"Information and control","volume":"8","author":"Zadeh","year":"1965","journal-title":"Fuzzy Sets"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"121439","DOI":"10.1016\/j.eswa.2023.121439","article-title":"An integrated fuzzy multi-measurement decision-making model for selecting optimization techniques of semiconductor materials","volume":"237","author":"Alamoodi","year":"2024","journal-title":"Expert Syst. 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