A Novel Approach to Decision‐Making Under Uncertainty Using Spherical Linear Diophantine Fuzzy Relations

Fuzzy relations are more advanced than crisp binary relations, which are applicable in control systems in artificial intelligence. Our research study develops a fuzzy spherical linear Diophantine fuzzy ( S L D F u ) relation as a more advanced tool to handle uncertainty in decision‐making. It has greater flexibility than fuzzy relations, traditional intuitionistic fuzzy ( I F u ) relations, and linear Diophantine fuzzy ( L D F u ) relations. We define union, intersection, inverse, complement, and composition in relation to S L D F u . We present reflexive, symmetric, and transitive relations in S L D F u relation. Likewise, we define the above operations with the help of numerical examples and establish that they form specific algebraic structures. In addition, we develop a score function to evaluate results and analyze the symmetry of decisions. We provide an application of the relation S L D F u in decision‐making as medical dignosis.