Complex linear Diophantine fuzzy sets and their cosine similarity measures with applications

Abstract In this paper, the concept of complex linear Diophantine fuzzy set (CLDFS), which is obtained by integrating phase term into structure (LDFS) and thus an extension LDFS, introduced. other words, ranges grades membership, non-membership, reference parameters in LDFS are extended from interval [0, 1] to unit circle plane. Besides, approach proposed remove conditions associated with complex-valued membership non-membership framework intuitionistic (CIFS), Pythagorean (CPyFS), q-rung orthopair (Cq-ROFS). It proved that each CIFS, CPyFS, Cq-ROFS a CLDFS, but not vice versa. addition, some operations relations on CLDFSs derived their fundamental properties investigated. The intuitive definitions cosine similarity measure (CSM) distance (CDM) between two introduced characteristic principles examined. An based CSM tackle medical diagnosis issues its performance tested dealing numerical examples. Finally, comparative study several existing approaches created advantages discussed.