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