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.

The main objective of this paper is to present a novel decision making algorithm using matrix representation of the inverse soft set defined in [ 10 ]. Therefore, we first introduce cardinality inverse soft matrix theory and its operations, products and algebraic structures in detail. Afterwards, an algorithmic solution employing the cardinality inverse soft matrix to find the optimum object and the ranking order of objects is proposed. The performance of algorithm named soft sum-row decision making algorithm is demonstrated by solving various decision problems. Also, we compare it with existing algorithms based on the soft set theory, soft matrix theory and inverse soft set theory. Moreover, we give Scilab codes of the algorithm and argue that this codes make the process of decision making composed of many objects, criteria and decision makers faster and easier.

In this paper, the symmetric difference operation for each of the soft sets and the soft matrices is defined and then their related properties are derived. Also, the concept of similarity measure for the soft matrices is introduced. Thus, we pioneer the budding phase of the use of soft matrices to find the similarity of soft sets. Through the soft matrices, we develop the Scilab code which facilitates the computation process of similarity measure among the soft sets composed of many parameters and alternatives. Moreover, it is shown with several examples that the similarity measure can be used for some cases involving the uncertainties in various areas. To confirm the consistency of the emerging similarity measure, we make comparisons with the preexisting similarity measures for the soft sets.