Circular Linear Diophantine Fuzzy Sets and Their Application in Medical Diagnosis

To address the uncertainty and imprecision in a complex system, the concept of the linear Diophantine fuzzy set (LDFS) was introduced, which is a fuzzy set extension that eliminates the constraints of current methodologies and gives the decision-maker complete freedom to select the grades, producing results that are expressive and flexible. A circular intuitionistic fuzzy set (C-IFS) is depicted by a circle with the membership and non-membership values as its center coordinates, addressing the ambiguity regarding membership and non-membership values. In this paper, we propose the notion of a circular linear Diophantine fuzzy set (C-LDFS) as a hybrid structure of both circular intuitionistic fuzzy sets and linear Diophantine fuzzy sets. In addition, some fundamental set operations on C-LDFSs are presented. Furthermore, a similarity metric for C-LDFS is also introduced in the paper. Additionally, we confirm the axiomatic requirement of the similarity measure and highlight a few of its traits. Finally, the proposed similarity metric is implemented in clinical decision-making to illustrate its efficacy.