Abstract
Fuzzy set theory resolved the crux of modeling uncertainty, vagueness, and imprecision. Many researchers have contributed to the development of the theory. This paper intends to define the innovative concept of the interval valued complex fuzzy relations (IVCFRs) using the proposed Cartesian product of two interval valued complex fuzzy sets (IVCFSs). Moreover, the types of IVCFRs are devised with some exciting results and properties. Furthermore, a couple of prodigious applications have been established as an illustration of the modeling capabilities of the proposed structures. The concept of interval valued complex fuzzy (IVCF) composite relations is used in the medical diagnosis of patients on the basis of symptoms. The inclusion of phase term in the grade of membership of IVCFRs facilitated modeling the periodic diseases. Additionally, another application of the Cartesian products and the IVCF equivalence relations is proposed that studies the life expectancies or mortality rates of patients with certain diseases. In addition, the effects of multiple illnesses on the life expectancy of a patient are also deliberated through IVCFRs. The proposed framework is also compared with the existing structures in the field of fuzzy set theory.