Complex T-Spherical Fuzzy Relations With Their Applications in Economic Relationships and International Trades

Abstract

Uncertainty is the unavoidable part of the life. In almost all circumstances, we regularly find ourselves in a state of uncertainty. Several reasons can lead to uncertainty, such as randomness, vagueness and rough knowledge. Fuzzy set (FS) theory deals with these kinds of information. Many generalizations had been made in the theory of FSs, such as intuitionistic FSs (IFSs), q-rung orthopair FSs (qROFSs), complex qROFSs (CqROFSs), spherical FSs (SFSs), T-spherical FSs (TSFSs), and complex TSFSs (CTSFSs). Among these generalizations of FSs, the CTSFSs are the most dominant generalization of the FSs. Although fuzzy relations (FRs), IF relations (IFRs) and complex FRs (CFRs) were defined in the literature, the concepts of relations have not yet been introduced in the CTSFSs. This paper unveils the novel concept of CTSF relations (CTSFRs), which provides the extensive generalizations of FRs. The proposed CTSFRs can give many generalized types of FRs, such as IFRs, CFRs, Pythagorean FRs, qROFRs, SFRs and TSFRs, etc. Additionally, some useful properties and results are obtained for CTSFRs. Moreover, a couple of applications demonstrate the usefulness of the proposed concepts. These CTSFRs can be used to depict the time-related interdependence of global market. Thus, we apply these CTSFRs to analyze the interdependence of the international trades among countries and compare the financial factors affecting business markets. Furthermore, the economic relationships with respect to time lag can be modeled by using the CTSFSs and the CTSFRs. Finally, a comparative analysis illuminates the supremacy of the proposed way in contrast with the existing ones.

Keywords

• Fuzzy sets (FSs)
• T-spherical FSs (TSFSs)
• complex TSFSs (CTSFSs)
• CTSF relations (CTSFRs)
• Cartesian product in CTSFSs
• CTSF composite relation