QIVIFS: Quaternion Approach of Interval-Valued Intuitionistic Fuzzy Sets with Applications in Renewable Energy System

Interval-valued intuitionistic fuzzy sets (IFSs) are more useful than IFSs for modelling incomplete information about real-world issues. This manuscript effort is to incorporate the concept of “quaternion numbers (QNs)” to “interval-valued” IFS (IVIFS) and hence presents the concept of quaternion IVIFS (QIVIFS). These types of QIVIFS can capable of capturing mixed features and express multiple dimensional IVIF information through the interval functions of real-belongingness, imaginary- belongingness, real non-belongingness, and imaginary non-belongingness. Then, the logic operations and order relationships of the QIVIFSs are introduced based on QNs. We also present the distance function for QIVIF numbers. The composite feature of QIVIFS to express multiple dimensional IVIF information is a suitable tool to analyze problems in more details. Finally, we develop an approach for renewable energy system (RES) on the basis of QIVIFSs.