Some Operations and Properties of the Cubic Intuitionistic Set with Application in Multi-Criteria Decision-Making
Shahzad Faizi,
Heorhii Svitenko,
Tabasam Rashid,
Sohail Zafar,
Wojciech Sałabun
Affiliations
Shahzad Faizi
Department of Mathematics, Virtual University of Pakistan, Lahore 54000, Pakistan
Heorhii Svitenko
Department of Software Engineering, Kharkiv National University of Radio Electronics, Nauky Ave. 14, 61166 Kharkiv, Ukraine
Tabasam Rashid
Department of Science and Humanities, University of Management and Technology, Lahore 54770, Pakistan
Sohail Zafar
Department of Science and Humanities, University of Management and Technology, Lahore 54770, Pakistan
Wojciech Sałabun
Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Żołnierska 49, 71-210 Szczecin, Poland
This paper proposes some operations on the cubic intuitionistic set along with useful properties. We propose the internal cubic intuitionistic set (ICIS), the external cubic intuitionistic set (ECIS), P-order, R-order order (P-(R-) order), P-union, R-union (P-(R-) union), P-intersection, and R-intersection (P-(R-) intersection). We further investigate several properties of the P-(R-) union and P-(R-) intersection of ICISs and ECISs, and present some examples in this context. Some important theorems related to ICISs and ECISs are also presented with proof. Finally, an application example is given to measure the effectiveness and significance of the proposed operations by solving a multi-criteria decision-making (MCDM) problem.
