Affiliations: [a]
School of Mathematics and Statistics Beijing Institute of Technology Beijing, P.R. China | [b]
Department of Mathematics and Statistics Hazara University, Mansehra, KPK, Pakistan
| [c]
Department of Mathematics Abdul Wali Khan University, Mardan, KPK, Pakistan
| [d]
Department of Mathematics Abbottabad University of Science and Technology, Abbottabad, KPK, Pakistan
| [e] Beijing key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, P.R. China
Abstract: Pythagorean fuzzy sets (PFSs) and interval-valued Pythagorean fuzzy sets (IVPFSs) play a vital role in decision-making processes. In this paper based on PFS and IVPFS we introduce the concept of Cubic Pythagorean fuzzy set in which membership degree is an IVPFS and non-membership degree is a PFS. We define some basic operation of Cubic Pythagorean fuzzy numbers (CPFNs). We define score and accuracy functions to compare CPFNs. We also define distance between CPFNs. Based on the defined operations we develop Cubic Pythagorean fuzzy weighted averaging (CPFWA) operator and Cubic Pythagorean fuzzy weighted geometric (CPFWG) operator. We discuss some properties of the developed operators such as idempotancy, boundedness and monotonicity. Moreover, we give a multi-attribute decision making, to show the validity and effectiveness of the developed approach. Finally, we compare our approach with the existing methods.
