Affiliations: [a] Department of Mathematics, Hazara University Mansehra, Pakistan
| [b] Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan
Correspondence:
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Corresponding author. Saleem Abdullah, Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan. E-mails: saleemabdullah@awkum.edu.pk.
Abstract: The concept of interval-valued Pythagorean fuzzy (IVPF) sets is capable of handling imprecise and ambiguous information and managing complex uncertainty in real-world applications. The focus of our this paper is to introduce some generalized operators, such as the generalized interval-valued Pythagorean fuzzy Einstein weighted averaging (abbreviated as GIVPFEWA) operator, the generalized interval-valued Pythagorean fuzzy Einstein ordered weighted averaging (abbreviated as GIVPFEOWA) operator, and the generalized interval-valued Pythagorean fuzzy Einstein hybrid averaging (abbreviated as GIVPFEHA) operator along with their some general properties, such as idempotency, commutativity, monotonicity and boundedness. Furthermore, the method for multiple attribute group decision making problems based on these operators was developed, and the operational processes were illustrated in detail. The main advantage of using the proposed methods and operators is that these operators and methods give a more complete view of the problem to the decision makers. These methods provide more general, more accurate and precise results as compared to the existing methods. Therefore these methods play a vital role in real world problems. Finally the proposed operators have been applied to decision-making problems to show the validity, practicality and effectiveness of the new approach. A systematic comparison between the existing work and the proposed work also has been given.
Keywords: GIVPFEWA operator, GIVPFEOWA operator, GIVPFEHA operator, Group decision-making
