Affiliations: [a]
Department of Mathematics, Hazara University Mansehra, KPK, Pakistan
| [b]
Department of Mathematics, Abdul Wali Khan University Mardan, KPK, Pakistan
Correspondence:
[*]
Corresponding author. Faisal Khan, Department of Mathematics, Hazara University Mansehra, KPK, Pakistan. E-mail: faisalmaths@hu.edu.pk.
Abstract: Since Pythagorean fuzzy sets and interval-valued Pythagorean fuzzy sets are better tools to deal with fuzziness and vagueness. Therefore, in this paper, we present the notion of Pythagorean cubic fuzzy sets in which the membership degree and non-membership degree are cubic fuzzy numbers which hold the conditions that the square sum of its membership degree is less than or equal to
〈1˜,1〉
. We define some basic operators and to compare two Pythagorean cubic fuzzy numbers we develop score and accuracy function. We also define the distance between two Pythagorean cubic fuzzy numbers. Based on the defined operators, we propose Pythagorean cubic fuzzy weighted averaging (PCFWA), Pythagorean cubic fuzzy weighted geometric (PCFWG), Pythagorean cubic fuzzy ordered weighted averaging (PCFOWA) and Pythagorean cubic fuzzy ordered weighted geometric (PCFOWG) operators. We discuss some of its operational laws of the established operators and suggest a multi criteria decision-making (MCDM) approach based on the developed operators. Moreover, the methods and operators proposed in this paper are providing more general, more accurate and precise results as compared to the existing methods because these methods and operators are the generalization of their existing methods. Furthermore, the method for multi-criteria decision-making problems based on these proposed operators was developed, and the operational processes were also illustrated in detail. Finally, an illustrative example is given to show the decision-making steps in detail of these proposed methods and operators to show the validity, practicality and effectiveness.
