Innovative Theoretical Approach: Bipolar Pythagorean Neutrosophic Sets (BPNSs) in Decision-Making
Noraini Ahmad*1, Zahari Rodzi*2,3, Faisal Al-Sharqi4,5, Ashraf Al-Quran6, Abdalwali Lutfi7, Zanariah Mohd Yusof8, Nor Aini Hassanuddin9
1 Pusat Asasi UiTM, UiTM Cawangan Selangor, Kampus Dengkil, 43800 Selangor, Malaysia
2 College of Computing, Informatics and Mathematics, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia
3 Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Malaysia
4 Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq
5 College of Engineering, National University of Science and Technology, Dhi Qar, Iraq
6 Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia
7 Department of Accounting, College of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia
8,9 College of Computing, Informatics and Mathematics, UiTM Cawangan Terengganu, Kampus Kuala Terengganu, 21080 Terengganu, Malaysia
Emails: norainiahmad@uitm.edu.my; zahari@uitm.edu.my; faisal.ghazi@uoanbar.edu.iq; aalquran@kfu.edu.sa; aalkhassawneh@kfu.edu.sa; zanariah297@uitm.edu.my; norai548@uitm.edu.my
Abstract
In this paper, the concept of bipolar Pythagorean fuzzy neutrosophic sets (BPNSs) will be introduced which represents an innovative synthesis, incorporating bipolarity, Pythagorean fuzzy sets, and neutrosophic sets to provide a comprehensive solution to the multifaceted issues encountered in decision-making challenges. BPNS is proposed to enhance the expressiveness and flexibility of the model by incorporating both positive and negative preferences that can lead to more accurate and realistic modeling of complex decision scenarios. The essential idea of BPNSs is defined and some definitions for instance complement, intersection, and union are described. The basic operation, the derivation of its properties, and the numerical example of the method are integrated to execute the proposed model.
Keywords: Pythagorean fuzzy set; Neutrosophic set; Bipolar fuzzy set; Decision-making problem