Possibility Fermatean Neutrosophic Soft Set
Shawkat Alkhazaleh1, Belal Batiha1, Areen Al-khateeb1*, Hamzeh Zureigat 1,2, Abedallah Al-shboul 1, Khaldoun Batiha 3
1 Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan,
2 Applied Science Research Center, Applied Science Private University, Al-Arab St. 21, Amman, 11931, Jordan,
3 Department of CS, Faculty of IT, Philadelphia University, Amman 19392, Jordan
Emails: s.alkhazaleh@jadara.edu.jo; b.bateha@jadara.edu.jo ; areen.k@jadara.edu.jo; hamzeh.zu@jadara.edu.jo;aalayyoup@yahoo.com; kh_batiha@philadelphia.edu.jo
Abstract
In this paper, we introduce the concept of Possibility Fermatean Neutrosophic Soft Set and define some related concepts such as Possibility Fermatean Neutrosophic Soft subset, Possibility Fermatean Neutrosophic Soft null set, and Possibility Fermatean Neutrosophic Soft universal set. Then, we define set-theoretical operations of Possibility Fermatean Neutrosophic Soft Sets such as union, intersection, and complement, and investigate some properties of these operations. We also introduce AND-product and OR-product operations between two Possibility Fermatean Neutrosophic Soft Sets. We propose a decision-making method called the Possibility Fermatean Neutrosophic Soft decision-making method (PFNS-decision-making method) which can be applied to decision-making problems involving uncertainty based on AND-product operation. We finally give a numerical example to display the application of the method that can be successfully applied to the problems.
Keywords: Fuzzy Set, Soft Set; Fuzzy Soft Set; Fermatean Fuzzy Set; Fermatean Fuzzy Soft Set; Intuitionistic Fuzzy Soft Set; Possibility Fuzzy Soft Set; Intuitionistic Possibility Fermatean Fuzzy Soft Set; Possibility Fermatean Neutrosophic Soft Set