Affiliations: [a] School of Mathematical Sciences, Nanjing Normal University, Nanjing, China
| [b] School of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou, China
| [c] Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt
| [d] Physics Department, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia
| [e] Department of Mathematics, Faculty of Science, Helwan University, Egypt
Correspondence:
[*]
Corresponding author. Ahmed Mostafa Khalil, Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt. Tel.: +0201157633794; E-mail: [email protected].
Abstract: In this article, we propose a novel concept of the generalized picture fuzzy soft set by combining the picture fuzzy soft set and the fuzzy parameter set. For possible applications, we explain five kinds of operations (e.g., subset, equal, union, intersection, and complement) based on generalized picture fuzzy soft sets. Then, we establish several theoretical operations of generalized picture fuzzy soft sets. In addition, we present the new type by using the AND operation of the generalized picture fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example. Finally, we give a comparison between the picture fuzzy soft set theory and the generalized picture fuzzy soft set theory. It is shown that our proposed (i.e., generalized picture fuzzy soft set theory) is viable and provide decision makers a more mathematical insight before making decisions on their options.
