International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1513 2020 2020 Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia Ashraf Al Al-Quran Department of Mathematical Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Malaysia Abd Ghafur .. Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq Faisal Al Al-Sharqi Department of Accounting, College of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia Abdalwali Lutfi Most complex problems in the real-world typically involve uncertain,incomplete and indeterminate two-dimensional data i.e. information pertaining to the attributes and the periodicity of the problem parameters. To meet the demand for models that has the ability to handle these information with these characteristics, the introduction of neutrosophic sets (NSs) was followed by their extension to the complex neutrosophic sets (CNSs). In this paper, we introduce the concept of Q- complex neutrosophic set (Q-CNS) by extending the ranges of the membership functions in Q-neutrosophic set (Q-NS) from [0,1] to the unit circle in the complex plane. Q-CNS plays a key role in the decision making theory, where the extra information provided by the elements of the Q-set serve in modeling of some decision making problems. Based on this new concept we define the basic theoretical operations such as complement, equality, subset, union, intersection, Q-complex neutrosophic product and Cartesian product. Some related examples are also given to enhance the understanding of the proposed concepts. The basic properties of these operators are also verified with supporting proofs. 2023 2023 08 19 10.54216/IJNS.200201 https://www.americaspg.com/articleinfo/21/show/1513