On Complex Fuzzy Soft Graph With Operations Sana Abu-Ghurra1 , Ghada Alafifi2 , Eman A. AbuHijleh3,∗ , Firas Safi4 1Mathematics Department, Faculty of Science, Applied Science Private University, Amman, Jordan 2 athematics Department, Science College, Philadelphia University, Amman, Jordan 3Department of Basic Sciences, Al-Zarqa University College, Al-Balqa Applied University, Zarqa 313, Jordan 4Department of Mathematics, Faculty of Science, Zarqa University, Zarqa, Jordan Emails: abugurcan@asu.edu.jo; gaffif@philadelphia.edu.jo; emanhjleh@bau.edu.jo; fsafi@u.edu.jo Abstract The goal of this paper is to study complex fuzzy soft graph (CFSG). We introduce the concept of complex fuzzy soft graph from apply complex fuzzy set on fuzzy soft graph. The notations and definitions of some operations on two complex fuzzy soft graphs presented such as union, cartesian product, tensor product, normal product and composition of two complex fuzzy soft graphs. Also, a decision-making (DM) problem on supply chain management is discussed. Keywords: Complex fuzzy soft graph; Union; cartesian product; Tensor product; Normal product and composition of two complex fuzzy soft graphs