Certain Operations on Complex Picture Fuzzy Graphs

• Published in: IEEE access Vol. 10; p. 1
• Main Authors: Shoaib, Muhammad, Mahmood, Waqas, Xin, Qin, Tchier, Fairouz, Tawfiq, Ferdous M. O.
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Cartesian coordinates; Cartesian products; Com-PFG; complement; composition; Decision making; direct product; Fuzzy sets; Graph theory; Graphs; join; Layout; order; Probabilistic logic; size; Terrain factors; Uncertainty; union
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2022.3216615

A complex picture fuzzy set (Com-PFS) is a motivating tool for more precisely interpreting fuzzy notions. Recently, all extensions of complex fuzzy graphs (Com-FGs) have become a growing research topic as they handle ambiguous situations more explicitly than complex intuitionistic fuzzy graphs (Comp-IFG) and picture fuzzy graphs (PFG). The primary goal of this study is to demonstrate the foundation of Com-PFG due to the drawback of the complex neutral membership function in Com-IFG. This paper introduces the concept of Com-PFGs and explains many of the approaches to their development. A Com-PFG has three complex membership functions. We define the order, size, degree of vertex, and total degree of vertex in Com-PFGs. We elaborate on primary operations including: complement, join, union, Cartesian product, direct product, and composition of Com-PFG. Finally, we discuss its use in decision-making problems.