Journal
IEEE ACCESS
Volume 10, Issue -, Pages 114284-114296Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/ACCESS.2022.3216615
Keywords
Fuzzy sets; Decision making; Uncertainty; Layout; Graph theory; Terrain factors; Probabilistic logic; Com-PFG; order; size; complement; union; join; Cartesian products; composition; direct product
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Funding
- King Saud University, Riyadh, Saudi Arabia [RSP-2021/401]
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This paper introduces the extension of complex fuzzy graphs - complex picture fuzzy set (Com-PFS), and explains its development methods and primary operations in detail. Com-PFG employs three complex membership functions to provide a more accurate representation of fuzzy situations, and discusses its application in decision-making problems.
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.
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