Certain Operations on Complex Picture Fuzzy Graphs

Muhammad Shoaib, Waqas Mahmood, Qin Xin, Fairouz Tchier, Ferdous M. O. Tawfiq

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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 (CompIFG) 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 ComPFG 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
Original languageEnglish
Pages (from-to)114284 - 114296
Number of pages13
JournalIEEE Access
Volume10, 2022
Publication statusPublished - 2022


  • Com-PFG
  • order
  • size
  • complement
  • union
  • join
  • Cartesian products
  • composition
  • direct product


Dive into the research topics of 'Certain Operations on Complex Picture Fuzzy Graphs'. Together they form a unique fingerprint.

Cite this