On Graph Structures in Fuzzy Environment Using Optimization Parameter

• Published in: IEEE access Vol. 9; pp. 75699 - 75711
• Main Authors: Rehman, Atiq Ur, Salabun, Wojciech, Faizi, Shahzad, Hussain, Muhammad, Watrobski, Jaroslaw
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Apexes; Flow charts; Fuzzy graph structure; Fuzzy logic; Fuzzy sets; Graph theory; Indexes; Optimization; Parameters; regular fuzzy graph structure; Urban areas; vertex degree; vertex total degree; weighted mean product; Workstations
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2021.3081505

This paper comprises the introduction of weighted mean products of fuzzy graph structures ( FGSs ) to construct weighted mean fuzzy graph structures ( WMFGSs ) with the help of optimization parameter, and establish some novel results after validating with examples, accordingly. The notions of regular and <inline-formula> <tex-math notation="LaTeX">m\mu _{k} </tex-math></inline-formula>-regular FGSs are described, where <inline-formula> <tex-math notation="LaTeX">m\in </tex-math></inline-formula>]0, 1] represents the degree of all vertices in <inline-formula> <tex-math notation="LaTeX">\widetilde {G} </tex-math></inline-formula> under mapping <inline-formula> <tex-math notation="LaTeX">\mu _{k} </tex-math></inline-formula>, and develop certain properties of regular WMFGSs . In addition, we create a flowchart to present common application procedures of fuzzy graphical frameworks to classify the advanced city out of some important Pakistani cities subject to certain parameters.