Certain Operations on Complex Picture Fuzzy Graphs

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

doi:10.1109/ACCESS.2022.3216615

Certain Operations on Complex Picture Fuzzy Graphs

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

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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
problems.

Original language	English
Pages (from-to)	114284 - 114296
Number of pages	13
Journal	IEEE Access
Volume	10, 2022
DOIs	https://doi.org/10.1109/ACCESS.2022.3216615
Publication status	Published - 2022

Keywords

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

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10.1109/ACCESS.2022.3216615Licence: CC BY

Cite this

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abstract = "A complex picture fuzzy set (Com-PFS) is a motivating tool for more precisely interpretingfuzzy notions. Recently, all extensions of complex fuzzy graphs (Com-FGs) have become a growing researchtopic 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 foundationof Com-PFG due to the drawback of the complex neutral membership function in Com-IFG. This paperintroduces 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 degreeof vertex in Com-PFGs. We elaborate on primary operations including: complement, join, union, Cartesianproduct, direct product, and composition of Com-PFG. Finally, we discuss its use in decision-makingproblems.",

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AU - Shoaib, Muhammad

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AU - Tchier, Fairouz

AU - Tawfiq, Ferdous M. O.

PY - 2022

Y1 - 2022

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KW - Com-PFG

KW - order

KW - size

KW - complement

KW - union

KW - join

KW - Cartesian products

KW - composition

KW - direct product

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JO - IEEE Access

JF - IEEE Access

ER -

Certain Operations on Complex Picture Fuzzy Graphs

Abstract

Keywords

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