Abstract
Fuzzy graphs (FGs) can play a useful role in natural and human-made structures, including process dynamics in physical, biological, and social systems. Since issues in everyday life are often uncertain due to inconsistent and ambiguous information, it is extremely difficult for an expert to model those difficulties using an FG. Indeterminate and inconsistent information related to real-valued problems can be studied through a picture of the fuzzy graph (PFG), while the FG does not provide mathematically acceptable information. In this regard, we are interested in reducing the limitations of FGs by introducing some new definitions and results for the PFG. This paper aims to describe and explore a few properties of PFGs, including the maximal product (MP), symmetric difference (SD), rejection (RJ), and residue product (RP). Furthermore, we also discuss the degree and total degree of nodes in a PFG. This study also demonstrates the application of a PFG in digital marketing and social networking.
Highlights
In 1965, Zadeh [1] presented the fuzzy set (FS) as an extension of the crisp set to deal with imprecise and unclear information in ambiguous situations, and it is effective and acceptable
The picture of the fuzzy graph (PFG) is a generalization of the Fuzzy graphs (FGs) and intuitionistic fuzzy graph (IFG)
A PFG can deal with uncertain problems, whereas an FG and IFG may not be effective in such contexts
Summary
In 1965, Zadeh [1] presented the fuzzy set (FS) as an extension of the crisp set to deal with imprecise and unclear information in ambiguous situations, and it is effective and acceptable It can be characterized by a true membership function similar to a probability function having ranges in [0, 1]. Shao et al [9] described new concepts of the bondage number in the intuitionistic fuzzy graph (IFG). In this study, we establish some new properties of the PFG, including MP, SD, RP, and RJ, which may be suggestive of some aspects of network design because it contains the additional neutral grade, while the FG and IFG may fail in networking due to lack of information.
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