Analysis of social networks and Wi-Fi networks by using the concept of picture fuzzy graphs
- PDF / 1,646,851 Bytes
- 13 Pages / 595.276 x 790.866 pts Page_size
- 101 Downloads / 214 Views
(0123456789().,-volV)(0123456789(). ,- volV)
METHODOLOGIES AND APPLICATION
Analysis of social networks and Wi-Fi networks by using the concept of picture fuzzy graphs Laszlo T. Koczy1 • Naeem Jan2,3 • Tahir Mahmood2 • Kifayat Ullah2,3
Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Atanassov’s intuitionistic fuzzy set described the uncertainty of real-life events with the help of a membership and a nonmembership degree. However, human opinion cannot be restricted to yes or no, but there is some abstinence and refusal degree as well. In such cases, picture fuzzy set is a suitable solution which described the abstinence and refusal grade of human opinion along with membership and non-membership grades. The aim of this paper is to analyse a social network and a wife network using the concept of picture fuzzy graph (PFG). For this purpose, the concept of PFG is proposed and some basic terms are demonstrated including complement, degree and bridges. The main advantage of the proposed PFG is that it describes the uncertainty in any real-life event with the help of four membership degrees where the traditional FG and IFG fail to be applied. The viability of PFG is shown by utilizing the concept in demonstrating two real-life problems including a social network and a Wi-Fi-network. A comparison of PFG with existing notions is established showing its superiority over the existing frameworks. Keywords Intuitionistic fuzzy graphs Picture fuzzy graphs Social networks Wi-Fi networks
1 Introduction Dealing with uncertain situations and insufficient information required some high potential tools. Graph is one such mathematical tool which effectively deals with large data. When there is some sort of uncertainty factors, FG is Communicated by V. Loia. & Naeem Jan [email protected]; [email protected] & Kifayat Ullah [email protected]; [email protected] Laszlo T. Koczy [email protected] Tahir Mahmood [email protected] 1
Department of Telecommunications and Media Informatics, Budapest University of Technology and Economics, Budapest, Hungary
2
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
3
Department of Data Analysis and Mathematical Modeling, Faculty of Bioscience Engineering, Ghent University, Ghent, Belgium
a tool that needs to be used. Due to its capacity of handling large data, graph theory is of some special interest as it can be applied to many problems including problems in management sciences (Harary 1959), social sciences (Harary and Norman 1953), computer sciences (Shirinivas et al. 2010), communication networks (Harary and Ross 1953), in description of group structures (Ross and Harary 1959), database theory (Kiss 1991) and economics (Keller 2007). The tool of fuzzy set (FS) proposed by Zadeh (1965) is considered to be the best tool so far due to its practicality to several potential problems. Kaufmann proposed the definition of FG in (Kaufmann 1973). A comprehensive study is achieved by Rosenfeld in (1
Data Loading...
