The notion of fuzzy graph (FG) is widely used in many problems arising from partial or incomplete descriptions of the real world and in particular from fields such as engineering, economics, computer science, social disciplines, or medical diagnostics, and has been used in many fields of pure mathematics as well as in several areas of applied sciences such as decision making, statistics and networking. In this paper we will deal with the graph of the picture fuzzy(symmetric) set using the notion of domination in picture fuzzy graph (PFG) as a generalization of both the concept of fuzzy graph domination and intuitionistic fuzzy graph (IFG) domination. The concepts of domination theory (DT) and double domination theory (DDT) of a PFG are introduced, studied and concretely applied to the real case of an election competition to determine the minimum number of citizens a politician should meet in person in order to win the election. The choice of fuzzification (symmetric) and defuzzification (anti-symmetric) methods depends on the specific application and the type of fuzzy sets being used, whether they are symmetric or anti-symmetric. There are various methods for each process, such as centroid, max-min, and weighted average methods for defuzzification. Finally, in the last section, drawing from the application example, the features and benefits of PFGs with respect to fuzzy graphs and intuitionistic fuzzy graphs are compared and discussed.

A Complete Breakdown of Politics Coverage Using the Concept of Domination and Double Domination in Picture Fuzzy Graph

Giorgio Nordo
Penultimo
Investigation
;
2023-01-01

Abstract

The notion of fuzzy graph (FG) is widely used in many problems arising from partial or incomplete descriptions of the real world and in particular from fields such as engineering, economics, computer science, social disciplines, or medical diagnostics, and has been used in many fields of pure mathematics as well as in several areas of applied sciences such as decision making, statistics and networking. In this paper we will deal with the graph of the picture fuzzy(symmetric) set using the notion of domination in picture fuzzy graph (PFG) as a generalization of both the concept of fuzzy graph domination and intuitionistic fuzzy graph (IFG) domination. The concepts of domination theory (DT) and double domination theory (DDT) of a PFG are introduced, studied and concretely applied to the real case of an election competition to determine the minimum number of citizens a politician should meet in person in order to win the election. The choice of fuzzification (symmetric) and defuzzification (anti-symmetric) methods depends on the specific application and the type of fuzzy sets being used, whether they are symmetric or anti-symmetric. There are various methods for each process, such as centroid, max-min, and weighted average methods for defuzzification. Finally, in the last section, drawing from the application example, the features and benefits of PFGs with respect to fuzzy graphs and intuitionistic fuzzy graphs are compared and discussed.
2023
File in questo prodotto:
File Dimensione Formato  
A Complete Breakdown of Politics Coverage Using the Concept of Domination and Double Domination in Picture Fuzzy Graph.pdf

solo utenti autorizzati

Descrizione: A Complete Breakdown of Politics Coverage Using the Concept of Domination and Double Domination in Picture Fuzzy Graph
Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 519.47 kB
Formato Adobe PDF
519.47 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3257918
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 2
social impact