Z-soft rough fuzzy graphs: A new approach to decision making

Article type: Research Article

Authors: Shah, Nasir^{a; *} | Mehmood, Nayyar^b | Rehman, Noor^a | Shabir, Muhammad^c | Ali, Muhammad Irfan^d

Affiliations: [a] Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan | [b] Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan; Department of Mathematical Sciences, United Arab Emirates University, Al-Ain, UAE | [c] Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan | [d] Department of Mathematics, Islamabad Model College for Girls, Islamabad, Pakistan

Correspondence: [*] Corresponding author. Nasir Shah, Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, Pakistan. E-mail: 8052@students.riu.edu.pk.

Abstract: The aim of this paper is to discuss the uncertainty in soft graphs and a new type of graphs, called Z-soft rough fuzzy graphs is introduced. The notions of Z-soft rough vertex graphs, Z-soft rough edge graphs and Z-soft rough fuzzy graphs are given, and their related properties are explored. The theory of graph approximation space is developed. To validate the applicability of Z-soft rough fuzzy graphs, we put forward an innovative approach to multicriteria group decision making problems.

Keywords: rough sets, soft graphs, Z-soft rough fuzzy graphs, decision making

DOI: 10.3233/JIFS-18993

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 4, pp. 4879-4891, 2018