MVLSC Home · Issue Contents · Forthcoming Papers
A Novel Approach to Picture Fuzzy Graphswith Application Towards the Selection Criteria
Yongsheng Rao, Saeed Kosari, Janusz Kacprzyk, Jana Shafi, Aysha Khan and Hossein Rashmanlou
The concept of vague picture fuzzy set (VPFS) is the most generalized from of fuzzy sets and is proven a useful tool to manipulate complications that arise due to incomplete information more effectively. Recently, many researchers investigated several concepts occuring in various fields such as social networks, computer networking, psychology, medical science, decision making etc based on various fuzzy graph structures. In this research work, we give the combination of both VPFSs and fuzzy graphs named vague picture fuzzy graphs (VPFGs) and provide its application in finding the best places to build a gas station. Initially, we introduce VPFGs and then study several concepts such as strong-VPFG, open neighborhood degree, total degree, busy value, homomorphism, isomorphism, and two new operations named rejection and symmetric difference on two VPFGs. Likewise, some properties of symmetric difference and rejection of VPFG have been discussed.
Keywords: Vague set, picture fuzzy set, symmetric difference, rejection, busy node, vague picture fuzzy graph
Mathematics Subject Classification: 05C99, 03E72. 16Y60