The Correlation Coefficient of Hesitancy Fuzzy Graphs in Decision Making

Abstract

The hesitancy fuzzy graphs (HFGs), an extension of fuzzy graphs, are useful tools for dealing with ambiguity and uncertainty in issues involving decision-making (DM). This research implements a correlation coefficient measure (CCM) to assess the strength of the association between HFGs in this article since CCMs have a high capacity to process and interpret data. The CCM that is proposed between the HFGs has better qualities than the existing ones. It lowers restrictions on the hesitant fuzzy elements' length and may be used to establish whether the HFGs are connected negatively or favorably. Additionally, a CCM-based attribute DM approach is built into a hesitant fuzzy environment. This article suggests the use of weighted correlation coefficient measures (WCCMs) using the CCM concept to quantify the correlation between two HFGs. The decision-making problems of hesitancy fuzzy preference relations (HFPRs) are considered. This research proposes a new technique for assessing the relative weights of experts based on the uncertainty of HFPRs and the correlation coefficient degree of each HFPR. This paper determines the ranking order of all alternatives and the best one by using the CCMs between each option and the ideal choice. In the meantime, the appropriate example is given to demonstrate the viability of the new strategies.