The State of Health (SoH) needs to be accurately estimated for Electric Vehicle (EV) batteries to manage performance, safety and longevity. This study aims to propose a data-driven method with the Random Forest Regression (RFR) model to accurately predict the SoH. This approach builds on historical battery performance data to train the RFR model, which is particularly useful for capturing complex nonlinear relationships between input features and the SoH metric. Whereas model-based methods require electrochemical models, and data-driven methods often rely on extensive laboratory testing, our method demonstrates a pathway to a computationally efficient, flexible, and accurate approach that works across a diversity of battery types and use cases. It used key features like voltage, current, temperature, and charge/discharge rates as predictors, which allows a comprehensive examination of the current and former battery behaviours. This model has been evaluated against various benchmark datasets and has shown a high level of accuracy and robustness.

The study of set of objects with imprecise knowledge and vague information is known as rough set theory. The diagrammatic representation of this type of information may be handled through graphs for better decision making. Tong He and K. Shi introduced the constructional processes of rough graph in 2006 followed by the notion of edge rough graph. They constructed rough graph through set approximations called upper and lower approximations. He et al developed the concept of weighted rough graph with weighted attributes. Labelling is the process of making the graph into a more sensible way. In this process, integers are assigned for vertices of a graph so that we will be getting distinct weights for edges. Weight of an edge brings the degree of relationship between vertices. In this paper we have considered the rough graph constructed through rough membership values and as well as envisaged a novel type of labeling called Even vertex ζ-graceful labeling as weight value for edges. In case of rough graph, weight of an edge will identify the consistent attribute even though the information system is imprecise. We have investigated this labeling for some special graphs like rough path graph, rough cycle graph, rough comb graph, rough ladder graph and rough star graph etc. This Even vertex ζ-graceful labeling will be useful in feature extraction process and it leads to graph mining.

Rough membership function defines the degree of relationship between conditional and decision attributes of an information system. It is defined by µ R X : U → [0, 1] where X is the subset of U under the relation R where U is the universe of discourse. It can be expressed in different forms like cardinality form, probabilistic form etc. In cardinality form,