Colouring of COVID-19 Affected Region Based on Fuzzy Directed Graphs

Graph colouring is the system of assigning a colour to each vertex of a graph.It is done in such a way that adjacent vertices do not have equal colour.It is fundamental in graph theory.It is often used to solve real-world problems like traffic light signalling,map colouring,scheduling,etc.Nowadays,social networks are prevalent systems in our life.Here,the users are considered as vertices,and their connections/interactions are taken as edges.Some users follow other popular users’profiles in these networks,and some don’t,but those non-followers are connected directly to the popular profiles.That means,along with traditional relationship(information flowing),there is another relation among them.It depends on the domination of the relationship between the nodes.This type of situation can be modelled as a directed fuzzy graph.In the colouring of fuzzy graph theory,edge membership plays a vital role.Edge membership is a representation of flowing information between end nodes of the edge.Apart from the communication relationship,there may be some other factors like domination in relation.This influence of power is captured here.In this article,the colouring of directed fuzzy graphs is defined based on the influence of relationship.Along with this,the chromatic number and strong chromatic number are provided,and related properties are investigated.An application regarding COVID-19 infection is presented using the colouring of directed fuzzy graphs.

Prognostic Kalman Filter Based Bayesian Learning Model for Data Accuracy Prediction

Data is always a crucial issue of concern especially during its prediction and computation in digital revolution.This paper exactly helps in providing efficient learning mechanism for accurate predictability and reducing redundant data communication.It also discusses the Bayesian analysis that finds the conditional probability of at least two parametric based predictions for the data.The paper presents a method for improving the performance of Bayesian classification using the combination of Kalman Filter and K-means.The method is applied on a small dataset just for establishing the fact that the proposed algorithm can reduce the time for computing the clusters from data.The proposed Bayesian learning probabilistic model is used to check the statistical noise and other inaccuracies using unknown variables.This scenario is being implemented using efficient machine learning algorithm to perpetuate the Bayesian probabilistic approach.It also demonstrates the generative function forKalman-filer based prediction model and its observations.This paper implements the algorithm using open source platform of Python and efficiently integrates all different modules to piece of code via Common Platform Enumeration(CPE)for Python.