Rough approximation models via graphs based on neighborhood systems

Neighborhood systems are used to approximate graphs as finite topological structures. Throughout this article, we construct new types of eight neighborhoods for vertices of an arbitrary graph, say, j-adhesion neighborhoods. Both notions of Allam et al. and Yao will be extended via j-adhesion neighborhoods. We investigate new types of j-lower approximations and j-upper approximations for any subgraph of a given graph. Then, the accuracy of these approximations will be calculated. Moreover, a comparison between accuracy measures and boundary regions for different kinds of approximations will be discussed. To generate j-adhesion neighborhoods and rough sets on graphs, some algorithms will be introduced. Finally, a sample of a chemical example for Walczak will be introduced to illustrate our proposed methods.

Automated summary

In this article, neighborhood systems are used to approximate graphs as finite topological structures. New types of eight neighborhoods, called j-adhesion neighborhoods, are constructed for vertices of any graph. The concepts of Allam et al. and Yao are extended through j-adhesion neighborhoods, and new types of j-lower and j-upper approximations for subgraphs of a given graph are investigated. The accuracy of these approximations is calculated and a comparison between accuracy measures and boundary regions for different types of approximations is discussed. Algorithms are introduced to generate j-adhesion neighborhoods and rough sets on graphs, and a chemical example is used to illustrate the proposed methods.