Rough approximation models via graphs based on neighborhood systems

Abstract

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 jupper 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.

On Three Types of Soft Rough Covering-Based Fuzzy Sets

“…Pawlak [1,2] developed the rough set theory for addressing the vagueness and granularity of information systems and data analysis. His theory and its generalizations since then have produced applications in different areas [3][4][5][6][7][8][9][10][11][12][13][14][15]. As mentioned above, a large variety of generalized rough set models have been investigated.…”

Covering Fuzzy Rough Sets via Variable Precision

“…Pawlak [1,2] presented the classical definition of rough sets as a valuable mathematical method to deal with the vagueness and granularity of information systems and data processing. His theory and its generalizations since then have produced applications in different areas [3][4][5][6][7][8][9][10][11][12][13].…”

The Number of Blocks of a Graph with Given Minimum Degree

“…However, the upper bound for b (G) remains open if G is a k-regular graph with k ≥ 4. One of the referees pointed out the possibility of the obtained results to some real-life applications and other fields (see [10][11][12] for instance).…”