Novel Graph Neighborhoods Emerging from Ideals

Ayşegül Çaksu Güler, Mehmet Ali Balcı (), Larissa M. Batrancea (), Ömer Akgüller and Lucian Gaban
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Ayşegül Çaksu Güler: Department of Mathematics, Faculty of Science, Ege University, 35100 Bornova, İzmir, Turkey
Mehmet Ali Balcı: Department of Mathematics, Faculty of Science, Muğla Sıtkı Koçman University, 48000 Menteşe, Muğla, Turkey
Larissa M. Batrancea: Department of Business, Babes-Bolyai University, 7 Horea Street, 400174 Cluj-Napoca, Romania
Ömer Akgüller: Department of Mathematics, Faculty of Science, Muğla Sıtkı Koçman University, 48000 Menteşe, Muğla, Turkey
Lucian Gaban: Faculty of Economics, “1 Decembrie 1918” University of Alba Iulia, 15-17 Unirii Street, 510009 Alba Iulia, Romania

Mathematics, 2023, vol. 11, issue 10, 1-17

Abstract: Rough set theory is a mathematical approach that deals with the problems of uncertainty and ambiguity in knowledge. Neighborhood systems are the most effective instruments for researching rough set theory in general. Investigations on boundary regions and accuracy measures primarily rely on two approximations, namely lower and upper approximations, by using these systems. The concept of the ideal, which is one of the most successful and effective mathematical tools, is used to obtain a better accuracy measure and to decrease the boundary region. Recently, a generalization of Pawlak’s rough set concept has been represented by neighborhood systems of graphs based on rough sets. In this research article, we propose a new method by using the concepts of the ideal and different neighborhoods from graph vertices. We examine important aspects of these techniques and produce accuracy measures that exceed those previously = reported in the literature. Finally, we show that our method yields better results than previous techniques utilized in chemistry.

Keywords: rough sets; graph topology; approximations; ideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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