Topological approach to generate new rough set models

Abstract

In this paper, we introduce a topological method to produce new rough set models. This method is based on the idea of “somewhat open sets” which is one of the celebrated generalizations of open sets. We first generate some topologies from the different types of $$N_\rho $$ N ρ -neighborhoods. Then, we define new types of rough approximations and accuracy measures with respect to somewhat open and somewhat closed sets. We study their main properties and prove that the accuracy and roughness measures preserve the monotonic property. One of the unique properties of these approximations is the possibility of comparing between them. We also compare our approach with the previous ones, and show that it is more accurate than those induced from open, $$\alpha $$ α -open, and semi-open sets. Moreover, we examine the effectiveness of the followed method in a problem of Dengue fever. Finally, we discuss the strengths and limitations of our approach and propose some future work.

Approximation operators and accuracy measures of rough sets from an infra-topology view

“…(see, Al-shami 2022 ) We call the approximations spaces and have the property of monotonicity accuracy (resp. monotonicity roughness) if (resp., ) whenever .…”

“…Järvinen and Radeleczki ( 2020 ) introduced the optimistic lower and upper approximations with respect to two equivalence relations. Many studies were contacted to explore and develop rough set notions depending on topological ideas such as Abo-Tabl ( 2014 ), Al-shami ( 2021b , 2022 ), Hosny ( 2018 ), Kondo and Dudek ( 2006 ), Salama ( 2020a ) and Singh and Tiwari ( 2020 ). Moreover, it was applied rough set concepts induced from some generalizations of topology such as minimal structure (Azzam et al.…”

On b-open Sets via Infra Soft Topological Spaces

“…Recently, topology has been applied to model some real-life issues as showed in [1,11,15,16,32,46,56,64]. To study topology via S-set theory, C ¸aǧman et al [51] and Shabir and Naz [65], in 2011, introduced the concept of soft topology(ST).…”

Improvement of Approximation Spaces Using Maximal Left Neighborhoods and Ideals

“…This development helps to deal with uncertainty and get rid of obstacles in decision-making problems as shown in [13], [22], [33]. Topological spaces are another significant approach to investigate approximation operators [5], [10], [24], [26], [37]. These approaches applied with ideal to construct new rough set models.…”