Topological approach to generate new rough set models

• DOI: 10.1007/s40747-022-00704-x
• Publication Date: 2022-03-14T04:12:31Z
• Authors: Tareq M. Al-shami
• Keywords: Rough Sets Theory and Applications; Intuitionistic Fuzzy Sets; Artificial intelligence; Social Sciences; Set (abstract data type); 02 engineering and technology; Multi-Criteria Decision Making; Management Science and Operations Research; Mathematical analysis; Decision Sciences; Machine learning; FOS: Mathematics; 0202 electrical engineering, electronic engineering, information engineering; Data mining; Probabilistic Rough Sets; Open set; Discrete mathematics; Computer science; Programming language; Algorithm; Computational Theory and Mathematics; Rough set; Computer Science; Physical Sciences; Rough Sets; Monotonic function; Mathematics

Abstract In this paper, we introduce a topological method to produce new rough set models. This is based on the idea of “somewhat open sets” which one celebrated generalizations sets. We first generate some topologies from different types $$N_\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>N</mml:mi><mml:mi>ρ</mml:mi></mml:msub></mml:math> -neighborhoods. Then, define approximations and accuracy measures with respect somewhat closed study their main properties prove that roughness preserve monotonic property. One unique these possibility comparing between them. also compare our approach previous ones, show it more accurate than those induced open, $$\alpha xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> -open, semi-open Moreover, examine effectiveness followed in problem Dengue fever. Finally, discuss strengths limitations propose future work.