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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Soleha Soleha
Department of Mathematics, Faculty of Science and Data Analytics, Sepuluh Nopember Institute of Technology, Surabaya
Mathematics

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Approximation Properties on a Set Based on Equivalence Relations and Dominance Relations Dian Winda Setyawati; Soleha Soleha; Rinurwati Rinurwati
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40603

Abstract

An equivalence relation on a set forms equivalence classes so that the concept of approximation is formed on that set (rough set). The concept of approximation on a set is developing very rapidly. Some papers replace the equivalence relation with other relations, one of which is the dominance relation. This paper provides the approximation properties that hold to the equivalence and dominance relations using the concept of three types of approximations defined on a set. In addition, it identifies the properties that hold in the equivalence relations but do not necessarily hold in the dominance relations. Furthermore, this paper proves that the three types of approximations on a set w.r.t an equivalence relation are identical, but this result does not necessarily hold for a dominance relation, especially for the third type.
Co-Authors Dian Winda Setyawati Rinurwati Rinurwati