OICC Press Fuzzy Optimization and Modeling Journal (FOMJ) 2676-7007 1 2 2020 10 01 Rough Set in Fuzzy Approximation Space with Fuzzy Equivalence Class 43 49 EN Mohadeseh Taginejad Department of Mathematics, Payame Noor University (PNU) Tehran, Iran Journal Article 2020 10 01 The rough set model was constructed in fuzzy approximation space. In this study, we first introduce the fuzzy relation, relative sets, and fuzzy equivalence class. Then, we prove some properties of the fuzzy equivalence class. Thereafter, the concept of fuzzy rough set is proposed over fuzzy relation and inverse fuzzy relation in fuzzy approximation space by means of relative sets and fuzzy equivalence class sets, and some propositions are proved. Also, some examples and dentitions are presented in this study