J. Math. Computer Sci., 28 (2023), 236–257 Online: ISSN 2008-949X Journal Homepage: www.isr-publications.com/jmcs New types of rough Pythagorean fuzzy UP-filters of UP- algebras Akarachai Satirad a , Ronnason Chinram b , Pongpun Julatha c , Rukchart Prasertpong d , Aiyared Iampan a,* a Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand. b Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand. c Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand. d Division of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, Nakhon Sawan 60000, Thailand. Abstract The aim of this paper is to introduce nine types of rough Pythagorean fuzzy sets in UP-algebras and nine types of rough sets in UP-algebras. Then we study relation of these rough Pythagorean fuzzy sets and new types of Pythagorean fuzzy UP- filter under equivalence (congruence) relation. Moreover, we will also discuss t-level subsets of rough Pythagorean fuzzy sets in UP-algebras to study the relationships between rough Pythagorean fuzzy sets and rough sets in UP-algebras which we defined them above. Finally, we discuss the concept of homomorphisms between IUP-algebras and also study the direct and inverse images of four special subsets. Keywords: UP-algebra, rough set, rough Pythagorean fuzzy set, t-level subset. 2020 MSC: 03G25, 03E72, 08A72. ©2023 All rights reserved. 1. Introduction and preliminaries The concept of fuzzy sets (FSs) was first considered by Zadeh [32] in 1965. Zadeh’s and others’ FS concepts have found numerous applications in mathematics and other fields. Following the introduction of the concept of FSs, various researchers were interviewed about generalizations of the concept of FSs, including: Atanassov [5] defined a new concept called an intuitionistic fuzzy set (IFS) which is a gener- alization of a FS, Yager [30] introduced a new class of non-standard fuzzy subsets called a Pythagorean fuzzy set (PFS) and the related idea of Pythagorean membership grades. The concept of rough sets (RSs) was first considered by Pawlak [20] in 1982. After the introduction of the concept of RSs, several authors have applied the concept of RSs to the generalizations of the concept of * Corresponding author Email addresses: akarachai.sa@gmail.com (Akarachai Satirad), ronnason.c@psu.ac.th (Ronnason Chinram), pongpun.j@psru.ac.th (Pongpun Julatha), rukchart.p@nsru.ac.th (Rukchart Prasertpong), aiyared.ia@up.ac.th (Aiyared Iampan) doi: 10.22436/jmcs.028.03.03 Received: 2021-04-15 Revised: 2022-05-02 Accepted: 2022-05-20