Uncorrected Author Proof Journal of Intelligent & Fuzzy Systems xx (20xx) x–xx DOI:10.3233/JIFS-210167 IOS Press 1 A topological reduction for predicting of a lung cancer disease based on generalized rough sets 1 2 3 M. K. El-Bably a and E. A. Abo-Tabl b,c,* 4 a Department of Mathematics, Faculty of Science, Tanta University, Egypt 5 b Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt 6 c Department of Mathematics, College of Science and Arts, Methnab, Qassim University, Buraida, Saudi Arabia 7 Abstract. The present work proposes new styles of rough sets by using different neighborhoods which are made from a general binary relation. The proposed approximations represent a generalization to Pawlak’s rough sets and some of its generalizations, where the accuracy of these approximations is enhanced significantly. Comparisons are obtained between the methods proposed and the previous ones. Moreover, we extend the notion of “nano-topology”, which have introduced by Thivagar and Richard [49], to any binary relation. Besides, to demonstrate the importance of the suggested approaches for deciding on an effective tool for diagnosing lung cancer diseases, we include a medical application of lung cancer disease to identify the most risk factors for this disease and help the doctor in decision-making. Finally, two algorithms are given for decision-making problems. These algorithms are tested on hypothetical data for comparison with already existing methods. 8 9 10 11 12 13 14 15 Keywords: Neighborhoods, topology, rough sets, generalized nano-topology, attributes reduction and lung cancer disease 16 1. Introduction 17 Rough set theory is a modern, non-statistical 18 approach to deal with uncertainty and vagueness pro- 19 posed by Pawlak [1, 2]. This theory presents a logical 20 and comprehensible view, to deal with vagueness and 21 uncertainty in the data collected from real-life sit- 22 uations. There are many applications of rough sets 23 ranging from algebra to decision-making problems 24 [3–13]. The essential thinking of this theory is built 25 simply on the indiscernibility and discernibility of 26 objects. The indiscernibility relation, which repre- 27 sents a relation of equivalence, induces a space of 28 approximation made up, of classes of equivalence 29 of indiscernible objects. The core of the Pawlak 30 approach is the approximations of rough sets by using 31 * Corresponding author. Dr. El-Sayed Ahmad Abo-Tabl, E-mail: abotabl@yahoo.com. the equivalence relation on the domain. However, the 32 restrictions on the equivalence relations in Pawlak 33 rough sets cause some problems and limitations of 34 theoretical and practical aspects. So, many proposals 35 have been made for generalizing these assumptions 36 [14–33]. 37 In several fields of science and engineering, for 38 instance, Chemistry, Biology, Image processing, 39 Information acquirement, and Pattern recognition, 40 Topology, and Rough set theories were applied. As a 41 result, how to conglomerate rough set philosophy and 42 topology structure becomes an important and likely 43 research subject that has significant attention from 44 specialists in this community [34–40]. In particular, 45 this topic was explored separately by Skowron [41] 46 and Wiweger [42] in 1988. This subject continued to 47 be discussed by Lin and developed a linking amongst 48 the fuzzy rough sets and topology [43]. Besides, 49 based on the philosophies of topology and neigh- 50 ISSN 1064-1246/$35.00 © 2021 – IOS Press. All rights reserved.