Mostafa K. El-BABLY, Abd El Fattah A. EL ATIK

Soft β -rough sets and their application to determine COVID-19

Soft rough set theory has been presented as a basic mathematical model for decision-making for many real-life data. However, soft rough sets are based on a possible fusion of rough sets and soft sets which were proposed by Feng et al. [20]. The main contribution of the present article is to introduce a modification and a generalization for Feng’s approximations, namely, soft β -rough approximations, and some of their properties will be studied. A comparison between the suggested approximations and the previous one [20] will be discussed. Some examples are prepared to display the validness of these proposals. Finally, we put an actual example of the infections of coronavirus (COVID-19) based on soft β -rough sets. This application aims to know the persons most likely to be infected with COVID-19 via soft β -rough approximations and soft β -rough topologies.

PDF

___

[1] Abo Khadra AA, El-Bably MK. Topological approach to tolerance space. Alexandria Engineering Journal 2008; 47: 575-580.
[2] Abo-Tabl EA. A comparison of two kinds of definitions of rough approximations based on a similarity relation. Information Sciences 2011; 181 (12): 2587-2596. doi: 10.1016/j.ins.2011.01.007
[3] Ali MI, Feng F,Liu X , Min WK, Shabir M. On some new operations in soft set theory. Computers & Mathematics with Applications 2009; 57 (9): 1547-1553. doi: 10.1016/j.camwa.2008.11.009
[4] Ali MI. A note on soft sets, rough soft sets and fuzzy soft sets. Applied Soft Computing 2011; 11 (4): 3329-3332. doi: 10.1016/j.asoc.2011.01.003
[5] Ali MI, Davaz B, Shabir M. Some properties of generalized rough sets. Information Sciences 2013; 224: 170-179. doi: 10.1016/j.ins.2012.10.026
[6] Ali A, Ali MI, Rehman N. Soft dominance based rough sets with applications in information systems. International Journal of Approximate Reasoning 2019; 113: 171-195. doi: 10.1016/j.ijar.2019.06.009
[7] Al-Shami TM, El-Shafei ME. T -soft equality relation. Turkish Journal of Mathematics 2020; 44: 1427-1441. doi: 10.3906/mat-2005-117
[8] Aras CG, Öztürk TY, Bayramov S. Separation axioms on neutrosophic soft topological spaces. Turkish Journal of Mathematics 2019; 43: 498-510. doi: 10.3906/mat-1805-110
[9] Babitha KV, Sunil JJ. Soft set relations and functions. Computers and Mathematics with Applications 2010; 60 (7): 1840-1849. doi: 10.1016/j.camwa.2010.07.014
[10] Babitha KV, Sunil JJ. Soft topologies generated by soft set relations. Handbook of Research on Generalized and Hybrid Set Structures and Applications for Soft Computing 2016; 118-126. doi: 10.4018/978-1-4666-9798-0.ch007
[11] Bakier MY, Allam AA, Abd-Allah SS. Soft rough topology. Annals of Fuzzy Mathematics and Informatics 2018; 15 (1): 9-16. doi: 10.30948/afmi.2018.15.1.9
[12] Cagman N, Karata S, Enginoglu S. Soft topology. Computers and Mathematics with Application 2011; 62 (1): 351-358. doi: 10.1016/j.camwa.2011.05.016
[13] Chen Y, Guo Y, Pan Y, Zhao ZJ. Structure analysis of the receptor binding of 2019-nCoV, Biochemical and Biophysical Research Communications 2020; 525 (1): 135-140. doi: 10.1016/j.bbrc.2020.02.071
[14] Dizman THS. Fuzzy soft topological spaces and the related category FST. Turkish Journal of Mathematics 2019; 43: 871-878. doi: 10.3906/mat-1810-49
[15] El Atik AA. Reduction based on similarity and decision-making. Journal of the Egyptian Mathematical Society 2020; 28 (22): 1-12. doi: 10.1186/s42787-020-00078-4
[16] El-Bably MK. Comparisons between near open sets and rough approximations. International Journal of Granular Computing, Rough Sets and Intelligent Systems 2015; 4 (1): 64-83. doi: 10.1504/IJGCRSIS.2015.074749
[17] El-Sayed M, El-Bably MK. Soft simply open set in soft topological space. Journal of Computational and Theoretical Nanoscience 2017; 14 (8): 4104-4113. doi: 10.1166/jctn.2017.6792
[18] El-Sayed M, Al Qubati AQ, El-Bably MK. Soft pre-rough sets and its applications in decision making. Mathematical Biosciences and Engineering 2020; 17 (5): 6045-6063. doi: 10.3934/mbe.2020321
[19] Feng F, Jun YB, Zhao X. Soft semi rings. Computers & Mathematics with Applications (Oxford, England) 2008; 56 (10): 2621-2628. doi: 10.1016/j.camwa.2008.05.011
[20] Feng F, Liu X, Fotea VL, Jun YB. Soft sets and soft rough sets. Information Sciences 2011; 181 (6): 1125-1137. doi: 10.1016/j.ins.2010.11.004
[21] Inan E, Ozturk MA. Fuzzy soft rings and fuzzy soft ideals. Neural Computing & Applications 2012. 21: 1-8. doi: 10.1007/s00521-011-0550-5
[22] Jafari S, El Atik AA, Latif RM, El-Bably MK. Soft topological spaces induced via soft relations. WSEAS Transactions on Mathematics 2021; 20: 1-8. doi: 10.37394/23206.2021.20.1
[23] Kamaci H. Introduction to N -soft algebraic structures. Turkish Journal of Mathematics 2020; 44: 2356-2379. doi: 10.3906/mat-1907-99
[24] Kampf G, Todt D, Pfaender S, Steinmann E. Persistence of coronaviruses on inanimate surfaces and their inactivation with biocidal agents. Journal of Hospital Infection 2020; 104 (3): 246-251. doi: 10.1016/j.jhin.2020.01.022
[25] Kandil A, El-Sheikh SA, Hosny M, Raafat M. Bi-ideal approximation spaces and their applications. Soft Computing 2020; 24: 12989-13001. doi: 10.1007/s00500-020-04720-2
[26] Kondo M. On the structure of generalized rough sets. Information Sciences 2006; 176 (5): 589-600. doi: 10.1016/j.ins.2005.01.001
[27] Lai CC et al. Asymptomatic carrier state, acute respiratory disease, and pneumonia due to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2): Facts and myths. Journal of Microbiology, Immunology and Infection 2020; 53 (3): 404-412. doi: 10.1016/j.jmii.2020.02.012
[28] Lai CC et al. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and coronavirus disease-2019 (COVID19): The epidemic and the challenges, International Journal of Antimicrobial Agents, International Journal of Antimicrobial Agents 2020; 55 (3): 105924. doi: 10.1016/j.ijantimicag.2020.105924
[29] Liu Y, Qin K, Martinez L. Improving decision making approaches based on fuzzy soft sets and rough soft sets. Applied Soft Computing 2018; 65: 320-332. doi: 10.1016/j.asoc.2018.01.012
[30] Maji PK, Biswas R, Roy AR. Fuzzy soft sets. Journal of Fuzzy Mathematics 2001; 9 (3): 589-602. [31] Maji PK, Biswas R, Roy AR. Soft set theory. Computers & Mathematics with Applications 2003; 45 (4-5): 555-562. doi: 10.1016/S0898-1221(03)00016-6
[32] Meng D, Zhang X, Qin K. Soft rough fuzzy sets and soft fuzzy rough sets. Computers and Mathematics with Applications 2011; 62 (12): 4635-4645. doi: 10.1016/j.camwa.2011.10.049
[33] Min WK. A note on soft topological spaces, Computers & Mathematics with Applications 2011; 62 (9): 3524-3528. doi: 10.1016/j.camwa.2011.08.068
[34] Molodtsov DA. Soft set theory-first results. Computers & Mathematics with Applications 1999; 37 (4-5): 19-31. DOI: https://doi.org/10.1016/S0898-1221(99)00056-5
[35] Nawar AS, El-Bably MK, El Atik AA. Certain types of coverings based rough sets with application. Journal of Intelligent & Fuzzy Systems 2020; 39 (3): 3085-3098. doi: 10.3233/JIFS-191542
[36] Özkan A, On near soft sets. Turkish Journal of Mathematics 2019; 43: 1005-1017. doi: 10.3906/mat-1811-57
[37] Pawlak Z. Rough sets. International Journal of Computing and Information Sciences 198;. 11 (5): 341-356. doi: 10.1007/BF01001956
[38] Pawlak Z, Skowron A. Rough membership function. Yeager RE, Fedrizzi M, Kacprzyk J.(Eds.), Advaces in the Dempster-Schafer of Evidence (251–271), New York: Wiley 1994. doi: 10.1016/S0377-2217(96)00382-7
[39] Pawlak Z. Rough set approach to knowledge-based decision support. European Journal of Operational Research 1997; 99 (1): 48-57. doi: 10.1016/S0377-2217(96)00382-7
[40] Robson B. Computers and viral diseases. Preliminary bioinformatics studies on the design of a synthetic vaccine and a preventative peptidomimetic antagonist against the SARS-CoV-2 (2019-nCoV, COVID-19) coronavirus. Computers in Biology and Medicine 2020; 119: 103670. doi: 10.1016/j.compbiomed.2020.103670
[41] Salman S, Salem ML. Routine childhood immunization may protect against COVID-19. Medical Hypotheses 2020; 140: 109689. doi: 10.1016/j.mehy.2020.109689
[42] Shabir M, Naz M. On soft topological spaces. Computers and Mathematics with Application 2011; 61 (7): 1786-1799. doi: 10.1016/j.camwa.2011.02.006
[43] Shabir M, Ali MI, Shaheen T. A nother approach to soft rough sets. Knowledge-Based Systems 2013; 40: 72-80. doi: 10.1016/j.knosys.2012.11.012
[44] Sharma H, Kumari K, Kar S. A rough set approach for forecasting models. Decision Making: Applications in Management and Engineering 2019; 3 (1): 1-21. doi: 10.31181/dmame2003001s
[45] Singh P, Huang YA. Four-way decision-making approach using interval-valued fuzzy sets, rough set and granular computing: a new approach in data classification and decision-making. Granular Computing 2020. 5: 397-409. doi: 10.1007/s41066-019-00165-7
[46] Som T. On soft relation and fuzzy soft relation. Journal of Fuzzy Mathematics 2009; 16 (3): 677-687.
[47] Suo M, Tao L, Zhu B, Chen Y, Lu C, Ding Y. Soft decision-making based on decision-theoretic rough set and Takagi-Sugeno fuzzy model with application to the autonomous fault diagnosis of satellite power system. Aerospace Science and Technology 2020. 106: 106108. doi: 10.1016/j.ast.2020.106108
[48] Yang X, Yu D, Yang J, Wu C. Generalization of soft set theory: from crisp to fuzzy case. Fuzzy Information and Engineering, ICFIE 2007; 40: 345-354. : doi: 10.1007/978-3-540-71441-5 − 39
[49] Yao YY. Generalized rough set models, Rough Sets in Knowledge Discovery 1, Polkowski L, Skowron A (Eds.). Physica Verlag, Heidelberg 1998; 286-318.
[50] Yao YY. Three-way decision and granular computing. International Journal of Approximate Reasoning 2018; 103: 107-123. doi: 10.1016/j.ijar.2018.09.005
[51] Yu Z, Wang D. Accuracy of approximation operators during covering evolutions. International Journal of Approximate Reasoning 2020; 117: 1-14. doi: 10.1016/j.ijar.2019.10.012