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Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 6045-6063. doi: 10.3934/mbe.2020321
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Soft pre-rough sets and its applications in decision making

  • 1.
    Department of Mathematics, College of Science and Arts, Najran University, Kingdom of Saudi Arabia
  • 2.
    Department of Mathematics, Faculty of Science, Tanta University, Egypt
  • Received: 05 July 2020 Accepted: 30 July 2020 Published: 14 September 2020

  • Soft rough set model represents a different mathematical model to which many real-life data can be connected. In fact, this theory represents a link between soft set and rough set theories. The main goal of the present paper is to introduce a new approach to modify and generalize soft rough sets. We are discussing and exploring the basic properties for these approaches. In addition, we use the suggested approaches as a mathematical modeling for an uncertain data and deal with the ambiguity. Comparisons among the proposed methods and the previous one are obtained. Finally, a medical application of the suggested approximations in decision making of diagnosis of COVID-19 is illustrated. Moreover, we develop an algorithm following these concepts and apply it to a decision making problem to demonstrate the applicability of the proposed methods.

    Citation: M. El Sayed, Abdul Gawad A. Q. Al Qubati, M. K. El-Bably. Soft pre-rough sets and its applications in decision making[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 6045-6063. doi: 10.3934/mbe.2020321

    Related Papers:

  • Soft rough set model represents a different mathematical model to which many real-life data can be connected. In fact, this theory represents a link between soft set and rough set theories. The main goal of the present paper is to introduce a new approach to modify and generalize soft rough sets. We are discussing and exploring the basic properties for these approaches. In addition, we use the suggested approaches as a mathematical modeling for an uncertain data and deal with the ambiguity. Comparisons among the proposed methods and the previous one are obtained. Finally, a medical application of the suggested approximations in decision making of diagnosis of COVID-19 is illustrated. Moreover, we develop an algorithm following these concepts and apply it to a decision making problem to demonstrate the applicability of the proposed methods.


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    [1] Z. Pawlak, Rough sets, Int. J. Inform. Computer Sci., 11 (1982), 341-356.
    [2] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.
    [3] D. A. Molodtsov, Soft set theory-first results, Computers Math. Appl., 37 (1999), 19-31.
    [4] E. A. Abo-Tabl, A comparison of two kinds of definitions of rough approximations based on a similarity relation, Inform. Sci., 181 (2011), 2587-2596.
    [5] K. Kin, J. Yang, Z. Pei, Generalized rough sets based on reflexive and transitive relations, Inform. Sci., 178 (2008), 4138-4141.
    [6] M. Kondo, On the structure of generalized rough sets, Inform. Sci., 176 (2006), 589-600.
    [7] Y. Y. Yao, Generalized rough set models, Rough Sets in Knowledge Discovery 1, L. Polkowski, A. Skowron (Eds.), Physica Verlag, Heidelberg (1998), 286-318.
    [8] A. A. Allam, M. Y., Bakeir, E. A., Abo-Tabl, New approach for basic rough set concepts. In: International workshop on rough sets, fuzzy sets, data mining, and granular computing, Lecture Notes in Artificial Intelligence, Springer, Regina, 3641 (2005), 64-73.
    [9] M. I. Ali, B. Davvaz, M. Shabir, Some properties of generalized rough sets, Inform. Sci., 224 (2013), 170-179.
    [10] A. A. Abo Khadra, B. M. Taher, M. K. El-Bably, Generalization of Pawlak approximation space, Proceeding of The International Conference on Mathematics: Trends and Developments, The Egyptian Mathematical Society, 3 (Cairo-2007), 335-346.
    [11] M. E. Abd El-Monsef, O. A. Embaby, M. K. El-Bably, Comparison between rough set approximations based on different topologies, Int. J. Granul. Comput. Rough Sets Intell. Systems, 3 (2014), 292-305.
    [12] M. El Sayed, Applications on simply alpha-approximation space based on simply alpha open sets, European J. Scient. Res., 120 2014), 7-14.
    [13] M. El Sayed, Generating simply approximation spaces by using decision tables, J. Comput. Theoret. Nanosci., 13 (2016), 7726-7730.
    [14] W. Zhu, Topological approaches to covering rough sets, Inform. Sci., 177 (2007), 1499-1508.
    [15] W. H. Xu, W. X. Zhang, Measuring roughness of generalized rough sets induced by a covering, Inform. Sci., 158 (2007), 2443-2455.
    [16] M. E. Abd El-Monsef, A. M. Kozae, M. K. El-Bably, On generalizing covering approximation space, J. Egyptian Math. Soc., 23 (2015), 535-545.
    [17] A. S. Nawar, M. K. El-Bably, A. A. El-Atik, Certain types of coverings based rough sets with application, J. Intell. Fuzzy Systems, (2020), (In press). DOI: 10.3233/JIFS-191542
    [18] M. Ali, H. Khan, L. H. Son, F. Smarandache, W. B. V. Kandasamy, New soft sets based class of linear algebraic codes, Symmetry, 10 (2018), 1-10.
    [19] N. Çağman, S. Enginoğlu, Soft matrix theory and its decision making, Comput. Math. Appl., 59 (2010), 3308-3314.
    [20] F. Karaaslan, Soft classes and soft rough classes with applications in decision making, Math. Probl. Eng., 2016, Article ID 1584528.
    [21] A. Kharal, B. Ahmad, Mappings on soft classes, New Math.Natural Comput., 7 (2011), 471-481.
    [22] S. Yuksel, T. Dizman, G. Yildizdan, U. Sert, Application of soft sets to diagnose the prostate cancer risk, J. Inequal. Appl., 229 (2013).
    [23] P. K. Maji, R. Roy, R. Biswas, An application of soft sets in decision making problem, Comput. Math. Appl., 44 (2002), 1077-1083.
    [24] Q. M. Sun, Z. L. Zhang, J. Liu, Soft sets and soft modules, Rough Sets Knowl. Technol., 5009 (2008), 403-409.
    [25] M. I. Ali, W. K. Mi, M. Shabir, On some new operations in soft set theory, Comput. Math. Appl., 57 (2009), 1547-1553.
    [26] M. I. Ali, A note on soft sets, rough soft sets and fuzzy soft sets, Appl. Soft Comput., 11 (2011), 3329-3332.
    [27] K. V. Babitha, J. J. Sunil, Soft topologies generated by soft set relations, Handbook Res. General. Hybrid Set Struct. Appl. Soft Comput., (2016), 118-126.
    [28] M. El-Sayed, M. K. El-Bably, Soft simply open set in soft topological space, J. Comput. Theor. Nanosci., 14 (2017), 4104-4113.
    [29] F. Karaaslan, N. Çağman, Bipolar soft rough sets and their applications in decision making, Afrika Matematika, 29 (2018), 823-839.
    [30] Y. Liu, K. Qin, L. Martínez, Improving decision making approaches based on fuzzy soft sets and rough soft sets, Appl. Soft Comput., 65 (2018), 320-332.
    [31] J. Zhan, B. Sun, Covering-based soft fuzzy rough theory and its application to multiple criteria decision making, Computat. Appl. Math., 38 (2019). DOI: 10.1007/s40314-019-0931-4
    [32] L. Zhang, J. Zhan, J. C. R. Alcantud, Novel classes of fuzzy soft β-coverings-based fuzzy rough sets with applications to multi-criteria fuzzy group decision making, Soft Comput., 23 (2019), 5327-5351.
    [33] S. K. Roy, S. Bera, Approximation of rough soft set and its application to lattice, Fuzzy Inform. Eng., 7 (2015), 379-387.
    [34] A. M. Khalil, S. G. Li, Y. Lin, H. X. Li, S. G. Ma, A new expert system in prediction of lung cancer disease based on fuzzy soft sets, Soft Comput., (2020). DOI: 10.1007/s00500-020-04787-x
    [35] M. El Sayed, Soft simply* generalized continuous mappings in soft topological space, J. Eng. Appl. Sci., 14 (2019), 3104-3112.
    [36] M. El Sayed, Some properties on soft simply star open sets in soft topological space, Nanosci. Nanotechnol. Letters, 12 (2020), 113-119.
    [37] F. Feng, X. Liu, V. Leoreanu-Fotea, Y. B. Jun, Soft sets and soft rough sets, Inform. Sci., 181 (2011), 1125-1137.
    [38] G. Kou, Y. Lu, Y. Peng, Y. Shi, Evaluation of classification algorithms using MCDM and rank correlation, Int. J. Inform. Technol. Decis. Mak., 11 (2012), 197-225.
    [39] C. Lin, G. Kou, Y. Peng, F. E. Alsaadi, Aggregation of the nearest consistency matrices with the acceptable consensus in AHP-GDM, Ann. Operat. Res., (2020), DOI: 0.31181/dmame2003001s
    [40] G. Kou, Y. Peng, G. Wang, Evaluation of clustering algorithms for financial risk analysis using MCDM methods, Inform. Sci., 275 (2014), 1-12.
    [41] G. Kou, C. Lin, A cosine maximization method for the priority vector derivation in AHP, European J. Operat. Res., 235 (2014), 225-232.
    [42] G. Kou, D. Ergu, Jennifer Shang, Enhancing data consistency in decision matrix: Adapting Hadamard model to mitigate judgment contradiction, European J. Operat. Res., 236 (2014), 261-271.
    [43] H. K. Sharma, K. Kumari, S. Kar, A rough set approach for forecasting models, Decis. Mak. Appl. Manag. Eng., 3 (2020), 1-21.
    [44] Z. Karavidic, D. Projovic, A multi-criteria decision-making (MCDM) model in the security forces operations based on rough sets, Decis. Mak. Appl. Manag. Eng., 1 (2018), 97-120.
    [45] F. Sinani, Z. Erceg, M. Vasiljevic, An evaluation of a third-party logistics provider: The application of the rough Dombi-Hamy mean operator, Decis. Mak. Appl. Manag. Eng., 3 (2020), 92-107.
    [46] P. K. Maji, R. Biswas, A. R. Roy, Fuzzy soft sets, J. Fuzzy Math., 9 (2001), 589-602.
    [47] A. R. Roy, P. K. Maji, A fuzzy soft set theoretic approach to decision making problems, J. Appl. Math., 203 (2007), 412-418.
    [48] G. Kampf, D. Todt, S. Pfaender, E. Steinmann, Persistence of coronaviruses on inanimate surfaces and their inactivation with biocidal agents, J. Hospital Infect., 104 (2020), 246-251.
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