New types of approximations via $\circledast$-$\beta$-soft fuzzy complement neighborhood and $\circledcirc$-$\beta$-soft fuzzy complement neighborhood and their applications in multiple attribute decision-making (MADM)

Khalil, Ahmed; Li, Shenggang; Yang, Hai-Long

doi:10.22111/ijfs.2025.50036.8834

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	New types of approximations via $\circledast$-$\beta$-soft fuzzy complement neighborhood and $\circledcirc$-$\beta$-soft fuzzy complement neighborhood and their applications in multiple attribute decision-making (MADM)
Iranian Journal of Fuzzy Systems
دوره 22، شماره 1، فروردین و اردیبهشت 2025، صفحه 185-207 اصل مقاله (663.35 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2025.50036.8834
نویسندگان
Ahmed Khalil^* ¹؛ Shenggang Li²؛ Hai-Long Yang³
¹Al-Azhar University
²College of Mathematics and Information Science, Shaanxi Normal University, 710062, Xian, P. R. China
³Shaanxi Normal University China
چکیده
A $\beta$-soft fuzzy complement neighborhood is the initial concept proposed by Zhang and Zhan (International Journal of Machine Learning and Cybernetics 10(2019) 1487-1502), which we will refer to in this study as $\circledast$-$\beta$- soft fuzzy complement neighborhood. In the present paper, we first introduce three new approximation types based on $\beta$-soft fuzzy covering via $\circledast$-$\beta$-soft fuzzy complement neighborhood, along with several essential features and examples. The new approximation types are significant because they satisfy the inclusion property (i.e., the upper approximation contains the lower approximation, which is one of the essential features of rough set models). In addition, we update some algorithms to a very easy-to-understand state. As a result, improved decision-making procedures will be observable and trustworthy in order to arrive at the optimal choice. Second, we offer a novel idea of $\circledcirc$-$\beta$-soft fuzzy complement neighborhood and then present three other new approximation types based on $\beta$-soft fuzzy covering via $\circledcirc$-$\beta$ soft fuzzy complement neighborhood, besides outlining some of its key characteristics and giving some examples. On the theoretical side, by using three other new approximations via $\circledcirc$-$\beta$-FCN${\mathscr A},$ we also study some basic fuzzy topology properties. Third, we use $\circledcirc$-$\beta$-FCN${\mathscr A}$ to construct a new method that can be applied to the MADM field. We illustrate this method using a real-world problem: a candidate seeking employment in a company. Finally, to demonstrate the advantages of the proposed work, we will compare our proposed method with published $\beta$-soft fuzzy MADM methods.
کلیدواژه‌ها
$\circledast$-$\beta$-Soft fuzzy complement neighborhood؛ $\circledcirc$-$\beta$-Soft fuzzy complement neighborhood؛ New types approximations؛ Inclusion property؛ MADM؛ Numerical example؛ Comparison

مراجع
1] D. Ahmed, B. Dai, A. M. Khalil, Picture m-polar fuzzy soft sets and their application in decision-making problems, Iranian Journal of Fuzzy Systems, 19(9) (2022), 161-173. https://doi.org/10.22111/IJFS.2022.7218 [2] M. Atef, A. E. F. El Atik, Some extensions of covering-based multigranulation fuzzy rough sets from new perspectives, Soft Computing, 25 (2021), 6633-6651. https://doi.org/10.1007/s00500-021-05659-8 [3] S. Biswas, D. Boˇzani´c, D. Pamuˇcar, D. Marinkovi´c, A spherical fuzzy based decision making framework with einstein aggregation for comparing preparedness of smes in quality 4.0, Facta Universitatis, Series: Mechanical Engineering, 21(3) (2023), 453-478. https://doi.org/10.22190/FUME230831037B [4] J. H. Dai, S. C. Gao, G. J. Zheng, Generalized rough set models determined by multiple neighborhoods generated from a similarity relation, Soft Computing, 12 (2017), 1-14. https://doi.org/10.1007/s00500-017-2672-x [5] L. D’eer, C. Cornelis, A comprehensive study of fuzzy covering based rough set models: Definitions, properties and interrelationships, Fuzzy Sets and Systems, 336 (2018), 1-26. https://doi.org/10.1016/j.fss.2017.06.010 [6] L. D’eer, C. Cornelis, L. Godo, Fuzzy neighborhood operators based on fuzzy coverings, Fuzzy Sets and Systems, 312 (2017), 17-35. https://doi.org/10.1016/j.fss.2016.04.003 [7] L. D’eer, N. Verbiest, C. Cornelis, L. Godo, A comprehensive study of implicator-conjunctor-based and noisetolerant fuzzy rough sets: Definitions, properties and robustness analysis, Fuzzy Sets and Systems, 275 (2015), 1-38. https://doi.org/10.1016/j.fss.2014.11.018 [8] W. S. Du, B. Q. Hu, Dominance-based rough set approach to incomplete ordered information systems, Information Sciences, 346-347 (2016), 106-129. https://doi.org/10.1016/j.ins.2016.01.098 [9] D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems, 17 (1990), 191-201. https://doi.org/10.1080/03081079008935107 [10] S. Greco, B. Matarazzo, R. Slowinski, Rough approximation by dominance relations, International Journal of Intelligent Systems, 17 (2002), 153-171. https://doi.org/10.1002/int.10014 [11] U. H¨ohle, A. P. ˇSostak, Axiomatic foundations of fixed-basis fuzzy topology, in: U. H¨ohle, S.E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets, Logic, Topology and Measure Theory, Kluwer Academic Publishers, Boston, (1999), 123-272. https://doi.org/10.1007/978-1-4615-5079-2_5 [12] Q. H. Hu, D. Yu, J. Liu, C. Wu, Neighborhood rough set based heterogeneous feature subset selection, Information Sciences, 178 (2008), 3577-3594. https://doi.org/10.1016/j.ins.2008.05.024 [13] A. M. Khalil, C. Dunqian, A. Abdelfatah, S. Florentin, R. A.Wedad, Combination of the single-valued neutrosophic fuzzy set and the soft set with applications in decision-making, Symmetry, 12 (2020), 1361. https://doi.org/10. 3390/sym12081361 [14] A. M. Khalil, S. G. Li, H. Garg, H. Li, S. Ma, New operations on interval-valued picture fuzzy set, interval-valued picture fuzzy soft set and their applications, IEEE Access, 7 (2019), 51236-51253. https://doi.org/10.1109/ ACCESS.2019.2910844 [15] A. M. Khalil, A. M. Zahran, R. Basheer, A novel diagnosis system for detection of kidney disease by a fuzzy soft decision-making problem, Mathematics and Computers in Simulation, 203 (2023), 271-305. https://doi.org/10. 1016/j.matcom.2022.06.014 [16] T. J. Li, Y. Leung, W. X. Zhang, Generalized fuzzy rough approximation operators based on fuzzy covering, International Journal of Approximate Reasoning, 48 (2008), 836-856. https://doi.org/10.1016/j.ijar.2008.01.006 [17] Z. Li, N. Xie, G. Wen, Soft coverings and their parameter reductions, Applied Soft Computing, 31 (2015), 48-60. https://doi.org/10.1016/j.asoc.2015.02.027 [18] Y. M. Liu, M. K. Luo, Fuzzy topology, World Scientific Publication, Singapore, 1998. https://doi.org/10.1142/ 3281 [19] L. W. Ma, On some types of neighborhood-related covering rough sets, International Journal of Approximate Reasoning, 53 (2012), 901-911. https://doi.org/10.1016/j.ijar.2012.03.004 [20] L. W. Ma, Some twin approximation operators on covering approximation spaces, International Journal of Approximate Reasoning, 56 (2015), 59-70. https://doi.org/10.1016/j.ijar.2014.08.003 [21] L. W. Ma, Two fuzzy covering rough set models and their generalizations over fuzzy lattices, Fuzzy Sets and Systems, 294 (2016), 1-17. https://doi.org/10.1016/j.fss.2015.05.002 [22] L. W. Ma, Couple fuzzy covering rough set models and their generalizations to CCD lattices, International Journal of Approximate Reasoning, 126 (2020), 48-69. https://doi.org/10.1016/j.ijar.2020.08.003 [23] T. Mahmood, M. Asif, U. Rehman, J. Ahmmad, T-bipolar soft semigroups and related results, Spectrum of Mechanical Engineering and Operational Research, 1(1) (2024), 258-271. https://doi.org/10.31181/smeor11202421 [24] P. K. Maji, R. Biswas, A. R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics, 203 (2001), 589-602. [25] P. K. Maji, A. R. Roy, R. Biswas, On intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics, 12 (2004), 669-683. [26] D. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37 (1999), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5 [27] A. S. Nawar, M. Atef, A. M. Khalil, Certain types of fuzzy soft β-covering based fuzzy rough sets with application to decision-making, Journal of Intelligent and Fuzzy Systems, 40 (2021), 10825-10836. https://doi.org/10.3233/ JIFS-201822 [28] Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11 (1982), 341-356. https: //doi.org/10.1007/BF01001956 [29] Z. Pawlak, Rough sets and intelligent data analysis, Information Sciences, 147 (2002), 1-12. https://doi.org/ 10.1016/S0020-0255(02)00197-4 [30] J. A. Pomykala, Approximation operations in approximation space, Bulletin of the Polish Academy of Sciences Mathematics, 35 (1987), 653-662. https://mathscinet.ams.org/mathscinet/relay-station?mr=937744 [31] J. A. Pomykala, On definability in the nondeterministic information system, Bulletin of the Polish Academy of Sciences Mathematics, 36 (1988), 193-210. https://zbmath.org/pdf/04110174.pdf [32] J. Su, Y. Wang, J. Li, A novel fuzzy covering rough set model based on generalized overlap functions and its application in MCDM, Symmetry, 15 (2023), 647. https://doi.org/10.3390/sym15030647 [33] B. Sun, W. Ma, Y. Qian, Multigranulation fuzzy rough set over two universes and its application to decision making, Knowledge-Based Systems, 123 (2017), 61-74. https://doi.org/10.1016/j.knosys.2017.01.036 [34] C. Wang, D. Chen, B. Sun, Q. Hu, Communication between information systems with covering based rough sets, Information Sciences, 216 (2012), 17-33. https://doi.org/10.1016/j.ins.2012.06.010 [35] X. Wang, A. M. Khalil, A new kind of generalized Pythagorean fuzzy soft set and its application in decisionmaking, Computer Modeling in Engineering and Sciences, 136(3) (2023), 2861-2871. https://doi.org/10.32604/ cmes.2023.026021 [36] C. Z. Wang, Y. P. Shi, X. D. Fan, M. W. Shao, Attribute reduction based on k-nearest neighborhood rough sets, International Journal of Approximate Reasoning, 106 (2019), 18-31. https://doi.org/10.1016/j.ijar.2018.12. 013 [37] B. Yang, B. Hu, A fuzzy covering-based rough set model and its generalization over fuzzy lattice, Information Sciences, 367 (2016), 463-486. https://doi.org/10.1016/j.ins.2016.05.053 [38] B. Yang, B. Hu, On some types of fuzzy covering-based rough sets, Fuzzy Sets and Systems, 312 (2017), 36-65. https://doi.org/10.1016/j.fss.2016.10.009 [39] B. Yang, B. Hu, Fuzzy neighborhood operators and derived fuzzy coverings, Fuzzy Sets and Systems, 370 (2019), 1-13. https://doi.org/10.1016/j.fss.2016.04.003 [40] Y. Yang, C. Liang, S. Ji, T. Liu, Adjustable soft discernibility matrix based on picture fuzzy soft sets and its applications in decision making, Journal of Intelligent and Fuzzy Systems, 29 (2015), 1711-1722. https://doi. org/10.3233/IFS-15164 [41] X. Yang, T. Y. Lin, J. Yang, Y. L. A. Dongjun, Combination of interval-valued fuzzy set and soft set, Computers and Mathematics with Applications, 58 (2009), 521-527. https://doi.org/10.1016/j.camwa.2009.04.019 [42] Y. Y. Yao, Relational interpretations of neighborhood operators and rough set approximation operators, Information Sciences, 111 (1998), 239-259. https://doi.org/10.1016/S0020-0255(98)10006-3 [43] S¸. Y¨uksel, Z. G. Erg¨ul, N. Tozlu, Soft covering based rough sets and their application, The Scientific World Journal, 2014 (2014), 1-9. https://doi.org/10.1155/2014/970893 [44] S¸. Y¨uksel, N. Tozlu, T. H. Dizman, An application of multicriteria group decision making by soft covering based rough sets, Filomat, 29 (2015), 209-219. https://doi.org/10.2298/FIL1501209Y [45] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65) 90241-X [46] J. Zhan, J. C. R. Alcantud, A novel type of soft rough covering and its application to multicriteria group decision making, Artificial Intelligence Review, 52 (2019), 2381-2410. https://doi.org/10.1007/s10462-018-9617-3 [47] J. Zhan, M. I. Ali, N. Mehmood, On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods, Applied Soft Computing, 56 (2017), 446-457. https://doi.org/10.1016/j.asoc.2017.03.038 [48] J. Zhan, Q. Liu, T. Herawan, A novel soft rough set: Soft rough hemirings and corresponding multicriteria group decision making, Applied Soft Computing, 54 (2017), 393-402. https://doi.org/10.1016/j.asoc.2016.09.012 [49] J. Zhan, B. Sun, Covering-based soft fuzzy rough theory and its application to multiple criteria decision making, Computational and Applied Mathematics, 38 (2019), 149. https://doi.org/10.1007/s40314-019-0931-4 [50] J. Zhan, Q. Wang, Certain types of soft coverings based rough sets with applications, International Journal of Machine Learning and Cybernetics, 10 (2019), 1065-1076. https://doi.org/10.1007/s13042-018-0785-x [51] J. Zhan, X. Zhang, Y. Yao, Covering based multigranulation fuzzy rough sets and corresponding applications, Artificial Intelligence Review, 53 (2020), 1093-1126. https://doi.org/10.1007/s10462-019-09690-y [52] J. Zhan, K. Zhu, A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Computing, 21 (2017), 1923-1936. https://doi.org/10.1007/s00500-016-2119-9 [53] L. Zhang, J. Zhan, Fuzzy soft β-covering based fuzzy rough sets and corresponding decision-making applications, International Journal of Machine Learning and Cybernetics, 10 (2019), 1487-1502. https://doi.org/10.1007/ s13042-018-0828-3 [54] 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 Computing, 23 (2019), 5327-5351. https://doi.org/10.1007/ s00500-018-3470-9 [55] J. L. Zhou, F. S. Xu, Y. Y. Guan, H. K. Wang, Three types of fuzzy covering-based rough set models, Fuzzy Sets and Systems, 423 (2021), 122-148. https://doi.org/10.1016/j.fss.2020.11.014 [56] W. Zhu, Topological approaches to covering rough sets, Information Sciences, 177 (2007), 1499-1508. https: //doi.org/10.1016/j.ins.2006.06.009
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New types of approximations via $\circledast$-$\beta$-soft fuzzy complement neighborhood and $\circledcirc$-$\beta$-soft fuzzy complement neighborhood and their applications in multiple attribute decision-making (MADM)