A novel decision-making technique based on T-rough bipolar fuzzy sets

Volume 33, Issue 3, pp 275--289 https://dx.doi.org/10.22436/jmcs.033.03.06

Publication Date: January 14, 2024 Submission Date: November 27, 2023 Revision Date: December 11, 2023 Accteptance Date: December 13, 2023

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 425 Downloads
• 1245 Views

Authors

N. Malik - Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan. M. Shabir - Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan. T. M. Al-shami - Department of Mathematics, Sana'a University, P.O. Box 1247, Sana'a, Yemen. - Department of Engineering Mathematics \(\&\) Physics, Faculty of Engineering \(\&\) Technology, Future University, New Cairo, Egypt. R. Gul - Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan. M. Arar - Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz, Riyadh, Saudi Arabia.

Abstract

In this paper, we hybridize the bipolar fuzzy set (BFS) theory with T-rough sets (T-RSs) and initiate the novel idea of T-rough BFSs (T-RBFSs). The concept presented in this article has never been discussed earlier. Moreover, we investigate the axiomatic systems of T-RBFSs in detail. Meanwhile, we address a decision-making (DM) problem having data endowed with fuzziness and bipolarity in the framework of the T-RBFSs. We also propose an algorithm for this application. This algorithm facilitates tackling the case when there is a team of decision-makers instead of a single decision-maker and when the objects of one set need to be approximated by grading the objects of some other set. Moreover, a practical application of T-RBFSs in DM problems is given, accompanied by a practical example, which provides the optimal and the worst decision between some objects. Finally, a comparative analysis of the recommended study with several prevailing approaches is given to endorse the advantages of the suggested research.

Share and Cite

Keywords

• T-rough sets
• bipolar fuzzy sets
• T-rough bipolar fuzzy sets
• decision-Making

MSC

•  03E72
•  62C86

References

• [1] M. Akram, W. A. Dudek, Regular bipolar fuzzy graphs, Neural Comput. Appl., 21 (2012), 197–205
  • View Article
  • Google Scholar


• [2] M. A. Alghamdi, N. O. Alshehri, M. Akram, Multi-criteria decision-making methods in bipolar fuzzy environment, Int. J. Fuzzy Syst., 20 (2018), 2057–2064
  • View Article
  • Google Scholar


• [3] T. M. Al-shami, An improvement of rough sets’ accuracy measure using containment neighborhoods with a medical application, Inform. Sci., 569 (2021), 110–124
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] T. M. Al-shami, Improvement of the approximations and accuracy measure of a rough set using somewhere dense sets, Soft Comput., 25 (2021), 14449–14460
  • View Article
  • Google Scholar
  • MATH


• [5] T. M. Al-shami, Bipolar soft sets: relations between them and ordinary points and their applications, Complexity, 2021 (2021), 14 pages
  • View Article
  • Google Scholar


• [6] T. M. Al-shami, Topological approach to generate new rough set models, Complex Intell. Syst., 8 (2022), 4101–4113
  • View Article
  • Google Scholar


• [7] T. M. Al-shami, (2,1)-Fuzzy sets: properties, weighted aggregated operators and their applications to multi-criteria decisionmaking methods, Complex Intell. Syst., 9 (2023), 1687–1705
  • View Article
  • Google Scholar


• [8] T. M. Al-shami, J. C. R. Alcantud, A. Mhemdi, New generalization of fuzzy soft sets: (a, b)-fuzzy soft sets, AIMS Math., 8 (2023), 2995–3025
  • View Article
  • MathSciNet
  • Google Scholar


• [9] T. M. Al-shami, I. Alshammari, Rough sets models inspired by supra-topology structures, Artif. Intell. Rev, 56 (2023), 6855–6883
  • View Article
  • Google Scholar


• [10] T. M. Al-shami, A. Mhemdi, Approximation operators and accuracy measures of rough sets from an infra-topology view, Soft Comput., 27 (2023), 1317–1330
  • View Article
  • Google Scholar


• [11] T. M. Al-shami, A. Mhemdi, Generalized frame for orthopair fuzzy sets: (m, n)-Fuzzy sets and their applications to multi-criteria decision-making methods, Information, 14 (2023), 1–21
  • View Article
  • Google Scholar


• [12] M. Banerjee, S. K. Pal, Roughness of a fuzzy set, Inform. Sci., 93 (1996), 235–246
  • View Article
  • MathSciNet
  • Google Scholar


• [13] B. Davvaz, A short note on algebraic T-rough sets, Inform. Sci., 178 (2008), 3247–3252
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] J. Deng, J. Zhan, E. Herrera-Viedma, F. Herrera, Regret Theory-Based Three-Way Decision Method on Incomplete Multiscale Decision Information Systems With Interval Fuzzy Numbers, IEEE Trans. Fuzzy Syst., 31 (2023), 982–996
  • View Article
  • Google Scholar


• [15] D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, Int. J. Gen. Syst., 17 (1990), 191–209
  • View Article
  • Google Scholar


• [16] D. Dubois, H. Prade, An introduction to bipolar representations of information and preferences, Int. J. Intell. Syst., 23 (2008), 866–877
  • View Article
  • Google Scholar


• [17] F. Feng, L. Changxing, B. Davvaz, M. I. Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Comput., 14 (2010), 899–911
  • View Article
  • Google Scholar
  • MATH


• [18] F. Feng, Y. B. Jun, X. Liu, L. Li, An adjustable approach to fuzzy soft set based decision making, J. Comput. Appl. Math., 234 (2010), 10–20
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] R. Gul, M. Shabir, Roughness of a set by (, )-indiscernibility of Bipolar fuzzy relation, Comput. Appl. Math., 39 (2020), 22 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] M. Gulistan, N. Yaqoob, A. Elmoasry, J. Alebraheem, Complex bipolar fuzzy sets: An application in a transport’s company, J. Intell. Fuzzy Syst., 40 (2021), 3981–3997
  • View Article
  • Google Scholar


• [21] Y. Han, Z. Lu, Z. Du, Q. Luo, S. Chen, A YinYang bipolar fuzzy cognitive TOPSIS method to bipolar disorder diagnosis, Comput. Methods Programs Biomed., 158 (2018), 1–10
  • View Article
  • Google Scholar


• [22] Y. Han, P. Shi, S. Chen, Bipolar-Valued Rough Fuzzy Set and Its Applications to the Decision Information System, IEEE Trans. Fuzzy Syst., 23 (2015), 2358–2370
  • View Article
  • Google Scholar


• [23] R. A. Hosny, B. A. Asaad, A. A. Azzam, T. M. Al-shami, Various topologies generated from Ej-neighbourhoods via ideals, Complexity, 2021 (2021), 11 pages
  • View Article
  • Google Scholar


• [24] H. Z. Ibrahim, T. M. Al-shami, M. Arar, M. Hosny, kn m-Rung Picture Fuzzy Information in a Modern Approach to Multi-Attribute Group Decision-Making, Complex Intell. Syst., (2023), 21 pages
  • View Article
  • Google Scholar


• [25] C. Jana, M. Pal, J. Q. Wang, Bipolar fuzzy Dombi aggregation operators and its application in multiple-attribute decisionmaking process, J. Ambient Intell. Human. Comput., 10 (2019), 3533–3549
  • View Article
  • Google Scholar


• [26] J. Kim, S. K. Samanta, P. K. Lim, J. G. Lee, K. Hur, Bipolar fuzzy topological spaces, Ann. Fuzzy Math. Inform., 17 (2019), 205–229
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [27] K. M. Lee, Bipolar-valued fuzzy sets and their basic operations, In: Proceedings of the International Conference, Bangkok, Thailand, (2000), 307–317
  • View Article
  • Google Scholar


• [28] K. M. Lee, Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets and bipolar-valued fuzzy sets, J. Korean Inst. Intell. Syst., 14 (2004), 125–129
  • View Article


• [29] M. Lu, J. R. Busemeyer, Do traditional chinese theories of Yi Jing (’Yin-Yang’and Chinese medicine go beyond western concepts of mind and matter, Mind Matter, 12 (2014), 37–59
  • View Article
  • Google Scholar


• [30] X. Ma, Q. Liu, J. Zhan, A survey of decision making methods based on certain hybrid soft set models, Artif. Intell. Rev., 47 (2017), 507–530
  • View Article
  • Google Scholar


• [31] T. Mahmood, S. Abdullah, M. Bilal, S. Rashid, Multiple criteria decision making based on bipolar valued fuzzy set, Ann. Fuzzy Math. Inform., 11 (2016), 1003–1009
  • View Article
  • Google Scholar
  • MATH


• [32] T. Mahmood, U. Ur Rehman, A novel approach towards bipolar complex fuzzy sets and their applications in generalized similarity measures, Int. J. Intell. Syst., 37 (2021), 535–567
  • View Article
  • Google Scholar


• [33] N. Malik, M. Shabir, Rough fuzzy bipolar soft sets and applications in decision-making problems, Soft Comput., 23 (2019), 1603–1614
  • View Article
  • Google Scholar


• [34] N. Malik, M. Shabir, T. M. Al-shami, R. Gul, M. Arar, M. Hosny, Rough bipolar fuzzy ideals in semigroups, Complex Intell. Syst., 9 (2023), 7197–7212
  • View Article
  • Google Scholar


• [35] N. Malik, M. Shabir, T. M. Al-shami, R. Gul, A. Mhemdi, Medical decision-making techniques based on bipolar soft information, AIMS Math., 8 (2023), 18185–18205
  • View Article
  • Google Scholar


• [36] D. Stanujkic, D. Karabasevic, E. K. Zavadskas, F. Smarandache, W. K. M. Brauers, A bipolar fuzzy extension of the MULTIMOORA method, Informatica, 30 (2019), 135–152
  • View Article
  • Google Scholar


• [37] Z. Pawlak, Rough sets, Internat. J. Comput. Inform. Sci., 11 (1982), 341–356
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [38] Z. Pawlak, A. Skowron, Rudiments of rough sets, Inform. Sci., 177 (2007), 3–27
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [39] M. Riaz, S. T. Tehrim, A robust extension of VIKOR method for bipolar fuzzy sets using connection numbers of SPA theory based metric spaces, Artif. Intell. Rev., 54 (2021), 561–591
  • View Article
  • Google Scholar


• [40] R. Sahu, S. R. Dash, S. Das, Career selection of students using hybridized distance measure based on picture fuzzy set and rough set theory, Decis. Mak.: Appl. Manag. Eng., 4 (2021), 104–126
  • View Article
  • Google Scholar


• [41] M. Shabir, M. I. Ali, Soft ideals and generalized fuzzy ideals in semigroups, New Math. Nat. Comput., 5 (2009), 599–615
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [42] M. Shabir, Y. B. Jun, Y. Nawaz, Characterizations of regular semgroups by (, )-fuzzy ideals, Comput. Math. Appl., 59 (2010), 161–175
  • View Article
  • Google Scholar


• [43] M. Shabir, Y. B. Jun, Y. Nawaz, Semigroups characterized by (, _qk)-fuzzy ideals, Comput. Math. Appl., 60 (2010), 1473–1493
  • View Article


• [44] H. Sharma, P. Sivaprakasam, M. Angamuthu, Generalized Z-fuzzy soft -covering based rough matrices and its application to MAGDM problem based on AHP method, Decis. Mak.: Appl. Manag. Eng., 6 (2023), 134–152
  • View Article
  • Google Scholar


• [45] J. Wang, X. Ma, Z. Xu, J. Zhan, Regret Theory-Based Three-Way Decision Model in Hesitant Fuzzy Environments and Its Application to Medical Decision, IEEE Trans. Fuzzy Syst., 30 (2022), 5361–5375
  • View Article
  • Google Scholar


• [46] G. Wei, F. E. Alsaadi, T. Hayat, A. Alsaedi, Bipolar fuzzy Hamacher aggregation operators in multiple attribute decision making, Int. J. Fuzzy Syst., 20 (2018), 1–12
  • View Article
  • MathSciNet
  • Google Scholar


• [47] H.-L. Yang, S.-G. Li, Z.-L. Guo, C.-H. Ma, Transformation of bipolar fuzzy rough set models, Knowl. Based Syst., 27 (2012), 60–68
  • View Article
  • Google Scholar


• [48] H.-L. Yang, S.-G. Li, S. Wang, J. Wang, Bipolar fuzzy rough set model on two different universes and its application, Knowl. Based Syst., 35 (2012), 94–101
  • View Article
  • Google Scholar


• [49] Y. Yao, Three-way decisions with probabilistic rough sets, Inform. Sci., 180 (2010), 341–353
  • View Article
  • MathSciNet
  • Google Scholar


• [50] L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353
  • View Article
  • Google Scholar
  • MATH


• [51] 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, Appl. Soft Comput., 56 (2017), 446–457
  • View Article
  • Google Scholar


• [52] J. Zhan, W. Wang, J. C. R. Alcantud, J. Zhan, A three-way decision approach with prospect-regret theory via fuzzy set pair dominance degrees for incomplete information systems, Inf. Sci., 617 (2022), 310–330
  • View Article
  • Google Scholar


• [53] W. R. Zhang, Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis, In: NAFIPS/IFIS/NASA’94. Proceedings of the first international joint conference of the North American fuzzy information processing society biannual conference. The Industrial Fuzzy Control and Intellige., IEEE, (1994), 305–309
  • View Article
  • Google Scholar


• [54] W. R. Zhang, Bipolar quantum logic gates and quantum cellular combinatoricsa logical extension to quantum entanglement, J. Quantum Inf. Sci., 3 (2013), 93–105
  • View Article
  • Google Scholar


• [55] W. R. Zhang, G-CPT Symmetry of Quantum Emergence and Submergence–An Information Conservational Multiagent Cellular Automata Unification of CPT Symmetry and CP Violation for Equilibrium-Based Many-World Causal Analysis of Quantum Coherence and Decoherence, J. Quantum Inf. Sci., 6 (2016), 62–97
  • View Article
  • Google Scholar


• [56] W. R. Zhang, A. K. Pandurangi, K. E. Peace, Y.-Q. Zhang, Z. Zhao, MentalSquares: a generic bipolar support vector machine for psychiatric disorder classification, diagnostic analysis and neurobiological data mining, Int. J. Data Min. Bioinform., 5 (2011), 532–557
  • View Article
  • Google Scholar


• [57] W. R. Zhang, K. E. Peace, Causality is logically definable—toward an equilibrium-based computing paradigm of quantum agents and quantum intelligence (QAQI)(Survey and research), J. Quantum Inf. Sci., 4 (2014), 227–268
  • View Article
  • Google Scholar


• [58] W.-R. Zhang, J. H. Zhang, Y. Shi, S.-S. Chen, Bipolar linear algebra and yinyang-N-element cellular networks for equilibrium-based biosystem simulation and regulation, J. Biol. Syst., 17 (2009), 547–576
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [59] B. Zhou, J. Chen, Q. Wu, D. Pamucar, W. Wang, L. Zhou, Risk priority evaluation of power transformer parts based on hybrid FMEA framework under hesitant fuzzy environment, Facta Univ. Ser.: Mech. Eng., 20 (2022), 399–420
  • View Article
  • Google Scholar