Search Advanced

AIMS Mathematics

2022, Volume 7, Issue 7: 13019-13052. doi: 10.3934/math.2022721
Previous Article Next Article
Research article

Cubic m-polar fuzzy topology with multi-criteria group decision-making

  • 1.
    Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
  • 2.
    Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
  • 3.
    Department of Mathematics, College of Science, University of Jeddah, Jeddah, Saudi Arabia
  • Received: 26 January 2022 Revised: 19 April 2022 Accepted: 22 April 2022 Published: 09 May 2022

  • MSC : 03E72, 94D05, 90B50

  • The concept of cubic m-polar fuzzy set (CmPFS) is a new approach to fuzzy modeling with multiple membership grades in terms of fuzzy intervals as well as multiple fuzzy numbers. We define some fundamental properties and operations of CmPFSs. We define the topological structure of CmPFSs and the idea of cubic m-polar fuzzy topology (CmPF topology) with P-order (R-order). We extend several concepts of crisp topology to CmPF topology, such as open sets, closed sets, subspaces and dense sets, as well as the interior, exterior, frontier, neighborhood, and basis of CmPF topology with P-order (R-order). A CmPF topology is a robust approach for modeling big data, data analysis, diagnosis, etc. An extension of the VIKOR method for multi-criteria group decision making with CmPF topology is designed. An application of the proposed method is presented for chronic kidney disease diagnosis and a comparative analysis of the proposed approach and existing approaches is also given.

    Citation: Muhammad Riaz, Khadija Akmal, Yahya Almalki, S. A. Alblowi. Cubic m-polar fuzzy topology with multi-criteria group decision-making[J]. AIMS Mathematics, 2022, 7(7): 13019-13052. doi: 10.3934/math.2022721

    Related Papers:

  • The concept of cubic m-polar fuzzy set (CmPFS) is a new approach to fuzzy modeling with multiple membership grades in terms of fuzzy intervals as well as multiple fuzzy numbers. We define some fundamental properties and operations of CmPFSs. We define the topological structure of CmPFSs and the idea of cubic m-polar fuzzy topology (CmPF topology) with P-order (R-order). We extend several concepts of crisp topology to CmPF topology, such as open sets, closed sets, subspaces and dense sets, as well as the interior, exterior, frontier, neighborhood, and basis of CmPF topology with P-order (R-order). A CmPF topology is a robust approach for modeling big data, data analysis, diagnosis, etc. An extension of the VIKOR method for multi-criteria group decision making with CmPF topology is designed. An application of the proposed method is presented for chronic kidney disease diagnosis and a comparative analysis of the proposed approach and existing approaches is also given.


    加载中


    [1] L. A. Zadeh, Fuzzy sets, Inform. Control., 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
    [2] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Inform. Sci., 8 (1975), 199–249. https://doi.org/10.1016/0020-0255(75)90036-5 doi: 10.1016/0020-0255(75)90036-5
    [3] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst., 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
    [4] K. T. Atanassov, Intuitionistic fuzzy sets: Theory and applications, Springer-Verlag Berlin Heidelberg GmbH, 283 (2012), 1–322. https://doi.org/10.1007/978-3-7908-1870-3 doi: 10.1007/978-3-7908-1870-3
    [5] R. R. Yager, Pythagorean fuzzy subsets, 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013, 57–61. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375
    [6] R. R. Yager, Pythagorean membership grades in multicriteria decision making, IEEE Trans. Fuzzy Syst., 22 (2014), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989 doi: 10.1109/TFUZZ.2013.2278989
    [7] R. R. Yager, Generalized orthopair fuzzy sets, IEEE Trans. Fuzzy Syst., 25 (2017), 1220–1230. https://doi.org/10.1109/TFUZZ.2016.2604005 doi: 10.1109/TFUZZ.2016.2604005
    [8] W. R. Zhang, Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multiagent decision analysis, NAFIPS/IFIS/NASA94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference, The Industrial Fuzzy Control and Intellige., (1994), 305–309. https://doi.org/10.1109/IJCF.1994.375115
    [9] W. R. Zhang, (Yin)(Yang) bipolar fuzzy sets, IEEE International Conference on Fuzzy Systems Proceedings, IEEE World Congress Comput. Intell., 1 (1998), 835–840. https://doi.org/10.1109/FUZZY.1998.687599 doi: 10.1109/FUZZY.1998.687599
    [10] J. Chen, S. Li, S. Ma, X. Wang, m-Polar fuzzy sets: An extension of bipolar fuzzy sets, Sci. World J., 2014 (2014), 1–8. https://doi.org/10.1155/2014/416530 doi: 10.1155/2014/416530
    [11] F. Smarandache, A unifying field in logics, neutrosophy: Neutrosophic probability, set and logic, Amer. Res. Press: Rehoboth, DE, USA., (1999). 1–141.
    [12] F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math., 24 (2005), 287–297. https://doi.org/10.1089/blr.2005.24.297 doi: 10.1089/blr.2005.24.297
    [13] B. C. Cuong, Picture fuzzy sets, J. Comput. Sci. Cybern., 30 (2014), 409–420. https://doi.org/10.15625/1813-9663/30/4/5032
    [14] Z. S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Trans. Fuzzy Syst., 15 (2007), 1179–1187. https://doi.org/10.1109/TFUZZ.2006.890678 doi: 10.1109/TFUZZ.2006.890678
    [15] H. Garg, Nancy, Linguistic single-valued neutrosophic prioritized aggregation operators and their applications to multiple-attribute group decision-making, J. Ambient. Intell. Human. Comput., 9 (2018), 1975–1997. https://doi.org/10.1007/s12652-018-0723-5 doi: 10.1007/s12652-018-0723-5
    [16] D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5 doi: 10.1016/S0898-1221(99)00056-5
    [17] N. agman, S. Enginoglu, Soft set theory and uniint decision making, Eur. J. Oper. Res., 207 (2010), 848–855. https://doi.org/10.1016/j.ejor.2010.05.004 doi: 10.1016/j.ejor.2010.05.004
    [18] Y. B. Jun, C. S. Kim, K. O. Yang, Cubic Sets, Annal. Fuzzy Math. Inform., 4 (2012), 83–98.
    [19] M. Riaz, M. R. Hashmi, MAGDM for agribusiness in the environment of various cubic m-polar fuzzy averaging aggregation operators, J. Intell. Fuzzy Syst., 37 (2019), 3671–3691. https://doi.org/10.3233/JIFS-182809 doi: 10.3233/JIFS-182809
    [20] M. Riaz, M. R. Hashmi, Linear Diophantine fuzzy set and its applications towards multi-attribute decision making problems, J. Intell. Fuzzy Syst., 37 (2019), 5417–5439. https://doi.org/10.3233/JIFS-190550 doi: 10.3233/JIFS-190550
    [21] M. Riaz, M. R. Hashmi. H. Kalsoom, D. Pamucar, Y. M. Chu, Linear Diophantine fuzzy soft rough sets for the selection of sustainable material handling equipment, Symmetry., 12 (2020), 1–39. https://doi.org/10.3390/sym12081215 doi: 10.3390/sym12081215
    [22] M. Riaz, M. R. Hashmi, D. Pamucar, Y. M. Chu, Spherical linear Diophantine fuzzy sets with modeling uncertainties in MCDM, Comput. Model. Eng. Sci., 126 (2021), 1125–1164. https://doi.org/10.32604/cmes.2021.013699 doi: 10.32604/cmes.2021.013699
    [23] P. Liu, Z. Ali, T. Mahmood, N. Hassan, Group decision-making using complex $q$-rung orthopair fuzzy Bonferroni mean, Int. J. Comput. Intell. Syst., 13 (2020), 822–851. https://doi.org/10.2991/ijcis.d.200514.001 doi: 10.2991/ijcis.d.200514.001
    [24] P. Liu, P. Wang, Multiple attribute group decision making method based on intuitionistic fuzzy Einstein interactive operations, Int. J. Fuzzy Syst., 22 (2020), 790–809. https://doi.org/10.1007/s40815-020-00809-w doi: 10.1007/s40815-020-00809-w
    [25] A. Jain, J. Darbari, A. Kaul, P. C. Jha, Selection of a green marketing strategy using MCDM under fuzzy environment, In: Soft Computing for Problem Solving, (2020), https://doi.org/10.1007/978-981-15-0184-5_43
    [26] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182–190. https://doi.org/10.1016/0022-247X(68)90057-7
    [27] D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets Syst., 88 (1997), 81–89. https://doi.org/10.1016/S0165-0114(96)00076-0 doi: 10.1016/S0165-0114(96)00076-0
    [28] M. Olgun, M. Unver, Yardimci, Pythagorean fuzzy topological spaces, Complex Intell. Syst., 5 (2019), 177–183. https://doi.org/10.1007/s40747-019-0095-2 doi: 10.1007/s40747-019-0095-2
    [29] N. Cagman, S. Karatas, S. Enginoglu, Soft topology, Comput. Math. Applic., 62 (2011), 351–358. https://doi.org/10.1016/j.camwa.2011.05.016
    [30] A. Saha, T. Senapati, R. R. Yager, Hybridizations of generalized Dombi operators and Bonferroni mean operators under dual probabilistic linguistic environment for group decision-making, Int. J. Intell. Syst., 11 (2021), 6645–6679. https://doi.org/10.1002/int.22563 doi: 10.1002/int.22563
    [31] A. Saha, H. Garg, D. Dutta, Probabilistic linguistic q-rung orthopair fuzzy generalized Dombi and Bonferroni mean operators for group decision-making with unknown weights of experts, Int. J. Intell. Syst., 12 (2021), 7770–7804. https://doi.org/10.1002/int.22607 doi: 10.1002/int.22607
    [32] C. Jana, G. Muhiuddin, M. Pal, D. Al-Kadi, Intuitionistic fuzzy Dombi hybrid decision-making method and their applications to enterprise financial performance evaluation, Math. Prob. Eng., 2021 (2021), 1–14. https://doi.org/10.1155/2021/3218133 doi: 10.1155/2021/3218133
    [33] C. Jana, M. Pal, J. Wang, Bipolar fuzzy Dombi prioritized aggregation operators in multiple attribute decision making, Soft Comput., 24 (2020), 3631–3646. https://doi.org/10.1007/s00500-019-04130-z. doi: 10.1007/s00500-019-04130-z
    [34] M. Akram, G. Ali, J. C. R. Alcantud, Attributes reduction algorithms for m-polar fuzzy relation decision systems, Int. J. Approx. Reas., 140 (2022), 232–254. https://doi.org/10.1016/j.ijar.2021.10.005 doi: 10.1016/j.ijar.2021.10.005
    [35] M. Akram, A. Luqman, J. C. R. Alcantud, Risk evaluation in failure modes and effects analysis: Hybrid TOPSIS and ELECTRE I solutions with Pythagorean fuzzy information, Neural Comput. Applic., 33 (2021), 5675–5703. https://doi.org/10.1007/s00521-020-05350-3 doi: 10.1007/s00521-020-05350-3
    [36] S. Ashraf, S. Abdullah, Decision aid modeling based on sine trigonometric spherical fuzzy aggregation information, Soft Comput., 25 (2021), 8549–8572. https://doi.org/10.1007/s00500-021-05712-6 doi: 10.1007/s00500-021-05712-6
    [37] A. O. Almagrabi, S. Abdullah, M. Shams, Y. D. Al-Otaibi, S. Ashraf, A new approach to q-linear Diophantine fuzzy emergency decision support system for COVID19, J. Ambient. Intell. Human. Comput., 13 (2021), 1687–1713. https://doi.org/10.1007/s12652-021-03130-y doi: 10.1007/s12652-021-03130-y
    [38] M. Ali, I. Deli, F. Smarandache, The theory of neutrosophic cubic sets and their applications in pattern recognition, J. Intell. Fuzzy Syst., 30 (2016), 1957–1963. https://doi.org/10.3233/IFS-151906 doi: 10.3233/IFS-151906
    [39] M. Ali, L. H. Son, I. Deli, N. D. Tien, Bipolar neutrosophic soft sets and applications in decision making, J. Intell. Fuzzy Syst., 33 (2017), 4077–4087. https://doi.org/10.3233/JIFS-17999 doi: 10.3233/JIFS-17999
    [40] J. Zhao, X. Y. You, H. C. Liu, S. M. Wu, An extended VIKOR method using intuitionistic fuzzy sets and combination weights for supplier selection, Symmetry, 9 (2017), 1–16. https://doi.org/10.3390/sym9090169 doi: 10.3390/sym9090169
    [41] R. Joshi, S. Kumar, An intuitionistic fuzzy information measure of order-$(\alpha, \beta)$ with a new approach in supplier selection problems using an extended VIKOR method, J. Appl. Math. Comput., 60 (2019), 27–50. https://doi.org/10.1007/s12190-018-1202-z doi: 10.1007/s12190-018-1202-z
    [42] J. H. Park, H. J. Cho, J. S. Hwang, Y. C. Kwun, Extension of the VIKOR method to dynamic intuitionistic fuzzy multiple attribute decision making, Third International Workshop on Advanced Computational Intelligence, (2010), 189–195. https://doi.org/10.1109/IWACI.2010.5585223
    [43] Z. Shouzhen, C. S. Ming, K. L. Wei, Multiattribute decision making based on novel score function of intuitionistic fuzzy values and modified VIKOR method, Inform. Sci., 488 (2019), 76–92. https://doi.org/10.1016/j.ins.2019.03.018 doi: 10.1016/j.ins.2019.03.018
    [44] V. Arya, S. Kumar, A novel VIKOR-TODIM Approach based on Havrda-Charvat-Tsallis entropy of intuitionistic fuzzy sets to evaluate management information system, Fuzzy Inform. Eng., 11 (2019), 357–384. https://doi.org/10.1080/16168658.2020.1840317 doi: 10.1080/16168658.2020.1840317
    [45] K. Devi, Extension of VIKOR method in intuitionistic fuzzy environment for robot selection, Expert Syst. Applic., 38 (2011), 14163–14168. https://doi.org/10.1016/j.eswa.2011.04.227 doi: 10.1016/j.eswa.2011.04.227
    [46] X. Luo, X. Wang, Extended VIKOR method for intuitionistic fuzzy multiattribute decision-making based on a new distance measure, Math. Prob. Eng., 2017 (2017), 1–16. https://doi.org/10.1155/2017/4072486 doi: 10.1155/2017/4072486
    [47] T. Y. Chen, Remoteness index-based Pythagorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysis, Inf. Fus., 41 (2018), 129–150. https://doi.org/10.1016/j.inffus.2017.09.003 doi: 10.1016/j.inffus.2017.09.003
    [48] F. Zhou, T. Y. Chen, An extended Pythagorean fuzzy VIKOR method with risk preference and a novel generalized distance measure for multicriteria decision-making problems, Neural Comput. Applic., 33 (2021), 11821–11844. https://doi.org/10.1007/s00521-021-05829-7 doi: 10.1007/s00521-021-05829-7
    [49] G. Bakioglu, A. O. Atahan, AHP integrated TOPSIS and VIKOR methods with Pythagorean fuzzy sets to prioritize risks in self-driving vehicles, Appl. Soft Comput., 99 (2021), 1–19. https://doi.org/10.1016/j.asoc.2020.106948 doi: 10.1016/j.asoc.2020.106948
    [50] A. Guleria, R. K. Bajaj, A robust decision making approach for hydrogen power plant site selection utilizing (R, S)-Norm Pythagorean Fuzzy information measures based on VIKOR and TOPSIS method, Int. J. Hydr. Energy., 45 (2020), 18802–18816. https://doi.org/10.1016/j.ijhydene.2020.05.091 doi: 10.1016/j.ijhydene.2020.05.091
    [51] M. Gul, Application of Pythagorean fuzzy AHP and VIKOR methods in occupational health and safety risk assessment: the case of a gun and rifle barrel external surface oxidation and colouring unit, Int. J. Occup. Safety Ergon., 26 (2020), 705–718. https://doi.org/10.1080/10803548.2018.1492251 doi: 10.1080/10803548.2018.1492251
    [52] M. Kirisci, I. Demir, N. Simsek, N. Topa, M. Bardak, The novel VIKOR methods for generalized Pythagorean fuzzy soft sets and its application to children of early childhood in COVID-19 quarantine, Neural Comput. Applic., 34 (2021), 1877–1903. https://doi.org/10.1007/s00521-021-06427-3 doi: 10.1007/s00521-021-06427-3
    [53] S. Dalapati, S. Pramanik, A revisit to NC-VIKOR based MAGDM strategy in neutrosophic cubic set environment, Neutrosophic Sets Sy., 21 (2018), 131–141. https://doi.org/10.20944/preprints201803.0230.v1 doi: 10.20944/preprints201803.0230.v1
    [54] S. Pramanik, S. Dalapati, S. Alam, T. K. Roy, NC-VIKOR based MAGDM strategy under neutrosophic cubic set environment, Neutrosophic Sets Sy., 20 (2018), 95–108. https://doi.org/10.20944/preprints201803.0230.v1 doi: 10.20944/preprints201803.0230.v1
    [55] S. Pramanik, S. Dalapati, S. Alam, T. K. Roy, VIKOR based MAGDM strategy under bipolar neutrosophic set environment, Neutrosophic Sets Sy., 19 (2018), 57–69. https://doi.org/10.20944/preprints201801.0006.v1 doi: 10.20944/preprints201801.0006.v1
    [56] L. Wang, H. Y. Zhang, J. Q. Wang, L. Li, Picture fuzzy normalized projection-based VIKOR method for the risk evaluation of construction project, Appl. Soft Comput., 64 (2018), 216–226. https://doi.org/10.1016/j.asoc.2017.12.014 doi: 10.1016/j.asoc.2017.12.014
    [57] V. Arya, S. Kumar, A picture fuzzy multiple criteria decision-making approach based on the combined TODIM-VIKOR and entropy weighted method, Cogn. Comput., 13 (2021), 1172–1184. https://doi.org/10.1007/s12559-021-09892-z doi: 10.1007/s12559-021-09892-z
    [58] R. Joshi, A novel decision-making method using R-Norm concept and VIKOR approach under picture fuzzy environment, Expert Syst. Applic., 147 (2020), 1–12. https://doi.org/10.1016/j.eswa.2020.113228 doi: 10.1016/j.eswa.2020.113228
    [59] V. Arya, S. Kumar, A new picture fuzzy information measure based on shannon entropy with applications in opinion polls using extended VIKOR-TODIM approach, Comp. Appl. Math., 39 (2020), 1–24. https://doi.org/10.1007/s40314-020-01228-1 doi: 10.1007/s40314-020-01228-1
    [60] M. J. Khan, P. Kumam, W. Kumam, A. N. A. Kenani, Picture fuzzy soft robust VIKOR method and its applications in decision-making, Fuzzy Inf. Eng., 13 (2021), 296–322. https://doi.org/10.1080/16168658.2021.1939632. doi: 10.1080/16168658.2021.1939632
    [61] C. Yue, Picture fuzzy normalized projection and extended VIKOR approach to software reliability assessment, Appl. Soft Comput., 88 (2020), 1–13. https://doi.org/10.1016/j.asoc.2019.106056. doi: 10.1016/j.asoc.2019.106056
    [62] P. Meksavang, H. Shi, S. M. Lin, H. C. Liu, An extended picture fuzzy VIKOR approach for sustainable supplier management and its application in the beef industry, Symmetry., 11 (2019), 1–19. https://doi.org/10.3390/sym11040468. doi: 10.3390/sym11040468
    [63] A. Singh, S. Kumar, Picture fuzzy Choquet integral-based VIKOR for multicriteria group decision-making problems, Gran. Comput., 6 (2021), 587–601. https://doi.org/10.1007/s41066-020-00218-2. doi: 10.1007/s41066-020-00218-2
  • Reader Comments
  • © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(1746) PDF downloads(78) Cited by(4)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(11)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog