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AIMS Mathematics

2022, Volume 7, Issue 7: 12650-12670. doi: 10.3934/math.2022700
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Research article

Generalized hesitant intuitionistic fuzzy N-soft sets-first result

  • 1.
    Department of Mathematics, Andalas University, Kampus UNAND Limau Manis, Padang, Indonesia
  • 2.
    Department of Economic Social of Agriculture, Andalas University, Kampus UNAND Limau Manis, Padang, Indonesia
  • Received: 30 November 2021 Revised: 05 April 2022 Accepted: 12 April 2022 Published: 28 April 2022

  • MSC : 03E72, 94D05

  • The study on N-soft sets (NSSs) has been significantly developed recently. Hybrid models such as fuzzy N-soft sets, Intuitionistic fuzzy N-soft sets, and hesitant fuzzy N-soft sets were introduced to combine fuzzy sets, intuitionistic fuzzy sets and hesitant fuzzy sets with NSSs. Related to the hybrid models, it was also constructed some complements, operations and related properties. This article aims to construct a new hybrid model called hesitant intuitionistic fuzzy N-soft sets (HIFNSSs) to combine intuitionistic fuzzy N-soft sets and hesitant fuzzy N-soft sets. Moreover, we generalise HIFNSSs to generalized hesitant intuitionistic fuzzy N-soft sets (GHIFNSSs) as a hybrid model between generalized hesitant intuitionistic fuzzy sets and N-soft sets. It was also defined some complements of GHIFNSSs, intersection and union operations between GHIFNSSs, and proved that the operations between some particular complements hold De Morgan Law. In applying a GHIFNSS, we provide an algorithm for decision-making problems and its numerical illustration.

    Citation: Admi Nazra, Jenizon, Yudiantri Asdi, Zulvera. Generalized hesitant intuitionistic fuzzy N-soft sets-first result[J]. AIMS Mathematics, 2022, 7(7): 12650-12670. doi: 10.3934/math.2022700

    Related Papers:

  • The study on N-soft sets (NSSs) has been significantly developed recently. Hybrid models such as fuzzy N-soft sets, Intuitionistic fuzzy N-soft sets, and hesitant fuzzy N-soft sets were introduced to combine fuzzy sets, intuitionistic fuzzy sets and hesitant fuzzy sets with NSSs. Related to the hybrid models, it was also constructed some complements, operations and related properties. This article aims to construct a new hybrid model called hesitant intuitionistic fuzzy N-soft sets (HIFNSSs) to combine intuitionistic fuzzy N-soft sets and hesitant fuzzy N-soft sets. Moreover, we generalise HIFNSSs to generalized hesitant intuitionistic fuzzy N-soft sets (GHIFNSSs) as a hybrid model between generalized hesitant intuitionistic fuzzy sets and N-soft sets. It was also defined some complements of GHIFNSSs, intersection and union operations between GHIFNSSs, and proved that the operations between some particular complements hold De Morgan Law. In applying a GHIFNSS, we provide an algorithm for decision-making problems and its numerical illustration.


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    [1] M. Akram, G. Ali, J. C. R. Alcantud, New decision-making hybridmodel: Intuitionistic fuzzy N-soft rough sets, Soft Comput., 23 (2019), 9853–9868.
    [2] M. Akram, A. Adeel, J. C. R. Alcantud, Hesitant fuzzy N-soft sets: A novel model with applications in decision making, J. Inte. Fuzzy Syst., 36 (2019), 6113–6127. https://doi.org/10.3233/JIFS-181972 doi: 10.3233/JIFS-181972
    [3] M. Akram, A. Adeel, J. C. R. Alcantud, Fuzzy N-soft sets: A novel model with applications in decision making, J. Intell. Fuzzy Syst., 35 (2018), 4757–4771.
    [4] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst., 20 (1986), 87–96. https://doi.org/10.1007/978-3-7908-1870-3 doi: 10.1007/978-3-7908-1870-3
    [5] K. V. Babitha, S. J. John, Hesitant fuzzy soft sets, J. New Result. Sci., 3 (2013), 98–107.
    [6] I. Beg, T. Rashid, Group decision making using intuitionistic hesitant fuzzy sets, Int. J. Fuzzy Log. Intell., 14 (2014), 181–187. https://doi.org/10.5391/IJFIS.2014.14.3.181 doi: 10.5391/IJFIS.2014.14.3.181
    [7] N. Ca$\check{g}$man, S. Karatas, Intuitionistic fuzzy soft set theory and its decision making, J. Intell. Fuzzy Syst., 24 (2013), 829–836.
    [8] F. Fatimah, D. Rosadi, R. B. F. Hakim, J. C. R. Alcantud, N-soft sets and their decision making algorithms, Soft Comput., 22 (2018), 3829–3842. https://doi.org/10.1007/s00500-017-2838-6 doi: 10.1007/s00500-017-2838-6
    [9] A. Khan, Y. Zhu, New algorithms for parameter reduction of intuitionistic fuzzy soft sets, Comput. Appl. Math., 39 (2020), 232. https://doi.org/10.1007/s40314-020-01279-4 doi: 10.1007/s40314-020-01279-4
    [10] P. K. Maji, R. Biswas, A. R. Roy, Fuzzy soft sets, J. Fuzzy Math., 9 (2001), 589–602.
    [11] D. Molodtsov, Soft set theory-first result, 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
    [12] A. Nazra, Syafruddin, R. Lestari, G. C. Wicaksono, Hesitant intuitionistic fuzzy soft sets, J. Phys.- Conf. Ser., 890 (2017), 012118. https://doi.org/10.1088/1742-6596/890/1/012118 doi: 10.1088/1742-6596/890/1/012118
    [13] A. Nazra, Syafruddin, G. C. Wicaksono, M. Syafwan, A study on generalized hesitant intuitionistic fuzzy soft sets, J. Phys.- Conf. Ser., 983 (2018), 012127. https://doi.org/10.1088/1742-6596/983/1/012127 doi: 10.1088/1742-6596/983/1/012127
    [14] A. Nazra, Y. Asdi, S. Wahyuni, H. Ramadhani, Zulvera, Generalized interval-valued hesitant intuitionistic fuzzy soft sets, J. Intell. Fuzzy Syst., 40 (2021), 11039–11050. https://doi.org/10.3233/JIFS-202185 doi: 10.3233/JIFS-202185
    [15] F. Xiao, A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems, IEEE T. Syst. Man Cy-S., 51 (2021), 3980–3992. https://doi.org/10.1109/TSMC.2019.2958635 doi: 10.1109/TSMC.2019.2958635
    [16] L. A. Zadeh, Fuzzy set, Inform. Control, 8 (1965), 338–353.
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