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AIMS Mathematics

2023, Volume 8, Issue 12: 30445-30461. doi: 10.3934/math.20231555
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Research article

Intuitionistic fuzzy monotonic DOWA operators

  • 1.
    School of Data Science and Intelligent Engineering, Xiamen Institute of Technology, Xiamen 361021, China
  • 2.
    School of Artificial Intelligence, Beijing Normal University, Beijing 100875, China
  • 3.
    Business School, Sichuan University, Wuhou District, Chengdu 610064, China
  • Received: 06 August 2023 Revised: 17 September 2023 Accepted: 21 September 2023 Published: 09 November 2023

  • MSC : 03E72, 28E10, 47S40

  • A new measure for intuitionistic fuzzy numbers (IFNs) is proposed to reflect the magnitude of IFNs, and a novel ranking approach for IFNs is presented based on this measure. Furthermore, the theoretical basis of the ranking method is investigated, and several intuitionistic fuzzy monotonic dependent ordered weighted averaging (IFMDOWA) operators are developed, such as the conservative IFMDOWA (COV-IFMDOWA) operator, positive intuitionistic fuzzy monotonic DOWA (POS-IFMDOWA) operator, conservative intuitionistic fuzzy hybrid monotonic dependent order weighted averaging (COV-IFHMDOWA) operator, and positive intuitionistic fuzzy hybrid monotonic dependent order weighted averaging (POS-IFHMDOWA) operator. Finally, a numerical example is given to illustrate the flexibility of our proposed monotonic dependent order weighted averaging operators in a practical decision making process.

    Citation: Zhichun Xie, Rong Ma, Deqing Li, Qianhui Wan, Wenyi Zeng, Xianchuan Yu, Zeshui Xu. Intuitionistic fuzzy monotonic DOWA operators[J]. AIMS Mathematics, 2023, 8(12): 30445-30461. doi: 10.3934/math.20231555

    Related Papers:

  • A new measure for intuitionistic fuzzy numbers (IFNs) is proposed to reflect the magnitude of IFNs, and a novel ranking approach for IFNs is presented based on this measure. Furthermore, the theoretical basis of the ranking method is investigated, and several intuitionistic fuzzy monotonic dependent ordered weighted averaging (IFMDOWA) operators are developed, such as the conservative IFMDOWA (COV-IFMDOWA) operator, positive intuitionistic fuzzy monotonic DOWA (POS-IFMDOWA) operator, conservative intuitionistic fuzzy hybrid monotonic dependent order weighted averaging (COV-IFHMDOWA) operator, and positive intuitionistic fuzzy hybrid monotonic dependent order weighted averaging (POS-IFHMDOWA) operator. Finally, a numerical example is given to illustrate the flexibility of our proposed monotonic dependent order weighted averaging operators in a practical decision making process.


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    [1] J. M. Zhan, J. J. Wang, W. P. Ding, Y. Y. Yao, Three-way behavioral decision making with hesitant fuzzy information systems: Survey and challenges, IEEE/CAA J. Automat. Sinica, 10 (2023), 330–350. https://doi.org/10.1109/JAS.2022.106061 doi: 10.1109/JAS.2022.106061
    [2] J. Deng, J. M. Zhan, Z. S. Xu, E. Herrera-Viedma, Regret-theoretic multiattribute decision-making model using three-way framework in multiscale information systems, IEEE Trans. Cybernet., 53 (2023), 3988–4001. https://doi.org/10.1109/TCYB.2022.3173374 doi: 10.1109/TCYB.2022.3173374
    [3] J. M. Zhan, J. Deng, Z. S. Xu, L. Martínez, A three-way decision methodology with regret theory via triangular fuzzy numbers in incomplete multi-scale decision information systems, IEEE Trans. Fuzzy Syst., 31 (2023), 2773–2787. https://doi.org/10.1109/TFUZZ.2023.3237646 doi: 10.1109/TFUZZ.2023.3237646
    [4] M. Grabisch, J. Marichal, R. Mesiar, E. Pap, Aggregative function, Cambridge: Cambridge University Press, 2009.
    [5] Z. S. Xu, Q. L. Da, An overview of operators for aggregating information, Int. J. Intell. Syst., 18 (2003), 953–969. https://doi.org/10.1002/int.10127 doi: 10.1002/int.10127
    [6] R. R. Yager, On ordered weighted averaging aggregation operators in multiciteria decision making, IEEE Trans. Syst. Man Cybernet., 18 (1988), 183–190. https://doi.org/10.1109/21.87068 doi: 10.1109/21.87068
    [7] R. R. Yager, Families of OWA operators, Fuzzy Set Syst., 59 (1993), 125–148. https://doi.org/10.1016/0165-0114(93)90194-M doi: 10.1016/0165-0114(93)90194-M
    [8] Z. S. Xu, An overview of methods for determining OWA weights, Int. J. Intell. Syst., 20 (2005), 843–865. https://doi.org/10.1002/int.20097 doi: 10.1002/int.20097
    [9] F. Herrera, E. Herrera-Viedma, F. Chiclana, A study of the origin and uses of the ordered weighted geometric operator in multicriteria decision making, Int. J. Intell. Syst., 18 (2003), 689–707. https://doi.org/10.1002/int.10106 doi: 10.1002/int.10106
    [10] X. W. Liu, H. W. Lou, Parameterized additive neat OWA operators with different orness levels, Int. J. Intell. Syst., 21 (2006), 1045–1072.
    [11] J. M. Fernández Salido, S. Murakami, Extending Yager's orness concept for the OWA aggregators to other mean operators, Fuzzy Sets Syst., 139 (2003), 515–542. https://doi.org/10.1016/S0165-0114(02)00369-X doi: 10.1016/S0165-0114(02)00369-X
    [12] X. W. Liu, The orness measures for two compound quasi-arithmetic mean aggregation operators, Internat. J. Approx. Reason., 51 (2010), 305–334. https://doi.org/10.1016/j.ijar.2009.10.003 doi: 10.1016/j.ijar.2009.10.003
    [13] B. S. Ahn, On the properties of OWA operator weights functions with constant level of orness, IEEE Trans. Fuzzy Syst., 14 (2006), 511–515. https://doi.org/10.1109/TFUZZ.2006.876741 doi: 10.1109/TFUZZ.2006.876741
    [14] D. P. Filev, R. R. Yager, On the issue of obtaining OWA operator weights, Fuzzy Sets Syst., 94 (1998), 157–169. https://doi.org/10.1016/S0165-0114(96)00254-0 doi: 10.1016/S0165-0114(96)00254-0
    [15] W. Y. Zeng, D. Q. Li, Y. D. Gu, Monotonic argument-dependent OWA operators, Int. J. Intell. Syst., 33 (2018), 1639–1659. https://doi.org/10.1002/int.21955 doi: 10.1002/int.21955
    [16] V. Torra, OWA operators in data modeling and reidentification, IEEE Trans. Fuzzy Syst., 12 (2004), 652–660. https://doi.org/10.1109/TFUZZ.2004.834814 doi: 10.1109/TFUZZ.2004.834814
    [17] X. Z. Sang, X. W. Liu, An analytic approach to obtain the least square deviation OWA operator weights, Fuzzy Sets Syst., 240 (2014), 103–116. https://doi.org/10.1016/j.fss.2013.08.007 doi: 10.1016/j.fss.2013.08.007
    [18] R. Fullér, P. Majlender, An analytic approach for obtaining maximal entropy OWA operator weights, Fuzzy Sets Syst., 124 (2001), 53–57. https://doi.org/10.1016/S0165-0114(01)00007-0 doi: 10.1016/S0165-0114(01)00007-0
    [19] V. Torra, The weighted OWA operator, Int. J. Intell. Syst., 12 (1998), 153–166.
    [20] R. R. Yager, OWA aggregation over a continuous interval argument with applications to decision making, IEEE Trans. Syst. Man Cybernet., 34 (2004), 1952–1963. https://doi.org/10.1109/TSMCB.2004.831154 doi: 10.1109/TSMCB.2004.831154
    [21] S. J. Chen, S. M. Chen, A new method for handling multicriteria fuzzy decision making problems using FN-IOWA operators, Cybern. Syst., 34 (2003), 109–137. https://doi.org/10.1080/01969720302866 doi: 10.1080/01969720302866
    [22] R. R. Yager, Centered OWA operators, Soft Comput., 11 (2007), 631–639. https://doi.org/10.1007/s00500-006-0125-z doi: 10.1007/s00500-006-0125-z
    [23] 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
    [24] M. M. Xia, Z. S. Xu, Hesitant fuzzy information aggregation in decision making, Internat. J. Approx. Reason., 52 (2011), 395–407. https://doi.org/10.1016/j.ijar.2010.09.002 doi: 10.1016/j.ijar.2010.09.002
    [25] J. C. R. Alcantud, G. Santos-García, M. Akram, OWA aggregation operators and multi-agent decisions with N-soft sets, Expert Syst. Appl., 203 (2022), 117430. https://doi.org/10.1016/j.eswa.2022.117430 doi: 10.1016/j.eswa.2022.117430
    [26] Z. S. Xu, Dependent OWA operators, In: Lecture Notes in Artificial Intelligence, Heidelberg: Springer, 3885 (2006), 172–178. https://doi.org/10.1007/11681960_18
    [27] Z. S. Xu, Q. L. Da, The uncertain OWA operator, Int. J. Intell. Syst., 17 (2002), 569–575.
    [28] Z. S. Xu, Dependent uncertain ordered weighted aggregation operators, Inform. Fusion, 9 (2008), 310–316. https://doi.org/10.1016/j.inffus.2006.10.008 doi: 10.1016/j.inffus.2006.10.008
    [29] G. W. Wei, Dependent uncertain linguistic OWA operator, In: Lecture notes in computer science, 5009 (2008), 156–163. https://doi.org/10.1007/978-3-540-79721-0_25
    [30] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–356. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
    [31] R. E. Bellman, L. A. Zadeh, Decision-making in a fuzzy environment, Management Sci., 17 (1970), 141–164. https://doi.org/10.1287/mnsc.17.4.B141 doi: 10.1287/mnsc.17.4.B141
    [32] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87–96.
    [33] J. C. R. Alcantud, Complemental fuzzy sets: A semantic justification of q-Rung orthopair fuzzy sets, IEEE Trans. Fuzzy Syst., 2023, 1–9. https://doi.org/10.1109/TFUZZ.2023.3280221 doi: 10.1109/TFUZZ.2023.3280221
    [34] E. Szmidt, J. Kacprzyk, Distance between intuitionistic fuzzy sets, Fuzzy Sets Syst., 114 (2000), 505–518.
    [35] A. G. Hatzimichailidis, G. A. Papakotas, V. G. Kaburlasos, A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems, Int. J. Intell. Syst., 27 (2012), 396–409. https://doi.org/10.1002/int.21529 doi: 10.1002/int.21529
    [36] B. Gohain, R. Chutia, P. Dutta, Distance measure on intuitionistic fuzzy sets and its application in decision-making, pattern recognition, and clustering problems, Int. J. Intell. Syst., 37 (2022), 2458–2501. https://doi.org/10.1002/int.22780 doi: 10.1002/int.22780
    [37] P. Melo-Pinto, P. Couto, H. Bustince, Image segmentation using Atanassov's intuitionistic fuzzy sets, Expert Syst. Appl., 40 (2013), 15–26. https://doi.org/10.1016/j.eswa.2012.05.055 doi: 10.1016/j.eswa.2012.05.055
    [38] S. M. Chen, J. M. Tan, Handling multicriteria fuzzy decision-making problems based on vague set theory, Fuzzy Set. Syst., 67 (1994), 163–172. https://doi.org/10.1016/0165-0114(94)90084-1 doi: 10.1016/0165-0114(94)90084-1
    [39] F. Feng, Y. Zheng, J. C. R. Alcantud, Q. Wang, Minkowski weighted score functions of intuitionistic fuzzy values, Mathematics, 8 (2020), 1143.
    [40] D. H. Hong, C. H. Choi, Multicriteria fuzzy decision-making problems based on vague set theory, Fuzzy Set. Syst., 114 (2000), 103–113. https://doi.org/10.1016/S0165-0114(98)00271-1 doi: 10.1016/S0165-0114(98)00271-1
    [41] X. M. Zhang, Z. S. Xu, A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making, Fuzzy Optim. Decis. Mak., 11 (2012), 135–146. https://doi.org/10.1007/s10700-012-9118-9 doi: 10.1007/s10700-012-9118-9
    [42] Z. Xing, W. Xiong, H. Liu, A Euclidean approach for ranking intuitionistic fuzzy values, IEEE Trans. Fuzzy Syst., 26 (2018), 353–365. https://doi.org/10.1109/TFUZZ.2017.2666219 doi: 10.1109/TFUZZ.2017.2666219
    [43] K. Guo, Amount of information and attitudinal-base method for ranking Atanassov's intuitionistic fuzzy values, IEEE Trans. Fuzzy Syst., 22 (2014), 177–188. https://doi.org/10.1109/TFUZZ.2013.2249586 doi: 10.1109/TFUZZ.2013.2249586
    [44] W. Z. Wang, X. W. Liu, Intuitionistic Fuzzy geometric aggregation operators based on Einstein operations, Int. J. Intell. Syst., 26 (2011), 1049–1075. https://doi.org/10.1002/int.20498 doi: 10.1002/int.20498
    [45] X. F. Zhao, G. W. Wei, Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making, Knowl. Based Syst., 37 (2013), 472–479. https://doi.org/10.1016/j.knosys.2012.09.006 doi: 10.1016/j.knosys.2012.09.006
    [46] Z. S. Xu, Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators, Knowl. Based Syst., 24 (2011), 749–760. https://doi.org/10.1016/j.knosys.2011.01.011 doi: 10.1016/j.knosys.2011.01.011
    [47] L. H. Chen, C. C. Hung, C. C. Tu, Considering the decision makers attitudinal character to solve multi-criteria decision-making problems in an intuitionistic fuzzy environment, Knowl. Based Syst., 36 (2012), 129–138. https://doi.org/10.1016/j.knosys.2012.06.012 doi: 10.1016/j.knosys.2012.06.012
    [48] Z. S. Xu, R. R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, Int. J. Gen. Syst., 35 (2006), 417–433. https://doi.org/10.1080/03081070600574353 doi: 10.1080/03081070600574353
    [49] 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
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