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Research Article

A multi-attribute decision-making method for ternary hybrid decision matrices in view of (T, S)-fuzzy rough sets with fuzzy preference relations

Received 18 Oct 2022, Accepted 04 Feb 2023, Published online: 23 Feb 2023

References

  • Aczél, J., & Alsina, C. (1987). Synthesizing iudgements: A functional equation approach. Mathematical Modelling, 9(3–5), 311–320. https://doi.org/10.1016/0270-02558790487-8
  • An, S., Hu, Q. H., & Wang, C. Z. (2021). Probability granular distance-based fuzzy rough set model. Applied Soft Computing, 102, 107064. https://doi.org/10.1016/j.asoc.2020.107064
  • Bezdek, J. C., Spillman, B., & Spillman, R. (1978). A fuzzy relation space for group decision theory. Fuzzy Sets and Systems, 1(4), 255–268. https://doi.org/10.1016/0165-01147890017-9
  • Chiclana, F., Herrera-Viedma, F., & Herrera-Viedma, E. (1998). Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets and Systems, 97(1), 33–48. https://doi.org/10.1016/S0165-01149600339-9
  • Chu, J. F., Wang, Y. M., Liu, X. W., & Liu, Y. C. (2020). Social network community analysis based large-scale group decision making approach with incomplete fuzzy preference relations. Information Fusion, 60, 98–120. https://doi.org/10.1016/j.inffus.2020.02.005
  • Cutello, V., & Montero, J. (1994). Fuzzy rationality measures. Fuzzy Sets and Systems, 62(1), 39–54. https://doi.org/10.1016/0165-01149490071-X
  • Dai, J. H., Hu, Q. H., Hu, H., & Huang, D. B. (2018). Neighbor inconsistent pair selection for attribute reduction by rough set approach. IEEE Transactions on Fuzzy Systems, 26(2), 937–950. https://doi.org/10.1109/TFUZZ.2017.2698420
  • Dai, J. H., Hu, H., Wu, W. Z., Qian, Y. H., & Huang, D. B. (2018). Maximal-discernibility-pair-based approach to attribute reduction in fuzzy rough sets. IEEE Transactions on Fuzzy Systems, 26(4), 2174–2187. https://doi.org/10.1109/TFUZZ.2017.2768044
  • Deli, I. (2021). Bonferroni mean operators of generalized trapezoidal hesitant fuzzy numbers and their application to decision-making problems. Soft Computing, 25(6), 4925–4949. https://doi.org/10.1007/s00500-020-05504-4
  • Deli, I., & Kahraman, C. (2020). A TOPSIS method by using generalized trapezoidal hesitant fuzzy numbers and application to a robot selection problem. Journal of Intelligent and Fuzzy Systems, 38(1), 779–793. https://doi.org/10.3233/JIFS-179448
  • Deli, I., & Karaaslan, F. (2021). Generalized trapezoidal hesitant fuzzy numbers and their applications to multi criteria decision-making problems. Soft Computing, 25(2), 1017–1032. https://doi.org/10.1007/s00500-020-05201-2
  • Dubois, D., & Prade, H. (1980). Fuzzy sets and systems: Theory and application. Academic Press.
  • Dubois, D., & Prade, H. (1990). Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems, 17(2–3), 191–209. https://doi.org/10.1080/03081079008935107
  • Facchinetti, G., Ricci, R. G., & Muzzioli, S. (1998). Note on ranking fuzzy triangular numbers. International Journal of Intelligent Systems, 13(7), 613–622. https://doi.org/10.1002/SICI1098-111X19980713:7<613:AID-INT2>3.0.CO;2-N
  • Figueira, J., Greco, S., & Ehrgott, M. (2005). Multiple criteria fecision analysis: State of the art surveys. Springer.
  • Gong, Z. W., Zhang, N., & Chiclana, F. (2018). The optimization ordering model for intuitionistic fuzzy preference relations with utility functions. Knowledge-Based Systems, 162, 174–184. https://doi.org/10.1016/j.knosys.2018.07.012
  • Harsanyi, J. C. (1955). Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. The Journal of Political Economy, 63(4), 309–321. https://doi.org/10.1086/257678
  • Hassan, Y. F. (2017). Rough set classification based on quantum logic. Journal of Experimental and Theoretical Artificial Intelligence, 29(6), 1325–1336. https://doi.org/10.1080/0952813X.2017.1354080
  • Herrera, F., Herrera-Viedma, E., & Chiclana, F. (2001). Multiperson decision-making based on multiplicative preference relations. European Journal of Operational Research, 129(2), 372–385. https://doi.org/10.1016/S0377-22179900197-6
  • Herrera-Viedma, E., Herrera, F., Chiclana, F., & Luque, M. (2004). Some issues on consistency of fuzzy preference relations. European Journal of Operational Research, 154(1), 98–109. https://doi.org/10.1016/S0377-22170200725-7
  • Hu, X. Y., Sun, B. Z., Wang, T., & Jiang, C. (2021). Double-quantitative decision rough set over two universes and application to African swine fever decision-making. Journal of Experimental and Theoretical Artificial Intelligence, 33(2), 331–347. https://doi.org/10.1080/0952813X.2020.1744195
  • Jiang, H. B., Zhan, J. M., & Chen, D. G. (2019). Covering-based variable precision (I, T)-fuzzy rough sets with applications to multi-attribute decision-making. IEEE Transactions on Fuzzy Systems, 27(8), 1558–1572.
  • Jia, X., & Wang, Y. M. (2022). Choquet integral-based intuitionistic fuzzy arithmetic aggregation operators in multi-criteria decision-making. Expert Systems with Applications, 191, 116242. https://doi.org/10.1016/j.eswa.2021.116242
  • Kumar, K., & Chen, S. M. (2022). Multiple attribute group decision making based on advanced linguistic intuitionistic fuzzy weighted averaging aggregation operator of linguistic intuitionistic fuzzy numbers. Information Sciences, 587, 813–824. https://doi.org/10.1016/j.ins.2021.11.014
  • Liu, P. S., Diao, H. Y., Zou, L., & Deng, A. S. (2020). Uncertain multi-attribute group decision making based on linguistic-valued intuitionistic fuzzy preference relations. Information Sciences, 508, 293–308. https://doi.org/10.1016/j.ins.2019.08.076
  • Liu, H. B., & Jiang, L. (2020). Optimizing consistency and consensus improvement process for hesitant fuzzy linguistic preference relations and the application in group decision making. Information Fusion, 56, 114–127. https://doi.org/10.1016/j.inffus.2019.10.002
  • Liu, F., You, Q. R., Hu, Y. K., & Zhang, W. G. (2021). The breaking of additively reciprocal property of fuzzy preference relations and its implication to decision making under uncertainty. Information Sciences, 580, 92–110. https://doi.org/10.1016/j.ins.2021.08.066
  • Luce, R. D., & Suppes, P. (1965). Preferences utility and subject probability. In R. D. Luce (Ed.), Handbook of mathematical psychology (Vol. 1, pp. 249–410). Wiley.
  • Luo, S., Miao, D. Q., Zhang, Z. F., Zhang, Y. J., & Hu, S. D. (2020). A neighborhood rough set model with nominal metric embedding. Information Sciences, 520, 373–388. https://doi.org/10.1016/j.ins.2020.02.015
  • Ma, J., Fan, Z. P., Jiang, Y. P., Mao, J. Y., & Ma, L. (2006). A method for repairing the inconsistency of fuzzy preference relations. Fuzzy Sets and Systems, 157 (1) , 20–33.
  • Mandal, P., & Ranadive, A. S. (2019). Fuzzy multi-granulation decision-theoretic rough sets based on fuzzy preference relation. Soft Computing, 23(1), 85–99. https://doi.org/10.1007/s00500-018-3411-7
  • Meng, F. Y., Chen, S. M., & Tang, J. (2020). Group decision making based on acceptable multiplicative consistency of hesitant fuzzy preference relations. Information Sciences, 524, 77–96. https://doi.org/10.1016/j.ins.2020.03.037
  • Meng, F. Y., Tan, C. Q., & Chen, X. H. (2017). Multiplicative consistency analysis for interval fuzzy preference relations: A comparative study. Omega, 68, 17–38. https://doi.org/10.1016/j.omega.2016.05.006
  • Meng, F. Y., Tang, J., & Fujita, H. (2019). Linguistic intuitionistic fuzzy preference relations and their application to multi-criteria decision making. Information Fusion, 46, 77–90. https://doi.org/10.1016/j.inffus.2018.05.001
  • Orlovsky, S. A. (1978). Decision-making with a fuzzy preference relation. Fuzzy Sets and Systems, 1(3), 155–167. https://doi.org/10.1016/0165-01147890001-5
  • Pawlak, Z. (1982). Rough sets. International Journal of Computer and Information Sciences, 11(5), 341–356. https://doi.org/10.1007/BF01001956
  • Ren, P. J., Xu, Z. S., Wang, X. X., & Zeng, X. J. (2021). Group decision making with hesitant fuzzy linguistic preference relations based on modified extent measurement. Expert Systems with Applications, 171, 114235. https://doi.org/10.1016/j.eswa.2020.114235
  • Rodríguez, R. M., Labella, Á., Dutta, B., & Martínez, L. (2021). Comprehensive minimum cost models for large scale group decision making with consistent fuzzy preference relations. Knowledge-Based Systems, 215, 106780. https://doi.org/10.1016/j.knosys.2021.106780
  • Saaty, T. L. (1986). Axiomatic foundation of the analytic hierarchy process. Management Science, 32(7), 841–845.
  • Schweizer, B., & Sklar, A. (1960). Statistical metrics spaces. Pacific Journal of Mathematics, 10(1), 313–334. https://doi.org/10.2140/pjm.1960.10.313
  • Sun, B. Z., & Ma, W. M. (2017). Fuzzy rough set over multi-universes and its application in decision making. Journal of Intelligent and Fuzzy Systems, 32(3), 1719–1734. https://doi.org/10.3233/JIFS-151977
  • Sun, B. Z., Ma, W. M., & Qian, Y. H. (2017). Multigranulation fuzzy rough set over two universes and its application to decision making. Knowledge-Based Systems, 123, 61–74. https://doi.org/10.1016/j.knosys.2017.01.036
  • Świtalski, Z. (2022). General consistency conditions for fuzzy interval-valued preference relations. Fuzzy Sets and Systems, 443, 137–159. https://doi.org/10.1016/j.fss.2021.09.023
  • Tanino, T. (1984). Fuzzy preference orderings in group decision making. Fuzzy Sets and Systems, 12(2), 117–131. https://doi.org/10.1016/0165-01148490032-0
  • Tanino, T. (1988). Fuzzy preference relations in group decision making. In J. Kacprzyk & M. Roubens (Eds.), Non-conventional preference relations in decision making (pp. 54–71). Springer-Verlag.
  • Wang, Y. M. (1998). Using the method of maximizing deviations to make decision for multiindicies. Systems Engineering and Electronics, 7(24–26), 31.
  • Wang, Z. J. (2019). A goal-programming-based heuristic approach to deriving fuzzy weights in analytic form from triangular fuzzy preference relations. IEEE Transactions on Fuzzy Systems, 27(2), 234–248. https://doi.org/10.1109/TFUZZ.2018.2852307
  • Wang, Q. M., Dai, J. H., & Xu, Z. S. (2022). A new three-way multi-criteria decision-making method with fuzzy complementary preference relations based on additive consistency. Information Sciences, 592, 277–305. https://doi.org/10.1016/j.ins.2022.01.025
  • Wang, C. Z., Huang, Y., Shao, M. W., & Fan, X. D. (2019). Fuzzy rough set-based attribute reduction using distance measures. Knowledge-Based Systems, 164, 205–212. https://doi.org/10.1016/j.knosys.2018.10.038
  • Wang, Z. J., Yang, X., & Jin, X. T. (2020). And-like-uninorm-based transitivity and analytic hierarchy process with interval-valued fuzzy preference relations. Information Sciences, 539, 375–396. https://doi.org/10.1016/j.ins.2020.05.052
  • Wu, Z. B., & Xu, J. P. (2016). Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations. Omega, 65, 28–40. https://doi.org/10.1016/j.omega.2015.12.005
  • Xu, Z. S. (2001). Algorithm for priority of fuzzy complementary judgement matrix. Journal of Systems Engineering, 16(4), 311–314. https://doi.org/10.1016/j.fss.2005.05.046
  • Xu, Z. S. (2002). Study on methods for multiple attribute decision making under some situations [ Unpublished doctoral dissertation]. Southeast University,
  • Xu, Z. S. (2004). . Uncertain multiple attribute decision making: Methods and applications (Beijing: Tsinghua University press).
  • Xu, Z. S. (2015). Deviation square priority method for distinct preference structures based on generalized multiplicative consistency. IEEE Transactions on Fuzzy Systems, 23(4), 1164–1180. https://doi.org/10.1109/TFUZZ.2014.2346794
  • Xu, Z. S., & Da, Q. L. (2002a). The ordered weighted geomrtric averaging operators. International Journal of Intelligent Systems, 17(7), 709–716. https://doi.org/10.1002/int.10045
  • Xu, Z. S., & Da, Q. L. (2002b). The uncertain OWA operator. International Journal of Intelligent Systems, 17(6), 569–575. https://doi.org/10.1002/int.10038
  • Xu, Z. S., & Da, Q. L. (2003). An overview of operators for aggregating information. International Journal of Intelligent Systems, 18(9), 953–969. https://doi.org/10.1002/int.10127
  • Xue, Z. A., Zhao, L. P., Sun, L., Zhang, M., & Xue, T. Y. (2020). Three-way decision models based on multigranulation support intuitionistic fuzzy rough sets. International Journal of Approximate Reasoning, 124, 147–172. https://doi.org/10.1016/j.ijar.2020.06.004
  • Xu, Y., Liu, S. F., Wang, J., & Shang, X. P. (2022). Consensus checking and improving methods for AHP with q-rung dual hesitant fuzzy preference relations. Expert Systems with Applications, 208, 117902. https://doi.org/10.1016/j.eswa.2022.117902
  • Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 18(1), 183–190. https://doi.org/10.1109/21.87068
  • Yager, R. R., & Filev, D. P. (1999). Induced ordered weighted averaging operators. IEEE Transactions on Systems, Man, and Cybernetics, 29(2), 141–150. https://doi.org/10.1109/3477.752789
  • Yang, D., Cai, M. J., Li, Q. G., & Xu, F. (2022). Multigranulation fuzzy probabilistic rough set model on two universes. International Journal of Approximate Reasoning, 145, 18–35. https://doi.org/10.1016/j.ijar.2022.03.002
  • Yazidi, A., Ivanovska, M., Zennaro, F. M., Lind, P. G., & Viedma, E. H. (2022). A new decision making model based on rank centrality for GDM with fuzzy preference relations. European Journal of Operational Research, 297(3), 1030–1041. https://doi.org/10.1016/j.ejor.2021.05.030
  • Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-99586590241-X
  • Zhang, Z. M., & Chen, S. M. (2021). Group decision making based on multiplicative consistency-and-consensus preference analysis for incomplete q-rung orthopair fuzzy preference relations. Information Sciences, 574, 653–673. https://doi.org/10.1016/j.ins.2021.07.044
  • Zhang, L. Y., Liang, C. L., Li, T., & Yang, W. T. (2022). A two-stage EDM method based on KU-CBR with the incomplete linguistic intuitionistic fuzzy preference relations. Computers & Industrial Engineering, 172, 108552. https://doi.org/10.1016/j.cie.2022.108552
  • Zhou, W., & Xu, Z. S. (2018). Probability calculation and element optimization of probabilistic hesitant fuzzy preference relations based on expected consistency. IEEE Transactions on Fuzzy Systems, 26(3), 1367–1378. https://doi.org/10.1109/TFUZZ.2017.2723349
  • Zimmermann, H. J. (1991). Fuzzy sets theory and its applications. Kluwer.

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