Decision self-information based on parameterized fuzzy β neighborhood and its application in three-way multi-attribute group decision-making

Wenbin Zheng; Jinjin Li; Shujiao Liao; Wenbin Zheng; Jinjin Li; Shujiao Liao

doi:10.3934/era.2022231

Electronic Research Archive

2022, Volume 30, Issue 12: 4553-4573. doi: 10.3934/era.2022231

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Research article

Decision self-information based on parameterized fuzzy β neighborhood and its application in three-way multi-attribute group decision-making

1.
School of Computer Science, Minnan Normal University, Zhangzhou 363000, China
2.
Key Laboratory of Data Science and Intelligence Application, Fujian Province University, Zhangzhou 363000, China
3.
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China

Received: 02 August 2022 Revised: 05 September 2022 Accepted: 07 October 2022 Published: 18 October 2022

As a special kind of entropy, decision self-information effectively considers the uncertainty information of both the lower and upper approximations. However, it is limited to rough binary relations, which limits its application to complex problems. In addition, parameterized fuzzy β covering, as an extension of the covering-based rough set model, can effectively characterize the similarity between samples. We combine decision self-information with a parameterized fuzzy β neighborhood to propose decision self-information in fuzzy environments, and we study its important properties. On this basis, a three-way multi-attribute group decision-making algorithm is established, and a practical problem is solved. The effectiveness of the proposed method is verified by experimental analysis.
- fuzzy β covering,
- self-information,
- three-way decision,
- multi-attribute decision-making
Citation: Wenbin Zheng, Jinjin Li, Shujiao Liao. Decision self-information based on parameterized fuzzy β neighborhood and its application in three-way multi-attribute group decision-making[J]. Electronic Research Archive, 2022, 30(12): 4553-4573. doi: 10.3934/era.2022231

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Abstract

As a special kind of entropy, decision self-information effectively considers the uncertainty information of both the lower and upper approximations. However, it is limited to rough binary relations, which limits its application to complex problems. In addition, parameterized fuzzy β covering, as an extension of the covering-based rough set model, can effectively characterize the similarity between samples. We combine decision self-information with a parameterized fuzzy β neighborhood to propose decision self-information in fuzzy environments, and we study its important properties. On this basis, a three-way multi-attribute group decision-making algorithm is established, and a practical problem is solved. The effectiveness of the proposed method is verified by experimental analysis.

References

[1]	W. Zakowski, Approximations in the space (U; π), Demonstr. Math., 16 (1983), 761–770. https://doi.org/10.1515/dema-1983-0319 doi: 10.1515/dema-1983-0319
[2]	Z. Pawlak, Rough sets, Int. J. Comput. Inf., 11 (1982), 341–356. https://doi.org/10.1007/BF01001956 doi: 10.1007/BF01001956
[3]	D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, Int. J. Gen. Syst., 17 (1990), 191–209. https://doi.org/10.1080/03081079008935107 doi: 10.1080/03081079008935107
[4]	L. Ma, On some types of neighborhood-related covering rough sets, Int. J. Approximate Reasoning, 53 (2012), 901–911. https://doi.org/10.1016/j.ijar.2012.03.004 doi: 10.1016/j.ijar.2012.03.004
[5]	L. D'eer, C. Cornelis, L. Godo, Fuzzy neighborhood operators based on fuzzy coverings, Fuzzy Sets Syst., 312 (2017), 17–35. https://doi.org/10.1016/j.fss.2016.04.003 doi: 10.1016/j.fss.2016.04.003
[6]	L. Ma, Two fuzzy covering rough set models and their generalizations over fuzzy lattices, Fuzzy Sets Syst., 294 (2016), 1–17. https://doi.org/10.1016/j.fss.2015.05.002 doi: 10.1016/j.fss.2015.05.002
[7]	J. Zhan, H. Jiang, Y. Yao, Covering-based variable precision fuzzy rough sets with PROMETHEE-EDAS methods, Inf. Sci., 538 (2020), 314–336. https://doi.org/10.1016/j.ins.2020.06.006 doi: 10.1016/j.ins.2020.06.006
[8]	K. Zhang, J. Dai, Three-way multi-criteria group decision-making method in a fuzzy β-covering group approximation space, Inf. Sci., 599 (2022), 1–24. https://doi.org/10.1016/j.ins.2022.03.055 doi: 10.1016/j.ins.2022.03.055
[9]	K. Zhang, J. Dai, Redefined fuzzy rough set models in fuzzy β-covering group approximation spaces, Fuzzy Sets Syst., 442 (2022), 109–154. https://doi.org/10.1016/j.fss.2021.10.012 doi: 10.1016/j.fss.2021.10.012
[10]	Z. Huang, J. Li, A fitting model for attribute reduction with fuzzy β covering, Fuzzy Sets Syst., 413 (2021), 114–137. https://doi.org/10.1016/j.fss.2020.07.010 doi: 10.1016/j.fss.2020.07.010
[11]	J. Dai, X. Zou, W. Wu, Novel fuzzy β-covering rough set models and their applications, Inf. Sci., 608 (2022), 286–312. https://doi.org/10.1016/j.ins.2022.06.060 doi: 10.1016/j.ins.2022.06.060
[12]	J. Dai, X. Zou, Y. Qian, X. Wang, Multi-fuzzy β-covering approximation spaces and their information measures, IEEE Trans. Fuzzy Syst., 2022 (2022), 1–15. http://doi.org/10.1109/TFUZZ.2022.3193448 doi: 10.1109/TFUZZ.2022.3193448
[13]	C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J., 27 (1948), 379–423. http://doi.org/10.1002/j.1538-7305.1948.tb01338.x doi: 10.1002/j.1538-7305.1948.tb01338.x
[14]	J. Liang, K. Chin, C. Dang, C. Yam, A new method for measuring uncertainty and fuzziness in rough set theory, Int. J. Gen. Syst., 31 (2002), 331–342. https://doi.org/10.1080/0308107021000013635 doi: 10.1080/0308107021000013635
[15]	Q. Zhang, Y. Chen, J. Yang, G. Wang, Fuzzy entropy: A more comprehensible perspective for interval shadowed sets of fuzzy sets, IEEE Trans. Fuzzy Syst., 28 (2020), 3008–3022. https://doi.org/10.1109/TFUZZ.2019.2947224 doi: 10.1109/TFUZZ.2019.2947224
[16]	S. Liao, Y. Lin, J. Li, H. Li, Y. Qian, Attribute-scale selection for hybrid data with test cost constraint: The approach and uncertainty measures, Int. J. Intell. Syst., 37 (2022), 3297–3333. https://doi.org/10.1002/int.22678 doi: 10.1002/int.22678
[17]	Z. Li, P. Zhang, X. Ge, N. Xie, G. Zhang, C. Wen, Uncertainty measurement for a fuzzy relation information system, IEEE Trans. Fuzzy Syst., 27 (2019), 2338–2352. https://doi.org/10.1109/TFUZZ.2019.2898158 doi: 10.1109/TFUZZ.2019.2898158
[18]	C. Wang, Q. He, M. Shao, Y. Xu, Q. Hu, A unified information measure for general binary relations, Knowl. Based Syst., 135 (2017), 18–28. https://doi.org/10.1016/j.knosys.2017.07.017 doi: 10.1016/j.knosys.2017.07.017
[19]	C. Wang, Q. He, M. Shao, Q. Hu, Feature selection based on maximal neighborhood discernibility, Int. J. Mach. Learn. Cybern., 9 (2018), 1929–1940. https://doi.org/10.1007/s13042-017-0712-6 doi: 10.1007/s13042-017-0712-6
[20]	C. Wang, Y. Huang, M. Shao, D. Chen, Uncertainty measures for general fuzzy relations, Fuzzy Sets Syst., 360 (2019), 82–96. https://doi.org/10.1016/j.fss.2018.07.006 doi: 10.1016/j.fss.2018.07.006
[21]	C. Wang, Y. Huang, M. Shao, Q. Hu, D. Chen, Feature selection based on neighborhood self-information, IEEE Trans. Cybern., 50 (2019), 4031–4042. https://doi.org/10.1109/TCYB.2019.2923430 doi: 10.1109/TCYB.2019.2923430
[22]	J. C. Harsanyi, Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility, J. Political Econ., 63 (1955), 309–321. https://doi.org/10.1086/257678 doi: 10.1086/257678
[23]	C. L. Hwang, K. Yoon, Multiple attribute decision making methods and applications a state-of-the-art survey, in Lecture Notes in Economics and Mathematical Systems, Springer, Berlin Heidelberg, 1981. https://doi.org/10.1007/978-3-642-48318-9_3
[24]	F. Zhu, J. XU, Y. Liu, J. Sun, Probabilistic hesitant fuzzy multi-attribute decision method based on signed distance and cross entropy, Control Decis., 35 (2020), 1977–1986. https://doi.org/10.13195/j.kzyjc.2018.1432 doi: 10.13195/j.kzyjc.2018.1432
[25]	F. Jia, P. Liu, A Novel three-way decision model under multiple-criteria environment, Inf. Sci., 471 (2019), 29–51. https://doi.org/10.1016/j.ins.2018.08.051 doi: 10.1016/j.ins.2018.08.051
[26]	M. Molla, B. Giri, P. Biswas, Extended PROMETHEE method with pythagorean fuzzy sets for medical diagnosis problems, Soft Comput., 25 (2021), 4503–4512. https://doi.org/10.1007/s00500-020-05458-7 doi: 10.1007/s00500-020-05458-7
[27]	M. Zhao, J. Qin, Y. Pan, W. Wu, Strategic weight manipulation in fuzzy multiple attribute decision making (in China), Control Decis., 36 (2021), 1259–1267. https://doi.org/10.13195/j.kzyjc.2019.0542 doi: 10.13195/j.kzyjc.2019.0542
[28]	K. Zhang, J. Zhan, W. Z. Wu, On multicriteria decision-making method based on a fuzzy rough set model with fuzzy α-neighborhoods, IEEE Trans. Fuzzy Syst., 29 (2021), 2491–2505. https://doi.org/10.1109/TFUZZ.2020.3001670 doi: 10.1109/TFUZZ.2020.3001670
[29]	Y. Wang, M. Miao, Application of exponential hesitation fuzzy entropy in multi-attribute decision making (in China), Control Decis., 37 (2022), 1460–1468. https://doi.org/10.13195/j.kzyjc.2020.1532 doi: 10.13195/j.kzyjc.2020.1532
[30]	Y. Yao, Three-way decisions with probabilistic rough sets, Inf. Sci., 180 (2010), 341–353. https://doi.org/10.1016/j.ins.2009.09.021 doi: 10.1016/j.ins.2009.09.021
[31]	F. Hu, M. Zhang, H. Yu, An active learning method based on three-way decision model (in China), Control Decis., 34 (2019), 718–726. https://doi.org/10.13195/j.kzyjc.2017.1342 doi: 10.13195/j.kzyjc.2017.1342
[32]	G. Tang, W. Yang, P. Liu, Three-way decisions based on decision-theoretic rough sets with interval type-2 fuzzy information (in China), Control Decis., 37 (2022), 1347–1356. https://doi.org/10.13195/j.kzyjc.2020.1536 doi: 10.13195/j.kzyjc.2020.1536
[33]	M. Li, G. Wang, Object-concept discernibility matrix-based approach to attribute reduction in three-way approximate concept lattice (in China), Control Decis., 31 (2016), 1779–1784. https://doi.org/10.13195/j.kzyjc.2015.1305 doi: 10.13195/j.kzyjc.2015.1305
[34]	J. Ye, J. Zhan, Z. Xu, A novel decision-making approach based on three-way decisions in fuzzy information systems, Inf. Sci., 541 (2020), 362–390. https://doi.org/10.1016/j.ins.2020.06.050 doi: 10.1016/j.ins.2020.06.050
[35]	K. Zhang, J. Dai, J. Zhan, A new classification and ranking decision method based on three-way decision theory and TOPSIS models, Inf. Sci., 568 (2021), 54–85. https://doi.org/10.1016/j.ins.2021.03.039 doi: 10.1016/j.ins.2021.03.039
[36]	J. Ye, J. Zhan, B. Sun, A three-way decision method based on fuzzy rough set models under incomplete environments, Inf. Sci., 577 (2021), 22–48. https://doi.org/10.1016/j.ins.2021.06.088 doi: 10.1016/j.ins.2021.06.088
[37]	Q. Zhang, Q. Xie, G. Wang, A novel three-way decision model with decision-theoretic rough sets using utility theory, Knowl. Based Syst., 159 (2018), 321–335. https://doi.org/10.1016/j.knosys.2018.06.020 doi: 10.1016/j.knosys.2018.06.020
[38]	J. Zhan, J. Ye, W. Ding, P. Liu, A novel three-way decision model based on utility theory in incomplete fuzzy decision systems, IEEE Trans. Fuzzy Syst., 30 (2022), 2210–2226. http://doi.org/10.1109/TFUZZ.2021.3078012 doi: 10.1109/TFUZZ.2021.3078012
[39]	J. Deng, J. Zhan, Z. Xu, E. Herrera-viedma, Regret-theoretic multi-attribute decision-making model using three-way framework in multi-scale information systems, IEEE Trans. Cybern., 2022 (2022), 1–14. http://doi.org/10.1109/TCYB.2022.3173374 doi: 10.1109/TCYB.2022.3173374
[40]	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., 2022 (2022). http://doi.org/10.1109/TFUZZ.2022.3176686 doi: 10.1109/TFUZZ.2022.3176686
[41]	J. Deng, J. Zhan, E. Herrera-viedma, F. Herrera, Regret theory-based three-way decision method on incomplete multi-scale decision information systems with interval fuzzy numbers, IEEE Trans. Fuzzy Syst., 2022 (2022), 1–15. http://doi.org/10.1109/TFUZZ.2022.3193453 doi: 10.1109/TFUZZ.2022.3193453

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