A novel probabilistic linguistic multi-attribute decision-making method based on Mahalanobis–Taguchi system and fuzzy measure

References

• Bai, C., Zhang, R., Qian, L., & Wu, Y. (2017). Comparisons of probabilistic linguistic term sets for multi-criteria decision making. Knowledge-Based Systems, 119, 284–291. https://doi.org/10.1016/j.knosys.2016.12.020
   Web of Science ®Google Scholar
• Chang, Z., & Cheng, L. (2015). Multi-attribute decision making method based on Mahalanobis-Taguchi system and fuzzy integral. Journal of Industrial Engineering/Engineering Management, 29(03), 107–115.
   Google Scholar
• Chang, Z., Cheng, L., & Cui, L. (2016). Interval Choquet fuzzy integral multi-attribute decision making method based on Mahalanobis-Taguchi system. Control Decision, 31(1), 180–186.
   Google Scholar
• Chao, K., Zhao, H., & Xu, Z. (2021). Hesitant Mahalanobis distance with applications to estimating the optimal number of clusters. International Journal of Intelligent Systems, 36(9), 5264–5306. https://doi.org/10.1002/int.22512
   Web of Science ®Google Scholar
• Chen, J., Cheng, L., Yu, H., & Hu, S. (2018). Rolling bearing fault diagnosis and health assessment using EEMD and the adjustment Mahalanobis–Taguchi system. International Journal of Systems Science, 49(1), 147–159. https://doi.org/10.1080/00207721.2017.1397804
   Web of Science ®Google Scholar
• Cheng, L., Yaghoubi, V., Van Paepegem, W., & Kersemans, M. (2021). Mahalanobis classification system (MCS) integrated with binary particle swarm optimization for robust quality classification of complex metallic turbine blades. Mechanical Systems and Signal Processing, 146, 107060. https://doi.org/10.1016/j.ymssp.2020.107060
   Web of Science ®Google Scholar
• Chen, S., Wang, J., & Wang, T. (2019). Cloud-based ERP system selection based on extended probabilistic linguistic MULTIMOORA method and Choquet integral operator. Computational and Applied Mathematics, 38(2), 1–32. https://doi.org/10.1007/s40314-019-0839-z
   Google Scholar
• Choquet, G. (1954). Theory of capacities. Annales de L’institut Fourier, 5, 131–295. https://doi.org/10.5802/aif.53
   Google Scholar
• Fei, L., & Feng, Y. (2021). Modeling interactive multiattribute decision-making via probabilistic linguistic term set extended by Dempster–Shafer theory. International Journal of Fuzzy Systems, 23(2), 599–613. https://doi.org/10.1007/s40815-020-01019-0
   Web of Science ®Google Scholar
• Gou, X., Liao, H., Xu, Z., & Herrera, F. (2017a). Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method: A case of study to evaluate the implementation status of haze controlling measures. Information Fusion, 38, 22–34. https://doi.org/10.1016/j.inffus.2017.02.008
   Web of Science ®Google Scholar
• Gou, X., & Xu, Z. (2016). Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets. Information Sciences, 372, 407–427. https://doi.org/10.1016/j.ins.2016.08.034
   Web of Science ®Google Scholar
• Gou, X., Xu, Z., & Liao, H. (2017b). Hesitant fuzzy linguistic entropy and cross-entropy measures and alternative queuing method for multiple criteria decision making. Information Sciences, 388–389, 225–246. https://doi.org/10.1016/j.ins.2017.01.033
   Web of Science ®Google Scholar
• Gou, X., Xu, Z., Liao, H., & Herrera, F. (2021). Probabilistic double hierarchy linguistic term set and its use in designing an improved VIKOR method: The application in smart healthcare. Journal of the Operational Research Society, 72(12), 2611–2630. https://doi.org/10.1080/01605682.2020.1806741
   Web of Science ®Google Scholar
• Gu, J., Zheng, Y., Tian, X., & Xu, Z. (2021). A decision-making framework based on prospect theory with probabilistic linguistic term sets. Journal of the Operational Research Society, 72(4), 879–888. https://doi.org/10.1080/01605682.2019.1701957
   Web of Science ®Google Scholar
• Han, E. (2020). Research progress on multi-criteria decision making method based on probabilistic linguistic term set. Computer Engineering and Applications, 10, 27–35. https://doi.org/10.3778/j.issn.1002-8331.2002-0265
   Google Scholar
• Herrera, F., Herrera-Viedma, E., & Martínez, L. (2008). A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Transactions on Fuzzy Systems, 16(2), 354–370. https://doi.org/10.1109/TFUZZ.2007.896353
   Web of Science ®Google Scholar
• Hu, J., Zhang, L., Liang, W., & Wang, Z. (2009). Incipient mechanical fault detection based on multifractal and MTS methods. Petroleum Science, 6(2), 208–216. https://doi.org/10.1007/s12182-009-0034-8
   Web of Science ®Google Scholar
• Ji, C., Liang, X., Peng, Y., Zhang, Y., Yan, X., & Wu, J. (2020). Multi-dimensional interval number decision model based on Mahalanobis-Taguchi System with grey entropy method and its application in reservoir operation scheme selection. Water, 12(3), 685. https://doi.org/10.3390/w12030685
   Web of Science ®Google Scholar
• Lee, Y.-C., & Teng, H.-L. (2009). Predicting the financial crisis by Mahalanobis–Taguchi system – Examples of Taiwan’s electronic sector. Expert Systems with Applications, 36(4), 7469–7478. https://doi.org/10.1016/j.eswa.2008.09.037
   Web of Science ®Google Scholar
• Lei, F., Wei, G., Gao, H., Wu, J., & Wei, C. (2020). TOPSIS method for developing supplier selection with probabilistic linguistic information. International Journal of Fuzzy Systems, 22(3), 749–759. https://doi.org/10.1007/s40815-019-00797-6
   Web of Science ®Google Scholar
• Li, P., & Wei, C. (2019). An emergency decision-making method based on D-S evidence theory for probabilistic linguistic term sets. International Journal of Disaster Risk Reduction, 37, 101178. https://doi.org/10.1016/j.ijdrr.2019.101178
   Web of Science ®Google Scholar
• Liang, D., Kobina, A., & Quan, W. (2018). Grey relational analysis method for probabilistic linguistic multi-criteria group decision-making based on geometric Bonferroni mean. International Journal of Fuzzy Systems, 20(7), 2234–2244. https://doi.org/10.1007/s40815-017-0374-2
   Web of Science ®Google Scholar
• Liao, H., Xu, Z., & Zeng, X.-J. (2014). Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Information Sciences, 271, 125–142. https://doi.org/10.1016/j.ins.2014.02.125
   Web of Science ®Google Scholar
• Lim, H. L., Huh, E.-H., Huh, D.-A., Sohn, J.-R., & Moon, K. W. (2019). Priority setting for the management of chemicals using the globally harmonized system and multivariate analysis: Use of the Mahalanobis-Taguchi system. International Journal of Environmental Research and Public Health, 16(17), 3119. https://doi.org/10.3390/ijerph16173119
   PubMed Web of Science ®Google Scholar
• Lin, M., Chen, Z., Xu, Z., Gou, X., & Herrera, F. (2021). Score function based on concentration degree for probabilistic linguistic term sets: An application to TOPSIS and VIKOR. Information Sciences, 551, 270–290. https://doi.org/10.1016/j.ins.2020.10.061
   Web of Science ®Google Scholar
• Lin, M., Wang, H., Xu, Z., Yao, Z., & Huang, J. (2018). Clustering algorithms based on correlation coefficients for probabilistic linguistic term sets. International Journal of Intelligent Systems, 33(12), 2402–2424. https://doi.org/10.1002/int.22040
   Web of Science ®Google Scholar
• Liu, H., Jiang, L., & Xu, Z. (2018). Entropy measures of probabilistic linguistic term sets. International Journal of Computational Intelligence Systems, 11(1), 45–57. https://doi.org/10.2991/ijcis.11.1.4
   Web of Science ®Google Scholar
• Liu, P., & Teng, F. (2019). Probabilistic linguistic TODIM method for selecting products through online product reviews. Information Sciences, 485, 441–455. https://doi.org/10.1016/j.ins.2019.02.022
   Web of Science ®Google Scholar
• Liu, P., Wang, X., Wang, P., Wang, F., & Teng, F. (2022). Sustainable medical supplier selection based on multi-granularity probabilistic linguistic term sets. Technological and Economic Development of Economy, 28(2), 381–418. https://doi.org/10.3846/tede.2022.15940
   Web of Science ®Google Scholar
• Meng, F., Zhang, Q., & Cheng, H. (2013). Approaches to multiple-criteria group decision making based on interval-valued intuitionistic fuzzy Choquet integral with respect to the generalized λ-Shapley index. Knowledge-Based Systems, 37, 237–249. https://doi.org/10.1016/j.knosys.2012.08.007
   Web of Science ®Google Scholar
• Mi, X., Liao, H., Wu, X., & Xu, Z. (2020). Probabilistic linguistic information fusion: A survey on aggregation operators in terms of principles, definitions, classifications, applications, and challenges. International Journal of Intelligent Systems, 35(3), 529–556. https://doi.org/10.1002/int.22216
   Web of Science ®Google Scholar
• Murofushi, T., & Sugeno, M. (1989). An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure. Fuzzy Sets and Systems, 29(2), 201–227. https://doi.org/10.1016/0165-0114(89)90194-2
   Web of Science ®Google Scholar
• Ohkubo, M., & Nagata, Y. (2021). Anomaly detection for unlabelled unit space using the Mahalanobis–Taguchi system. Total Quality Management & Business Excellence, 32(5–6), 591–605. https://doi.org/10.1080/14783363.2019.1616542
   Web of Science ®Google Scholar
• Pal, A., & Maiti, J. (2010). Development of a hybrid methodology for dimensionality reduction in Mahalanobis–Taguchi system using Mahalanobis distance and binary particle swarm optimization. Expert Systems with Applications, 37(2), 1286–1293. https://doi.org/10.1016/j.eswa.2009.06.011
   Web of Science ®Google Scholar
• Pang, Q., Wang, H., & Xu, Z. (2016). Probabilistic linguistic term sets in multi-attribute group decision making. Information Sciences, 369, 128–143. https://doi.org/10.1016/j.ins.2016.06.021
   Web of Science ®Google Scholar
• Rodriguez, R., M., Martinez, L., & Herrera, F. (2012). Hesitant fuzzy linguistic term sets for decision making. IEEE Transactions on Fuzzy Systems, 20(1), 109–119. https://doi.org/10.1109/TFUZZ.2011.2170076
   Web of Science ®Google Scholar
• Sakeran, H., Abu Osman, N., A., & Abdul Majid, M. S. (2019). Gait classification using Mahalanobis–Taguchi system for health monitoring systems following anterior cruciate ligament reconstruction. Applied Sciences, 9(16), 3306. https://doi.org/10.3390/app9163306
   Google Scholar
• Soylemezoglu, A., Jagannathan, S., & Saygin, C. (2010). Mahalanobis Taguchi System (MTS) as a prognostics tool for rolling element bearing failures. Journal of Manufacturing Science and Engineering, 132(5), 051014. https://doi.org/10.1115/1.4002545
   Web of Science ®Google Scholar
• Spearman, C. (1904). The proof and measurement of association between two things. The American Journal of Psychology, 15(1), 72. https://doi.org/10.2307/1412159
   Google Scholar
• Su, Y., Zhao, M., Wei, C., & Chen, X. (2022). PT-TODIM method for probabilistic linguistic MAGDM and application to industrial control system security supplier selection. International Journal of Fuzzy Systems, 24(1), 202–215. https://doi.org/10.1007/s40815-021-01125-7
   Web of Science ®Google Scholar
• Sugeno, M. (1993). Fuzzy measures and fuzzy integrals-A survey. In Readings in fuzzy sets for intelligent systems (pp. 251–257). Elsevier. https://doi.org/10.1016/B978-1-4832-1450-4.50027-4
   Google Scholar
• Taguchi, G., & Jugulum, R. (2002). The Mahalanobis-Taguchi strategy: A pattern technology system. John Wiley & Sons.
   Google Scholar
• Teng, F., & Liu, P. (2021). A large group decision-making method based on a generalized Shapley probabilistic linguistic Choquet average operator and the TODIM method. Computers & Industrial Engineering, 151, 106971. https://doi.org/10.1016/j.cie.2020.106971
   Web of Science ®Google Scholar
• Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25(6), 529–539. https://doi.org/10.1002/int.20418
   Web of Science ®Google Scholar
• Wan, S.-P., Cheng, W.-B H., & Dong, J.-Y. (2021). Interactive multi-criteria group decision-making with probabilistic linguistic information for emergency assistance of COVID-19. Applied Soft Computing, 107, 107383. https://doi.org/10.1016/j.asoc.2021.107383
   PubMed Web of Science ®Google Scholar
• Wu, X., Liao, H., Xu, Z., Hafezalkotob, A., & Herrera, F. (2018). Probabilistic linguistic MULTIMOORA: A multicriteria decision making method based on the probabilistic linguistic expectation function and the improved Borda rule. IEEE Transactions on Fuzzy Systems, 26(6), 3688–3702. https://doi.org/10.1109/TFUZZ.2018.2843330
   Web of Science ®Google Scholar
• Xie, W., Xu, Z., Ren, Z., & Wang, H. (2018). Probabilistic linguistic analytic hierarchy process and its application on the performance assessment of Xiongan New Area. International Journal of Information Technology & Decision Making, 17(06), 1693–1724. https://doi.org/10.1142/S0219622017500420
   Google Scholar
• Yager, R. R. (2009). On generalized Bonferroni mean operators for multi-criteria aggregation. International Journal of Approximate Reasoning, 50(8), 1279–1286. https://doi.org/10.1016/j.ijar.2009.06.004
   Web of Science ®Google Scholar
• Yang, N., Zhang, M., Wangdu, F., & Li, R. (2021). Identification of critical components of complex product based on hybrid intuitionistic fuzzy set and improved Mahalanobis-Taguchi system. Journal of Systems Science and Systems Engineering, 30(5), 533–551. https://doi.org/10.1007/s11518-021-5503-7
   Web of Science ®Google Scholar
• Yu, W., Zhang, H., & Li, B. (2019). Operators and comparisons of probabilistic linguistic term sets. International Journal of Intelligent Systems, 34(7), 1476–1504. https://doi.org/10.1002/int.22104
   Web of Science ®Google Scholar
• Yuan, J., Li, Y., Luo, X., Zhang, Z., Ruan, Y., & Zhou, Q. (2020). A new hybrid multi-criteria decision-making approach for developing integrated energy systems in industrial parks. Journal of Cleaner Production, 270, 122119. https://doi.org/10.1016/j.jclepro.2020.122119
   Web of Science ®Google Scholar
• Zadeh, L. A. (1965). Fuzzy sets. Information & Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
   Google Scholar
• Zhang, R., Gou, X., & Xu, Z. (2021). A multi-attribute decision-making framework for Chinese medicine medical diagnosis with correlation measures under double hierarchy hesitant fuzzy linguistic environment. Computers & Industrial Engineering, 156, 107243. https://doi.org/10.1016/j.cie.2021.107243
   Web of Science ®Google Scholar
• Zhang, D., Li, Y., & Wu, C. (2020). An extended TODIM method to rank products with online reviews under intuitionistic fuzzy environment. Journal of the Operational Research Society, 71(2), 322–334. https://doi.org/10.1080/01605682.2018.1545519
   Web of Science ®Google Scholar
• Zhang, R., Xu, Z., & Gou, X. (2023). ELECTRE II method based on the cosine similarity to evaluate the performance of financial logistics enterprises under double hierarchy hesitant fuzzy linguistic environment. Fuzzy Optimization and Decision Making, 22, 23-49. https://doi.org/10.1007/s10700-022-09382-3
   Web of Science ®Google Scholar
• Zhang, Y., Xu, Z., & Liao, H. (2017). A consensus process for group decision making with probabilistic linguistic preference relations. Information Sciences, 414, 260–275. https://doi.org/10.1016/j.ins.2017.06.006
   Web of Science ®Google Scholar
• Zhang, Y., Xu, Z., Wang, H., & Liao, H. (2016). Consistency-based risk assessment with probabilistic linguistic preference relation. Applied Soft Computing, 49, 817–833. https://doi.org/10.1016/j.asoc.2016.08.045
   Web of Science ®Google Scholar
• Zhang, Z., Yang, L., Cao, Y., & Xu, Y. (2022). An improved FMEA method based on ANP with probabilistic linguistic term sets. International Journal of Fuzzy Systems, 24, 2905–2930. https://doi.org/10.1007/s40815-022-01302-2
   Google Scholar
• Zhao, M., Shen, X., He, Y., & Bai, M. (2018). Probabilistic linguistic entropy and cross-entropy measures for multiple criteria decision making. Systems Engineering-Theory & Practice, 38(10), 2679–2689.
   Google Scholar