Abstract
Optimal scale selection (OSS) is a fundamental topic in the studies of multi-scale decision tables (MSDTs). Multi-scale set-valued decision tables (MSSVDTs) widely exist in practical applications, and the attribute value is a linguistic set-value. Existing studies of OSS in the MSDT with cost-sensitive learning have constructed total cost mainly from two aspects: test cost and delay cost. Moreover, they are given subjectively, resulting in a lack of objectivity in the construction of total cost. Therefore, constructing a relatively objective and comprehensive total cost for OSS based on cost-sensitive learning is worthwhile in MSSVDTs. In this paper, we firstly propose a quantization method to reasonably transform the linguistic set-value into a numerical value according to the granular structures. Then, based on three-way decisions with decision-theoretic rough sets, loss functions of every object on different scales are constructed, and uncertainty is quantified. Afterwards, loss functions are introduced into the construction of total cost with regard to OSS. This helps us obtain relatively objective total cost, including test cost, delay cost, and misclassification cost. Furthermore, in light of the idea of Technique for Order Preferences by Similarity to an Ideal Solution, we design an OSS algorithm to select the optimal scale according to the ordered change of uncertainty and total cost. Finally, the feasibility and effectiveness of the proposed algorithm are verified through experiments on UCI data sets.




Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data availability
The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.
References
Bao H, Wu WZ, Zheng JW, Li TJ (2021) Entropy based optimal scale combination selection for generalized multi-scale information tables. Int J Mach Learn Cybern 12(5):1427–1437
Chen YM, Zeng ZQ, Zhu QX, Tang CH (2016) Three-way decision reduction in neighborhood systems. Appl Soft Comput 38:942–954
Chen YS, Li JJ, Huang JX (2019) Matrix method for the optimal scale selection of multi-scale information decision systems. Mathematics 7(3):290–306
Chen Y, Hu J, Zhang QH, Wang GY (2020) Multi-scale set-valued information system and its optimal scale selection. J Shanxi Univ Nat Sci Ed 43(4):765–775
Chen YS, Li JJ, Lin RD, Chen DX, Huang ZH (2022) Multi-scale set value decision information system. Control Decis 37(2):455–463 ((in Chinese))
Chen YS, Li JH, Li JJ, Lin RD, Chen DX (2022) A further study on optimal scale selection in dynamic multi-scale decision information systems based on sequential three-way decisions. Int J Mach Learn Cybern 13(5):1505–1515
Chen YS, Li JH, Li JJ, Chen DX, Lin RD (2023) Sequential 3WD-based local optimal scale selection in dynamic multi-scale decision information systems. Int J Approx Reason 152:221–235
Cheng YL, Zhang QH, Wang GY, Hu BQ (2020) Optimal scale selection and attribute reduction in multi-scale decision tables based on three-way decision. Inf Sci 541:36–59
Cheng YL, Zhang QH, Wang GY (2021) Optimal scale combination selection for multi-scale decision tables based on three-way decision. Int J Mach Learn Cybern 12(2):281–301
Deng J, Zhan JM, Wu WZ (2021) A three-way decision methodology to multi-attribute decision-making in multi-scale decision information systems. Inf Sci 568:175–198
Guo ZX, Mi JS (2005) An uncertainty measure in rough fuzzy sets. Fuzzy Syst Math 19(4):135–140
Hao C, Li JH, Fan M, Liu WQ, Tsang EC (2017) Optimal scale selection in dynamic multi-scale decision tables based on sequential three-way decisions. Inf Sci 415:213–232
Hu J, Chen Y, Zhang QH, Wang GY (2022) Optimal scale selection for generalized multi-scale set-valued decision systems. J Comput Res Dev 59(5):2027–2038 (in Chinese)
Jia F, Liu PD (2019) A novel three-way decision model under multiple-criteria environment. Inf Sci 471:29–51
Li HY, Yu H, Fan M, Liu D, Li HX (2022) Incremental sequential three-way decision based on continual learning network. Int J Mach Learn Cybern 13(6):1633–1645
Li ZW, Zhang PF, Xie NX, Zhang GQ, Wen CF (2020) A novel three-way decision method in a hybrid information system with images and its application in medical diagnosis. Eng Appl Artif Intell 92:103651–103666
Li JH, Feng Y (2023) Update of optimal scale in dynamic multi-scale decision information systems. Int J Approx Reason 152:310–324
Liu D, Liang DC, Wang CC (2016) A novel three-way decision model based on incomplete information system. Knowl Based Syst 91:32–45
Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356
Pawlak Z, Skowron A (1993) Rough membership functions: a tool for reasoning with uncertainty. Banach Cent Publ 28:135–150
Qian YH, Dang CY, Liang JY, Tang DW (2009) Set-valued ordered information systems. Inf Sci 179(16):2809–2832
She YH, Li JH, Yang HL (2015) A local approach to rule induction in multi-scale decision tables. Knowl Based Syst 89:398–410
Yoon K, Hwang CL (1995) Multiple attribute decision making: an introduction. Sage Publications, pp 38–39
UC Irvine machine learning repository (2022) http://archive.ics.uci.edu/ml/. Accessed 13 Jan 2022
Wu WZ, Leung Y (2011) Theory and applications of granular labelled partitions in multi-scale decision tables. Inf Sci 181(18):3878–3897
Wu WZ, Leung Y (2013) Optimal scale selection for multi-scale decision tables. Int J Approx Reason 54(8):1107–1129
Wu WZ, Chen Y, Xu YH (2016) Optimal granularity selections in consistent incomplete multi-granular labeled decision systems. Pattern Recognit Artif Intell 29(2):108–115
Wu WZ, Chen CJ, Li TJ, Xu YH (2016) Comparative study on optimal granularities in inconsistent multi-granular labeled decision systems. Pattern Recognit Artif Intell 29:1095–1103
Wu WZ, Qian YH, Li TJ, Gu SM (2017) On rule acquisition in incomplete multi-scale decision tables. Inf Sci 378:282–302
Wang P, Zhang PF, Li ZW (2019) A three-way decision method based on Gaussian kernel in a hybrid information system with images: An application in medical diagnosis. Appl Soft Comput 77:734–749
Xu YH, Wu WZ, Tan AH (2017) Optimal scale selections in consistent generalized multi-scale decision tables. In: International Joint Conference on Rough Sets. Olsztyn, Poland, pp 185–198
Yao YY (2007) Decision-theoretic rough set models. In: International Conference on rough sets and knowledge technology. Canada, Toronto, pp 1–12
Yao YY (2009) Three-way decision: an interpretation of rules in rough set theory. In: International Conference on rough sets and knowledge technology. Gold Coast, Australia, pp 642–649
Yao YY (2010) Three-way decisions with probabilistic rough sets. Inf Sci 180(3):341–353
Yao YY, She Y (2016) Rough set models in multigranulation spaces. Inf Sci 327:40–56
Yao YY (2016) Three-way decisions and cognitive computing. Cognit Comput 8(4):543–554
Yao YY (2021) The geometry of three-way decision. Appl Intell 51(9):6298–6325
Yang JL, Yao YY (2020) Semantics of soft sets and three-way decision with soft sets. Knowl Based Syst 194:105538–105549
Yang JL, Yao YY (2021) A three-way decision based construction of shadowed sets from Atanassov intuitionistic fuzzy sets. Inf Sci 577:1–21
Yang XP, Li TJ, Tan AH (2020) Three-way decisions in fuzzy incomplete information systems. Int J Mach Learn Cybern 11(3):667–674
Yang X, Li TR, Liu D, Fujita H (2020) A multilevel neighborhood sequential decision approach of three-way granular computing. Inf Sci 538:119–141
Zhan JM, Zhang K, Wu WZ (2021) An investigation on Wu-Leung multi-scale information systems and multi-expert group decision-making. Expert Syst Appl 170:114542–114558
Zhang XQ, Zhang QH, Cheng YL, Wang GY (2020) Optimal scale selection by integrating uncertainty and cost-sensitive learning in multi-scale decision tables. Int J Mach Learn Cybern 11(5):1095–1114
Acknowledgements
This work is supported by National Science Foundation of China (Nos. 61673285), Sichuan Science and Technology Program of China (Nos. 2021YJ0085), and Natural Science Foundation of Sichuan Province (Nos. 2022NSFSC0569, Nos. 2022NSFSC0929).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Li, R., Yang, J. & Zhang, X. Optimal scale selection based on three-way decisions with decision-theoretic rough sets in multi-scale set-valued decision tables. Int. J. Mach. Learn. & Cyber. 14, 3719–3736 (2023). https://doi.org/10.1007/s13042-023-01860-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-023-01860-3