Evidence-Theory-Based Optimal Scale Combinations in Generalized Multi-scale Covering Decision Systems
WANG Jinbo1,2, WU Weizhi1,2
1. School of Information Engineering, Zhejiang Ocean University, Zhoushan 316022; 2. Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhejiang Ocean University, Zhou-shan 316022
Abstract：Multi-scale data analysis is a hot research direction in the field of granular computing. It simulates the mode of human thinking to establish effective computation models for dealing with multi-level complex data and information. A critical problem in multi-scale data analysis is to select a suitable sub-system from a given system for final classification or decision, and the combination of scale level of each attribute corresponding to the sub-system is called an optimal scale combination of the system. To solve the problem of knowledge acquisition in generalized multi-scale covering decision systems, scale combinations are firstly characterized by belief and plausibility functions in consistent generalized multi-scale covering decision systems. Then, the concepts of seven types of optimal scale combinations in inconsistent generalized multi-scale covering decision systems are defined and their relationships are clarified. It is showed that there are actually four different types of optimal scale combinations. Moreover, it is illuminated that belief and plausibility functions can be applied to characterize lower-approximation optimal scale combinations and upper-approximation optimal scale combinations in inconsistent generalized multi-scale covering decision systems, respectively. Finally, it is illustrated that the proposed methods can be applied to the optimal scale combination selection in incomplete generalized multi-scale decision systems and generalized multi-scale set-valued decision systems, respectively.
[1] PEDRYCZ W. Granular Computing: An Introduction // Proc of the Joint 9th IFSA World Congress and 20th NAFIPS International Conference. Washington, USA: IEEE, 2001, III: 1349-1354. [2] LIN T Y. Granular Computing: Structures, Representations, and Applications // Proc of the 9th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Berlin, Germany: Springer, 2003: 16-24. [3] YAO Y Y. Granular Computing: Basic Issues and Possible Solutions [C/OL]. [2021-10-14]. http://www2.cs.uregina.ca/~yyao/PAPERS/basic.pdf. [4] 庞继芳,宋鹏,梁吉业.面向决策分析的多粒度计算模型与方法综述.模式识别与人工智能, 2021, 34(12): 1120-1130. (PANG J F, SONG P, LIANG J Y. Review on Multi-granulation Computing Models and Methods for Decision Analysis. Pattern Reco-gnition and Artificial Intelligence, 2021, 34(12): 1120-1130.) [5] PAWLAK Z. Rough Sets: Theoretical Aspects of Reasoning about Data. Berlin, Germany: Springer, 1991. [6] YAO Y Y. Constructive and Algebraic Methods of the Theory of Rough Sets. Information Sciences, 1998, 109(1/2/3/4): 21-47. [7] YAO Y Y. Relational Interpretations of Neighborhood Operators and Rough Set Approximation Operators. Information Sciences, 1998, 111(1/2/3/4): 239-259. [8] ZHANG W X, MI J S. Incomplete Information System and Its Optimal Selections. Computers and Mathematics with Applications, 2004, 48(5/6): 691-698. [9] CHEN D G, ZHANG X X, LI W L. On Measurements of Covering Rough Sets Based on Granules and Evidence Theory. Information Sciences, 2015, 317: 329-348. [10] CHEN D G, LI W L, ZHANG X, et al. Evidence-Theory-Based Numerical Algorithms of Attribute Reduction with Neighborhood-Covering Rough Sets. International Journal of Approximate Reaso-ning, 2014, 55(3): 908-923. [11] TAN A H, LI J J, LIN Y J, et al. Matrix-Based Set Approximations and Reductions in Covering Decision Information Systems. International Journal of Approximate Reasoning, 2015, 59: 68-80. [12] ZHU W, WANG F Y. Reduction and Axiomization of Covering Generalized Rough Sets. Information Sciences, 2003, 152: 217-230. [13] COUSO I, DUBOIS D. Rough Sets, Coverings and Incomplete Information. Fundamenta Informaticae, 2011, 108(3/4): 223-247. [14] YAO Y Y, YAO B X. Covering Based Rough Set Approximations. Information Sciences, 2012, 200: 91-107. [15] WU W Z, LEUNG Y. Theory and Applications of Granular Labelled Partitions in Multi-scale Decision Tables. Information Sciences, 2011, 181(18): 3878-3897. [16] WU W Z, QIAN Y H, LI T J, et al. On Rule Acquisition in Incomplete Multi-scale Decision Tables. Information Sciences, 2017, 378: 282-302. [17] LI F, HU B Q. A New Approach of Optimal Scale Selection to Multi-scale Decision Tables. Information Sciences, 2017, 381: 193-208. [18] LI F, HU B Q, WANG J. Stepwise Optimal Scale Selection for Multi-scale Decision Tables via Attribute Significance. Knowledge-Based Systems, 2017, 129: 4-16. [19] WU W Z, LEUNG Y. A Comparison Study of Optimal Scale Combination Selection in Generalized Multi-scale Decision Tables. International Journal of Machine Learning and Cybernetics, 2020, 11: 961-972. [20] LI W K, LI J J, HUANG J X, et al. A New Rough Set Model Based on Multi-scale Covering. International Journal of Machine Learning and Cybernetics, 2021, 12: 243-256. [21] 陈应生,李进金,林荣德,等.多尺度覆盖决策信息系统的布尔矩阵方法.模式识别与人工智能, 2020, 33(9): 776-785. (CHEN Y S, LI J J, LIN R D, et al. Boolean Matrix Approach for Multi-scale Covering Decision Information System. Pattern Recognition and Artificial Intelligence, 2020, 33(9): 776-785.) [22] CHEN D X, LI J J, LIN R D, et al. Information Entropy and Optimal Scale Combination in Multi-scale Covering Decision Systems. IEEE Access, 2020, 8: 182908-182917. [23] 陈应生,李进金,林荣德,等.多尺度集值决策信息系统.控制与决策, 2022, 37(2): 455-463. (CHEN Y S, LI J J, LIN R D, et al. Multi-scale Set Value Decision Information System. Control and Decision, 2022, 37(2): 455-463.) [24] 胡 军,陈 艳,张清华,等.广义多尺度集值决策系统最优尺度选择[J/OL]. [2021-10-14]. http://kns.cnki.net/kcms/detail/11.1777.TP.20210824.1528.008.html. (HU J, CHEN Y, ZHANG Q H, et al. Optimal Scale Selection for Generalized Multi-scale Set-Valued Decision Systems[J/OL]. [2021-10-14]. http://kns.cnki.net/kcms/detail/11.1777.TP.20210824.1528.008.html [25] SHAFER G.A Mathematical Theory of Evidence. Princeton, USA: Princeton University Press, 1976. [26] YAO Y Y, LINGRAS P J. Interpretations of Belief Functions in the Theory of Rough Sets. Information Sciences, 1998, 104(1/2): 81-106. [27] WU W Z, LEUNG Y, ZHANG W X. Connections between Rough Set Theory and Dempster-Shafer Theory of Evidence. International Journal of General Systems, 2002, 31(4): 405-430. [28] WU W Z, LEUNG Y, MI J S. On Generalized Fuzzy Belief Functions in Infinite Spaces. IEEE Transactions on Fuzzy Systems, 2009, 17(2): 385-397. [29] 吴伟志,米据生,李同军.无限论域中的粗糙近似空间与信任结构.计算机研究与发展, 2012, 49(2): 327-336. (WU W Z, MI J S, LI T J. Rough Approximation Spaces and Be-lief Structures in Infinite Universes of Discourse. Journal of Computer Research and Development, 2012, 49(2): 327-336.) [30] TAN A H, WU W Z, LI J J, et al. Evidence-Theory-Based Numerical Characterization of Multigranulation Rough Sets in Incomplete Information Systems. Fuzzy Sets and Systems, 2016, 294: 18-35. [31] 吴伟志,庄宇斌,谭安辉,等.不协调广义多尺度决策系统的尺度组合.模式识别与人工智能, 2018, 31(6): 485-494. (WU W Z, ZHUANG Y B, TAN A H, et al. Scale Combinations in Inconsistent Generalized Multi-scale Decision Systems. Pattern Recognition and Artificial Intelligence, 2018, 31(6): 485-494.) [32] 吴伟志,杨丽,谭安辉,等.广义不完备多粒度标记决策系统的粒度选择.计算机研究与发展, 2018, 55(6): 1263-1272. (WU W Z, YANG L, TAN A H, et al. Granularity Selections in Generalized Incomplete Multi-granular Labeled Decision Systems. Journal of Computer Research and Development, 2018, 55(6): 1263-1272.) [33] 车晓雅,李磊军,米据生.基于证据理论刻画多粒度覆盖粗糙集的数值属性.智能系统学报, 2016, 11(4): 481-486. (CHE X Y, LI L J, MI J S. Evidence-Theory-Based Numerical Characterization of Multi-granulation Covering Rough Sets. CAAI Transactions on Intelligent Systems, 2016, 11(4): 481-486.)
2022, Vol. 35 
