Optimal Scale Selection in Multi-scale Contexts Based on Granular Scale Rules
HAO Chen1, FAN Min1, LI Jinhai1, YIN Yunqiang1, WANG Dujuan2
1.Faculty of Science, Kunming University of Science and Technology, Kunming 650500 2.School of Management Science and Engineering, Dalian University of Technology, Dalian 116024
Abstract Firstly, several kinds of multi-scale contexts are defined firstly, the notion of a scale rule is put forward, and some properties of scale rules are discussed. Secondly, decision scale is introduced into multi-scale contexts to form multi-scale decision contexts, and the redundancy between scale rules is also investigated. Moreover, granular scale rules are employed to define the consistency of multi-scale decision context, and an optimal scale selection method is presented grounded on the consistency guarantee of the multi-scale decision context. Finally, numerical experiments show the effectiveness of the proposed method.
Fund:Supported by National Natural Science Foundation of China (No.61562050,61573173,61305057), Fundamental Research Funds for the Central Universities (No.DUT15QY32)
[1] ZADEH L A. Fuzzy Sets and Information Granularity // KLIR G J, YUAN B, eds. Advances in Fuzzy Systems-Applications and Theory. Amsterdam, The Netherlands: North-Holland, 1996, 6: 3-18. [2] ZADEH L A. Towards a Theory of Fuzzy Information Granulation and Its Centrality in Human Reasoning and Fuzzy Logic. Fuzzy Sets and Systems, 1997, 90(2): 111-127. [3] PEDRYCZ W. Allocation of Information Granularity in Optimization and Decision-Making Models: Towards Building the Foundations of Granular Computing. European Journal of Operational Research, 2014, 232(1): 137-145. [4] ZHANG X Y, MIAO D Q. Quantitative Information Architecture, Granular Computing and Rough Set Models in the Double-Quantitative Approximation Space of Precision and Grade. Information Sciences, 2014, 268: 147-168. [5] LI J H, MEI C L, XU W H, et al. Concept Learning via Granular Computing: A Cognitive Viewpoint. Information Sciences, 2015, 298: 447-467. [6] 钱宇华.复杂数据的粒化机理与数据建模.博士学位论文.太原:山西大学, 2011. (QIAN Y H. Granulation Mechanism and Data Modeling for Complex Data. Ph.D Dissertation. Taiyuan, China: Shanxi University, 2011.) [7] YAO Y Y. Three-Way Decisions with Probabilistic Rough Sets.Information Sciences, 2010, 180(3): 341-353. [8] KEET C M. A Formal Theory of Granularity: Toward Enhancing Biological and Applied Life Sciences Information Systems with Gra-nularity. Ph.D Dissertation.Bozen, Italy: University of Bozen-Bolzano, 2008. [9] WU W Z, LEUNG Y, MI J S. Granular Computing and Knowledge Reduction in Formal Contexts. IEEE Trans on Knowledge and Data Engineering, 2008, 21(10): 1461-1474. [10] WU W Z, LEUNG Y. Theory and Applications of Granular Labelled Partitions in Multi-scale Decision Tables. Information Sciences, 2011, 181(18): 3878-3897. [11] WU W Z, LEUNG Y. Optimal Scale Selection for Multi-scale Decision Tables. International Journal of Approximate Reasoning, 2013, 54(8): 1107-1129. [12] GU S M, WU W Z, ZHENG Y. Rule Acquisition in Consistent Multi-scale Decision Systems // Proc of the 8th International Conference on Fuzzy Systems and Knowledge Discovery. Shanghai, China, 2011: 386-389. [13] GU S M, WU W Z. Knowledge Acquisition in Inconsistent Multi-Scale Decision Systems // Proc of the 6th International Conference on Rough Sets and Knowledge Technology. Banff, Canada, 2011: 669-678. [14] WILLE R. Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts // Rival I, ed. Ordered Sets. Dordrecht, The Netherlands: Kluwer Academic Publishers, 1981: 445-470. [15] LI J H, MEI C L, KUMAR C A, et al. On Rule Acquisition in Decision Formal Contexts. International Journal of Machine Lear-ning and Cybernetics, 2013, 4(6): 721-731. [16] LI J H, MEI C L, L Y J. Incomplete Decision Contexts: Appro-ximate Concept Construction, Rule Acquisition and Knowledge Reduction. International Journal of Approximate Reasoning, 2013, 54(1): 149-165.
2016, Vol. 29 
