|
|
Double-Quantitative Integration of Three-Way Decisions and Three-Way Attentions |
ZHANG Xianyong1,2, YANG Jilin2, TANG Xiao1,2 |
1.College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066 2. Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu 610066 |
|
|
Abstract The conditional probability used in three-way decisions only exhibits relativity, and thus the introduction and integration of absoluteness measures are useful for rule extraction. The absolute conditional probability is mined to establish three-way attentions, and the double-quantitative integration of three-way decisions and attentions is investigated. Firstly, the relative and absolute conditional probabilities are extracted, and their systematic relationships are analyzed to reveal their heterogeneity and complementarity. Then, three-way attentions are produced by the absolute conditional probability, and their double-quantitative integration with three-way decisions is made. Thus, the integrated region type and basic semantics (granule) system are achieved. Finally, a statistical decision table is provided for illustration. Based on the absolute conditional probability, three-way attentions become a new type of three-way patterns, and their double-quantitative integration with three-way decisions shows systematicness and applicability.
|
Received: 30 September 2016
|
|
About author:: (ZHANG Xianyong(Corresponding author), born in 1978, Ph. D., associate professor. His research interests include rough sets, granular computing and data mining. ) (YANG Jilin, born in 1981, Ph. D., associate professor. Her research interests include rough sets and data mining.) (TANG Xiao, born in 1981, Ph. D., associate professor. His research interests include rough sets and granular computing.) |
|
|
|
[1] NAUMAN M, AZAM N, YAO J T. A Three-Way Decision Making Approach to Malware Analysis Using Probabilistic Rough Sets. Information Sciences, 2016, 374: 193-209. [2] WANG G Y, MA X, YU H. Monotonic Uncertainty Measures for Attribute Reduction in Probabilistic Rough Set Model. International Journal of Approximate Reasoning, 2015, 59: 41-67. [3] YAO Y Y, WONG S K M. A Decision Theoretic Framework for Approximating Concepts. International Journal of Man-Machine Studies, 1992, 37(6): 793-809. [4] FANG B W, HU B Q. Probabilistic Graded Rough Set and Double Relative Quantitative Decision-Theoretic Rough Set. International Journal of Approximate Reasoning, 2016, 74: 1-12. [5] ZIARKO W. Variable Precision Rough Set Model. Journal of Computer and System Sciences, 1993, 46(1): 39-59. [6] YAO Y Y, LIN T Y. Generalization of Rough Sets Using Modal Lo-gics. Intelligent Automation and Soft Computing, 1996, 2(2): 103-119. [7] LIU C H, MIAO D Q, ZHANG N. Graded Rough Set Model Based on Two Universes and Its Properties. Knowledge-Based Systems, 2012, 33: 65-72. [8] ZHANG X Y, MIAO D Q. Quantitative Information Architecture, Granular Computing and Rough Set Models in the Double-Quantitative Approximation Space on Precision and Grade. Information Sciences, 2014, 268: 147-168.
[9] 张贤勇,苗夺谦.基于逻辑或的双量化粗糙集模型的计算分析与属性约简.模式识别与人工智能, 2014, 27(9): 778-786. (ZHANG X Y, MIAO D Q. Calculation Analysis and Attribute Reduction for Double-Quantitative Rough Set Model Based on Logical OR. Pattern Recognition and Artificial Intelligence, 2014, 27(9): 778-786.) [10] XU W H, GUO Y T. Generalized Multigranulation Double-Quantitative Decision-Theoretic Rough Set. Knowledge-Based Systems, 2016, 105: 190-205. [11] FAN B J, TSANG E C C, XU W H, et al. Double-Quantitative Rough Fuzzy Set based Decisions: A Logical Operations Method. Information Sciences, 2017, 378: 264-281. [12] LI W T, XU W H. Double-Quantitative Decision-Theoretic Rough Set. Information Sciences, 2015, 316: 54-67. [13] SLEZAK D, ZIARKO W. The Investigation of the Bayesian Rough Set Model. International Journal of Approximate Reasoning, 2005, 40(1/2): 81-91. [14] HU B Q. Three-Way Decisions Space and Three-Way Decisions. Information Sciences, 2014, 281: 21-52. [15] PETERS J F, RAMANNA S. Proximal Three-Way Decisions: Theory and Applications in Social Networks. Knowledge-Based Systems, 2016, 91: 4-15. [16] ZHANG Y, YAO J T. Gini Objective Functions for Three-Way Classifications. International Journal of Approximate Reasoning, 2017, 81: 103-114. |
|
|
|