Abstract In consideration of the generalized application of confusion matrix as an important algorithmic measurement tool in machine learning field, a three-way decision measure system of the probabilistic rough set is constructed based on three-way decision confusion matrix. Then, the properties of partial three-way decision measures are discussed. A multi-object optimization function model for three-way decisions thresholds computing is proposed as well. In this model, multi-object optimization functions are considered as weighted sums of three-way decisions measures ,and a new semantic interpretation is acquired for solving the optimal threshold. Finally, the solving process of accepting and rejecting thresholds of the model is demonstrated via an case. By comparing with the classic Pawlak rough set method and confusion matrix model, the confusion matrix model can better balance the accurate rate and the commitment rate for three-way decisions.
About author:: (XU Jianfeng, born in 1973, Ph.D. candidate, associate professor. His research inte-rests include data mining, rough set and three-way decisions.) (MIAO Duoqian(Corresponding author), born in 1964, Ph.D., professor. His research interests include granular computing, rough set, Web intelligence, data mining and machine learning.) (ZHANG Yuanjian, born in 1990, Ph.D. candidate. His research interests include three-way decisions, rough set and machine learning.)
[1] YAO Y Y. An Outline of a Theory of Three-Way Decisions // Proc of the International Conference on Rough Sets and Current Trends in Computing. Berlin, Germany: Springer, 2012. DOI: 10.1007/978-3-642-32115-3_1. [2] ZHOU B, YAO Y Y, LUO J G. Cost-Sensitive Three-Way Email Spam Filtering. Journal of Intelligent Information Systems, 2014, 42(1): 19-45. [3] 张志飞,苗夺谦,聂建云,等.否定句的情感不确定性度量及分类.计算机研究与发展, 2015, 52(8): 1806-1816. (ZHANG Z F, MIAO D Q, NIE J Y, et al. Sentiment Uncertainty Measure and Classification of Negative Sentences. Journal of Computer Research and Development, 2015, 52(8): 1806-1816.) [4] LI H X, ZHANG L B, HUANG B, et al. Sequential Three-Way Decision and Granulation for Cost-Sensitive Face Recognition. Knowledge-Based Systems, 2016, 91: 241-251. [5] YAO Y Y. Three-Way Decisions with Probabilistic Rough Sets. Information Sciences, 2010, 180(3): 341-353. [6] ZIARKO W. Probabilistic Rough Sets // Proc of the International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular- Soft Computing. Berlin, Germany: Springer, 2005: 283-293. [7] 公茂果,焦李成,杨咚咚,等.进化多目标优化算法研究.软件学报, 2009, 20(2): 271-289. (GONG M G, JIAO L C, YANG D D, et al. Research on Evolutionary Multi-objective Optimization Algorithms. Journal of Software, 2009, 20(2): 271-289.) [8] DENG X F, YAO Y Y. A Multifaceted Analysis of Probabilistic Three-Way Decisions. Fundamenta Informaticae, 2014, 132: 291-313. [9] ZHANG Y, YAO J T. Gini Objective Functions for Three-Way Classifications. International Journal of Approximate Reasoning, 2017, 81: 103-114. [10] JIA X Y, TANG Z M, LIAO W H, et al. On an Optimization Re-presentation of Decision-Theoretic Rough Set Model. International Journal of Approximate Reasoning, 2014, 55(1): 156-166. [11] CHEBROLU S, SANJEEVI S G. Attribute Reduction in Decision-Theoretic Rough Set Model Using Particle Swarm Optimization with the Threshold Parameters Determined Using LMS Training Rule. Procedia Computer Science, 2015, 57: 527-536.
2017, Vol. 30 
