基于变精度上近似与程度下近似的双量化边界及其算法

计算机科学 ›› 2013, Vol. 40 ›› Issue (9): 216-220.

基于变精度上近似与程度下近似的双量化边界及其算法

张贤勇

四川师范大学数学与软件科学学院成都610068 同济大学计算机科学与技术系上海201804

出版日期:2018-11-16 发布日期:2018-11-16
基金资助:
本文受国家自然科学基金(61203285,61273304,60970061,11071178),中国博士后科学基金(2012M520930),四川省教育厅重点项目(12ZA138)资助

Double-quantitative Boundary and its Algorithms Based on Variable Precision Upper Approximation and Grade Lower Approximation

ZHANG Xian-yong

Online:2018-11-16 Published:2018-11-16

摘要/Abstract

摘要： 近似空间中,精度与程度结合形成的双量化是一个创新课题。利用笛卡尔积进行量化信息合成,基于变精度上近似与程度下近似探讨双量化边界及其算法。首先,基于上述两个近似,自然地构建了双量化扩张粗糙集模型,定义了双量化扩张边界。接着,分析了该边界的双量化语义,得到了该边界的精确刻画与数学性质；为计算该边界,提出了近似集算法与信息粒算法,进行了算法分析与算法比较,得到了信息粒算法具有更优的算法空间复杂性的重要结论。最后,应用一个医疗实例对该边界及其算法进行了说明。该边界扩张了经典Pawlak边界,并对局部不确定性进行了双量化的完备与精细刻画,这对双量化的不确定性分析与应用具有重要意义。

关键词: 粗糙集,粒计算,不确定性,双量化,边界中图法分类号TP18文献标识码A

Abstract: The double-quantification with precision and grade acts as a novel project in the approximate space．By the Cartesian-Product combination of quantitative information,this paper aimed to explore a double-quantitative boundary and its algorithms based on the variable precision upper approximation and grade lower approximation．First,a double-quantitative expansion-model was naturally constructed by the two approximations,and the double-quantitative expansion-boundary was correspondingly defined．Then,the double-quantitative semantics was analyzed for the boundary,and its precise description and mathematical properties were obtained,in order to calculate the boundary.The approximation-set algorithm and information-granule algorithm were proposed,analyzed and compared.The information-granule algorithm has more advantages on the space complexity．Finally,a medical example was provided to illustrate the boundary and its algorithms．The boundary expands the Pawlak-boundary,and makes the complete and fine double-quantitative descriptions for partial uncertainty,thus,it has a great significance for the uncertainty analyses and applications with respect to the double-quantification.

Key words: Rough set,Granular computing,Uncertainty,Double-quantification,Boundary

张贤勇. 基于变精度上近似与程度下近似的双量化边界及其算法[J]. 计算机科学, 2013, 40(9): 216-220. https://doi.org/

ZHANG Xian-yong. Double-quantitative Boundary and its Algorithms Based on Variable Precision Upper Approximation and Grade Lower Approximation[J]. Computer Science, 2013, 40(9): 216-220. https://doi.org/

参考文献

[1] Pawlak Z．Rough sets [J]．International Journal of Computer and Information Sciences,1982,11(5):341-356
[2] Yao Y Y．The superiority of three-way decision in probabilistic rough set models [J]．Information Sciences,2011,181:1080-1096
[3] Ziarko W．Variable precision rough set model [J]．Journal ofComputer and System Sciences,1993,46(1):39-59
[4] Yao Y Y,Wong S K M,Lingras P．A decision-theoretic rough set model [C]∥The 5th International Symposium on Methodo-logies for Intelligent Systems．North-Holland,New York,1990:17-25
[5] Yao Y Y,Lin T Y．Generalization of rough sets using modal lo-gics [J]．Intelligent Automation and Soft Computing,1996,2(2):103-120
[6] Inuiguchi M,Yoshioka Y,Kusunoki Y．Variable-precision dominance-based rough set approach and attribute reduction [J]．International Journal of Approximate Reasoning,2009,50(8):1199-1214
[7] Wang J Y,Zhou J．Research of reduct features in the variable precision rough set model [J]．Neurocomputing,2009,72:2643-2648
[8] Mi J S,Wu W Z,Zhang W X．Approaches to knowledge reduction based on variable precision rough set model [J]．Information Sciences,2004,159(3/4):255-272
[9] Yanto I T R,Vitasari P,Herawan T,et al．Applying variable precision rough set model for clustering student suffering study’sanxiety [J]．Expert Systems with Applications,2012,39(1):452-459
[10] Yao Y Y,Lin T Y．Graded rough set approximations based on nested neighborhood systems[C]∥ Proceedings of 5th EuropeanCongress on intelligent techniques and Soft computing,EUFIT’97．Verlag Mainz,Aachen,1997:196-200
[11] Liu C H,Miao D Q,Zhang N,et al．Graded rough set modelbased on two universes and its properties [J]．Knowledge-Based Systems,2012,33:65-72
[12] Xu W H,Liu S H,Wang Q R,et al．The first type of graded rough set based on rough membership function[C]∥2010Se-venth International Conference on Fuzzy Systems and Knowledge Discovery(FSKD)．Yantai,China,2010:1922-1926
[13] Zhang X Y,Mo Z W,Xiong F,et al．Comparative study of variable precision rough set model and graded rough set model [J]．International Journal of Approximate Reasoning,2012,53(1):104-116
[14] Parthalain N M,Shen Q,Jensen R．A distance measure approach to exploring the rough set boundary region for attribute reduction [J]．IEEE Transactions on Knowledge and Data Enginee-ring,2010,22(3):305-317
[15] Parthalain N M,Shen Q．Exploring the boundary region of tolerance rough sets for feature selection [J]．Pattern Recognition,2009,42(5):655-667

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed