Abstract：A concept of interval set is introduced into decision formal contexts to study attribute reduction of interval-set concept lattices. Firstly, the conditional and decision interval-set concept lattices are constructed, and a refinement between them is also introduced. Then, the interval-set consistent set and interval-set reduction are defined. Furthermore, the corresponding approaches for judging the interval-set consistent sets are shown. By introducing the discernibility interval-set attribute matrix, methods for obtaining the interval-set attribute reductions are given.
[1] WILLE R. Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts // RIVAL I, ed. Ordered Sets. Berlin, Germany: Springer-Verlag, 1981: 445-470. [2] GANTER B, WILLE R. Formal Concept Analysis: Mathematical Foundations. Berlin, Germany: Springer-Verlag, 1999. [3] WANG L D, LIU X D. Concept Analysis via Rough Set and AFS Algebra. Information Sciences, 2008, 178(21): 4125-4137. [4] 梁吉业,王俊红.基于概念格的规则产生集挖掘算法.计算机研究与发展, 2004, 41(8): 1339-1344. (LIANG J Y, WANG J H. An Algorithm for Extracting Rule-Gene-rating Sets Based on Concept Lattice. Journal of Computer Research and Development, 2004, 41(8): 1339-1344.) [5] 仇国芳.基于变精度概念格的决策推理方法.系统工程理论与实践, 2010, 30(6): 1092-1098. (QIU G F. Approaches to Reasoning in Decision Making Based on Variable Threshold Concept Lattices. Systems Engineering-Theory and Practice, 2010, 30(6): 1092-1098.) [6] ACHARJYA D P, DAS T K. A Framework for Attribute Selection Marketing Using Rough Computing and Formal Concept Analysis. IIMB Management Review, 2017, 29(2): 122-135. [7] CHEN J K, MI J S, LIN Y J. A Graph Approach for Knowledge Reduction in Formal Contexts. Knowledge-Based Systems, 2018, 148:177-188. [8] 张文修,仇国芳.基于粗糙集的不确定决策.北京:清华大学出版社, 2005. (ZHANG W X, QIU G F. Uncertain Decision Making Based on Rough Sets. Beijing, China: Tsinghua University Press, 2005.) [9] 魏 玲,祁建军,张文修.决策形式背景的概念格属性约简.中国科学(E辑), 2008, 38(2): 195-208. (WEI L, QI J J, ZHANG W X. Attribute Reduction Theory of Concept Lattice Based on Decision Formal Contexts. Science in China(Series E), 2008, 38(2): 195-208.) [10] LI J H, MEI C L, LÜ Y J. A Heuristic Knowledge-Reduction Method for Decision Formal Contexts. Computers and Mathematics with Applications, 2011, 61(4): 1096-1106. [11] 李金海,梅长林,张红英,等.基于遗传算法的决策形式背景的属性约简方法及其在决策分析中的应用.小型微型计算机系统, 2015, 36 (8): 1803-1808. (LI J H, MEI C L, ZHANG H Y, et al. Attribute Reduction Method for Formal Decision Contexts Based on Genetic Algorithm and Its Application to Decision-Making Analysis. Journal of Chinese Computer Systems, 2015, 36(8): 1803-1808.) [12] LI J H, KUMAR C A, MEI C L, et al. Comparison of Reduction in Formal Decision Contexts. International Journal of Approximate Reasoning, 2017, 80: 100-122. [13] SHAO M W, LEUNG Y, WU W Z. Rule Acquisition and Complexity Reduction in Formal Decision Contexts. International Journal of Approximate Reasoning, 2014, 55: 259-274. [14] 李金海,吕跃进.基于概念格的决策形式背景属性约简及规则提取.数学的实践与认识, 2009, 39 (7): 182-188. (LI J H, LÜ Y J. Attribute Reduction and Rules Extraction in Decision Formal Context Based on Concept Lattice. Mathematics in Practice and Theory, 2009, 39(7): 182-188.) [15] 李同军,徐颖聪,吴伟志,等.基于决策规则的形式背景属性约简.模式识别与人工智能, 2017, 30(9): 769-778. (LI T J, XU Y C, WU W Z, et al. Attribute Reduction of Formal Contexts Based on Decision Rules. Pattern Recognition and Artificial Intelligence, 2017, 30(9): 769-778.) [16] NETO S M, ZÁRATE L E, SONG M A J. Handling High Dimensionality Contexts in Formal Concept Analysis via Binary Decision Diagrams. Information Sciences, 2018, 429: 361-376. [17] XIE J P, YANG M H, LI J H, et al. Rule Acquisition and Optimal Scale Selection in Multi-scale Formal Decision Contexts and Their Applications to Smart City. Future Generation Computer Systems, 2018, 73(1): 1-30. [18] 张 涛,师浩斌,李 林,等.决策连续形式背景的可视化数据离散化方法.计算机应用研究, 2016, 33(2): 388-391, 395. (ZHANG T, SHI H B, LI L, et al. Visual Discretization for Decision Continuous Formal Context. Application Research of Compu-ters, 2016, 33(2): 388-391, 395.) [19] 祖鸿娇,解 滨,米据生.不完备决策形式背景的概念构建与属性约简.计算机科学, 2017, 44(9): 83-87. (ZU H J, XIE B, MI J S. Concept Construction and Attribute Reduction in Incomplete Decision Formal Contexts. Computer Science, 2017, 44(9): 83-87.) [20] YAO Y Y. Interval-Set Algebra for Qualitative Knowledge Representation // Proc of the 5th International Conference on Computing and Information. Washington, USA: IEEE, 1993: 370-374. [21] 马建敏,姚红娟,景 嫄.区间集概念格 // 徐伟华,李金海,魏 玲,等,编.形式概念分析理论与应用.北京:科学出版社, 2016: 69-88. (MA J M, YAO H J, JING Y. Interval-Set Concept Lattice // XU W H, LI J H, WEI L, et al., eds. Formal Concept Lattice: Theory and Application. Beijing, China: Science Press, 2016: 69-88.) [22] 朱治春,魏 玲.基于类背景的双向规则的获取.西北大学学报(自然科学版), 2015, 45(4): 517-524. (ZHU Z C, WEI L. Two-Way Rules Acquisition Based on Class Contexts. Journal of Northwest University(Natural Science Edition), 2015, 45(4): 517-524.)
2018, Vol. 31 
