粒和粗集研究及与证据理论相结合在不完备数据处理中的应用
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摘要
本文以相容关系的最大相容类为基础,建立了meet、ioin等多个粒的新扩展粗集模型,定义了新的上下近似集、精度等,探讨了它们之间的相互关系,设计了粒和近似集的求解算法。研究了改进变精度限制容差关系粗集模型及规则挖掘,提出了不完备信息系统下属性依赖及依赖度等概念,给出了依赖度的新计算公式。讨论了容差关系即相容关系与冲突关系、完全覆盖与一般覆盖之间的关系以及各自的性质,得到了判断一般覆盖为完全覆盖若干必要充分条件的定理,设计了3个无冲突集合划分算法,为求最优的集合划分提供了有价值的参考。提出了弱协调性和受限默认确定性决策规则等概念,探讨了利用区分矩阵和区分函数优化受限默认确定性决策规则的条件。丰富了决策规则形式的多样性。研究了容差关系下属性移动时近似集的更新公式,提出了默认确定性决策规则包括受限默认确定规则的增量学习方法。利用粒概念下的不同近似集按优势关系的分解,实现了文档查询扩充,增强了信息检索的灵活性。探讨了粒、粗集理论和D-S证据理论相结合在不完备数据融合系统中的目标识别方法,建立了多个mass函数、信任度和似然度以及规则合成公式,为确定置信区间提供了选择自由度。分析了本文所设计算法的时间复杂度。通过实例,验证了诸研究的有效性和可行性。
Based on maximal compatible classes according to compatible relation,the present dissertation builds several new extended rough set models using granules such as meet and join granules and etc,defines new upper and lower approximations and precision measures, explores their interactions and designs algorithms for solving these granules and upper and lower approximations.It studies an improved variable limited tolerance rough set model and its rule mining,proposes concepts of attribute dependency and dependency degree in incomplete information system and gives out new calculate formula for the dependency degree.It discusses not only the relationships between tolerance relation and collision relation but also the relationships between complete covering and general covering and their properties,obtains some necessary and sufficient conditions for a general covering to become a complete covering,designs three algorithms for partitioning set without confliction.This provides a valuable reference for optimal set partition.It suggests the concepts of week consistence and limited default and definite decision rules and discusses conditions under which rules may be reduced to be optimal using discernibility matrix and discernibility functions.This enriches the diversity of decision rule formulations.It studies updating formulas while an attribute moves out and in under tolerance relation and proposes an incremental learning approach for decision rules including limited default and definite decision rules.Using decompositions of different upper and lower approximations in the sense of granule concepts put forward by us by dominance relation,it implements document query expansions and then enhances flexibilities in information retrieval.It investigates target identification approaches in incomplete data fusion systems by using a combination of granule,rough set and Dempster-Shafer evidence theory,establishing several mass assignment functions,belief functions,plausible functions and merging formulas.It supplies a free selection dimension for determining belief intervals.It analyses time complexity for algorithms designed in the thesis and verifies the validation and feasibility of each study here.
Based on maximal compatible classes according to compatible relation,the present dissertation builds several new extended rough set models using granules such as meet and join granules and etc,defines new upper and lower approximations and precision measures, explores their interactions and designs algorithms for solving these granules and upper and lower approximations.It studies an improved variable limited tolerance rough set model and its rule mining,proposes concepts of attribute dependency and dependency degree in incomplete information system and gives out new calculate formula for the dependency degree.It discusses not only the relationships between tolerance relation and collision relation but also the relationships between complete covering and general covering and their properties,obtains some necessary and sufficient conditions for a general covering to become a complete covering,designs three algorithms for partitioning set without confliction.This provides a valuable reference for optimal set partition.It suggests the concepts of week consistence and limited default and definite decision rules and discusses conditions under which rules may be reduced to be optimal using discernibility matrix and discernibility functions.This enriches the diversity of decision rule formulations.It studies updating formulas while an attribute moves out and in under tolerance relation and proposes an incremental learning approach for decision rules including limited default and definite decision rules.Using decompositions of different upper and lower approximations in the sense of granule concepts put forward by us by dominance relation,it implements document query expansions and then enhances flexibilities in information retrieval.It investigates target identification approaches in incomplete data fusion systems by using a combination of granule,rough set and Dempster-Shafer evidence theory,establishing several mass assignment functions,belief functions,plausible functions and merging formulas.It supplies a free selection dimension for determining belief intervals.It analyses time complexity for algorithms designed in the thesis and verifies the validation and feasibility of each study here.
引文
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