基于模糊格的超盒粒计算分类器*

摘要

Representation, relation and operation of granules are the main research content of granular computing. A hyperbox granule is represented by a vector including a beginning point and an end point. The inconsistency between the partial ordering relation in vector space and the partial ordering relation in hyperbox granule space is analyzed and then eliminated by the order-preserving function. The fuzzy inclusion relation between two hyperbox granules is formed by nonlinear positive valuation function and the order-preserving function between the lattice and its dual lattice. The join operator and decomposition operator between two granules are designed to achieve the granules with different granularity. The algebraic system which is composed of hyperbox granule set, fuzzy inclusion relation and the operators between two granules is proved as fuzzy lattice. Hyperbox granular computing classifiers are formed based on fuzzy lattice, and verified by classification problems on machine learning dataset. The experimental results show that hyperbox granular computing classifiers have a generalization ability comparable to that of fuzzy lattice reasoning classifiers with less number of hyperbox granules.%粒的表示、粒之间的关系和运算是粒计算的主要研究内容。利用向量表示超盒粒，分析向量之间的偏序关系和超盒粒之间的偏序关系的不一致性，并引入保序函数消除该不一致性。利用格和其对偶格之间的非线性正评价函数和保序函数构造超盒粒之间模糊包含关系。为得到不同粒度的粒，设计超盒粒之间的合并算子和分解算子，证明由超盒粒集、超盒粒之间的模糊包含关系、合并算子、分解算子构成的代数系统是模糊格，构造基于模糊格的超盒粒计算分类器。用机器学习数据集中的分类问题，验证该分类器具有和模糊格推理分类器相同的推广能力并减少超盒粒的数量。