智能系统学报2025，Vol.20Issue(2)：305-315,11.DOI:10.11992/tis.202309028
从随机集落影到随机点落影——隶属函数用于机器学习
From random set falling shadows to a random point falling shadow:membership functions for machine learning
摘要
Abstract
Obtaining membership functions from sample distributions is essential and challenging.Wang Peizhuang's random set falling shadow theory uses set-valued statistics to derive membership functions,bridging the gap between statistics and fuzzy logic.However,traditional samples do not include set values,limiting the practical applicability of this theory.Lu Chenguang addressed this issue by using a semantic information method to derive two formulas for op-timizing membership functions based on sample distributions.This method,known as the random point falling shadow method,is compatible with set-valued statistics.The resulting membership functions have applications in multilabel classification,maximum mutual information classification,mixed models,and Bayesian confirmation.Furthermore,the similarity function and estimated mutual information in modern deep learning techniques are special cases of the mem-bership function and semantic mutual information.The maximum semantic information criterion is compatible with the maximum likelihood criterion,and the regularized least square error criterion,and the membership function is more transferable and easier to construct than likelihood functions or inverse probability functions.Thus,the membership function and the semantic information method hold considerable potential for widespread use in machine learning.关键词
模糊集合/隶属函数/样本分布/语义信息测度/机器学习/多标签分类/最大互信息分类/混合模型/贝叶斯确证Key words
fuzzy set/membership function/sampling distribution/semantic information measure/machine learning/multilabel classification/maximum mutual information classification/mixed model/Bayesian confirmation分类
信息技术与安全科学引用本文复制引用
汪培庄,鲁晨光..从随机集落影到随机点落影——隶属函数用于机器学习[J].智能系统学报,2025,20(2):305-315,11.基金项目
国家自然科学基金重大项目(9688007-1). （9688007-1）
