知识嵌入的贝叶斯MA型模糊系统

模糊系统的独特优势在于其高度的可解释性,然而传统的基于聚类的模糊系统往往需要使用输入空间的全部特征且常出现模糊集交叉的现象,系统的可解释性不高;此外,此类模糊系统对高维数据处理时还会因使用大量的特征而使规则过于复杂.针对此问题,探讨了一种知识嵌入的贝叶斯MA型模糊系统(knowledge embedded Bayesian Mamdan-Assilan type fuzzy system, KE-B-MA).首先,KE-B-MA使用DC(dont care)方法进行知识嵌入的模糊集划分,对模糊隶属度函数中心和输入空间特征的选择进行有效指导,其获得的规则可对应于不同的特征空间.其次,KE-B-MA基于贝叶斯推理使用马尔可夫蒙特卡洛(Markov chain Monte Carlo, MCMC)方法对模糊规则的前后件参数同时学习,所得结果为全局最优解.实验结果表明:与一些经典模糊系统相比,KE-B-MA具有令人满意的分类性能且具有更强的可解释性和清晰性.

Knowledge Embedded Bayesian MA Fuzzy System

The most distinctive characteristic of fuzzy system is its high interpretability. But the fuzzy rules obtained by classical cluster based fuzzy systems commonly need to cover all features of input space and often overlap each other. Specially, when facing the high-dimension problem, the fuzzy rules often become more sophisticated because of too much features involved in antecedent parameters. In order to overcome these shortcomings, based on the Bayesian inference framework, knowledge embedded Bayesian Mamdan-Assilan type fuzzy system (KE-B-MA) is proposed by focusing on the Mamdan-Assilan (MA) type fuzzy system. First, the DC (dont care) approach is incorporated into the selection of fuzzy membership centers and features of input space. Second, in order to enhance the classification performance of obtained fuzzy systems, KE-B-MA learns both antecedent and consequent parameter of fuzzy rules simultaneously by a Markov chain Monte Carlo (MCMC) method, and the obtained parameters can be guaranteed to be global optimal solutions. The experimental results on a synthetic dataset and several UCI machine datasets show that the classification accuracy of KE-B-MA is comparable to several classical fuzzy systems with distinctive ability of providing explicit knowledge in the form of interpretable fuzzy rules. Rather than being rivals, fuzziness in KE-B-MA and probability can be well incorporated.