多重多维模糊推理算法的连续性和逼近性

On Continuity Properties and Approximation Properties of Algorithms for Multiple & Multi-dimensional Fuzzy Reasoning

针对多重、多维模糊推理情形,细致地研究了几类模糊推理算法是否满足连续性和逼近性,并进一步讨论了这几类算法对逼近误差的传播性能。把模糊推理算法看成是一个模糊集合到另一个模糊集合的映射,选用海明距离作为两模糊集的距离度量方法,证明了在模糊假言推理和模糊拒取式推理情形,几类多重多维模糊算法都拥有连续性。当多重多维模糊算法满足还原性时就具有逼近性;该模糊算法都不会放大逼近误差。结果对构建模糊控制系统和模糊专家系统时选用和分析模糊推理算法有一定的指导作用。

For the first time, the authors research carefully on kinds of inference algorithms, which are algorithms for multiple fuzzy reasoning and multi-dimensional fuzzy reasoning , hold the continuity properties and approximation properties, moreover, investigate also how the approximation errors are propagated by classes of inference algorithms. Therefore, a fuzzy inference algorithm is viewed as a mapping from fuzzy set to fuzzy set. Hamming distance formula is used as computing distance between two fuzzy sets. The authors prove that classes of algorithms hold continuity properties in the case of fuzzy modus ponens and fuzzy modus tollens. The authors point out al- gorithms hold approximation hold approximation property only if the algorithms hold consistency property; The classes of algorithms do not make approximation errors magnified when they hold approximation property. The research results of the paper are useful for selection and analysis of algorithms for fuzzy inference while practical fuzzy control systems and fuzzy expert systems are designed.