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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。
In the case of multiple and multidimensional fuzzy reasoning, it is studied carefully whether several types of fuzzy inference algorithms satisfy continuity and approximation, and further discuss the propagation performance of these types of algorithms for approximation error. The fuzzy reasoning algorithm is regarded as a mapping from one fuzzy set to another fuzzy set, and the distance measurement method using Hamming distance as two fuzzy sets is proved. In fuzzy hypothetical reasoning and fuzzy rejecting reasoning cases, several kinds of multidimensional multidimensional Fuzzy algorithms have continuity. When multidimensional fuzzy algorithm satisfies the reducibility, it has approximation; the fuzzy algorithm will not enlarge the approximation error. The result can guide and select fuzzy inference algorithm when constructing fuzzy control system and fuzzy expert system.