Abstract: How to implement FMP algorithm with the fuzzy implication operator family H(p,λ) is given on the basis of triple I method and [α]-triple I method. The fuzzy systems of triple I method and their response ability are studied which based on implication operator family H(p,λ). It is pointed that this fuzzy systems based on implication operator family H(p,λ) are not universal approximators, it’s with only step output ability. The probability theory significance of fuzzy systems based on the implication operator family H(p,λ) is revealed, the probability distribution is given, and it plays “system core” roles at fuzzy system.

Key words: fuzzy system, implication operator family H(p,λ), triple I algorithm, α-triple I method, conditional mathematical expectation, probability distribution

摘要： 针对蕴涵算子族H(p,λ)，给出了FMP问题三I支持算法和α-三I支持算法的计算公式；讨论了基于三I算法的模糊系统及其响应性能，结果表明，蕴涵算子族H(p,λ)的模糊系统只具有阶跃输出能力，不具有函数逼近泛性；揭示了蕴涵算子族H(p,λ)的模糊系统的概率意义，给出了其概率分布，它充当模糊系统的“系统内核”作用。

关键词: 模糊系统, 蕴涵算子族H(p, &lambda, ), 三I算法, &alpha, -三I支持算法, 条件数学期望, 概率分布