建立《概率论自然公理系统》中的第组和第组公理。

Two groups of axioms in the natural axiom system of probability theory are set up.

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最后，对提出的自适应交叉概率和自适应变异概率利用遗传算法的公理化理论进行了收敛性的证明。

We proved the convergence of GA which we proposed adaptive fitness functions, adaptive crossover probability and adaptive mutation probability.

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作者提出一组有理数概率下效用函数存在的公理，并证明该公理体系下的效用表示定理。

This paper puts forward a set of axioms and proves the existence and uniqueness of utility function with rational probabilities on the set of axioms.

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