This paper managed to induce probability theory (sigma system) and possibility theory (max system) respectively from the clearly-defined randomness and fuzziness, while focusing the question why the key axiom of "maxitivity" is adopted for possibility measure. Such an objective is achieved by following three steps: a) the establishment of mathematical definitions of randomness and fuzziness; b) the development of intuitive definition of possibility as measure of fuzziness based on compatibility interpretation; c) the abstraction of the axiomatic definitions of probability/ possibility from their intuitive definitions, by taking advantage of properties of the well-defined randomness and fuzziness. We derived the conclusion that "max" is the only but un-strict disjunctive operator that is applicable across the fuzzy event space, and is an exact operator for extracting the value from the fuzzy sample space that leads to the largest possibility of one. Then a demonstration example of stock price prediction is presented, which confirms that max inference indeed exhibits distinctive performance, with an improvement up to 18.99%, over sigma inference for the investigated application. Our work provides a physical foundation for the axiomatic definition of possibility for the measure of fuzziness, which hopefully would facilitate wider adoption of possibility theory in practice.

翻译：本文致力于从明确定义的随机性与模糊性分别导出概率论（sigma系统）与可能性理论（max系统），并重点探讨可能性测度为何采用“最大性”这一关键公理。该目标通过以下三个步骤实现：a) 建立随机性与模糊性的数学定义；b) 基于相容性解释发展可能性的直观定义，将其作为模糊性的测度；c) 利用明确定义的随机性与模糊性之性质，从直观定义中抽象出概率/可能性的公理化定义。我们得出结论：“max”是唯一适用于整个模糊事件空间的非严格析取算子，且是从模糊样本空间中提取导致可能性最大值的精确算子。随后，本文以股价预测为例进行演示，结果表明在所研究的应用中，max推理相较于sigma推理确实表现出显著优势，性能提升高达18.99%。本研究为模糊性测度的可能性公理化定义提供了物理基础，有望推动可能性理论在实践中的更广泛应用。