We propose two new doxastic extensions of fuzzy \L ukasiewicz logic in which their semantics are Kripke-based with both fuzzy atomic propositions and fuzzy accessibility relations. A class of these extensions is equipped with uninformed belief operator, and the other class is based on a new notion of skeptical belief. We model a fuzzy version of muddy children problem and a CPA-security experiment using uniformed belief and skeptical belief, respectively. Moreover, we prove soundness and completeness for both of these belief extensions.

翻译：我们提出两种新的模糊逻辑的16级延伸,其语义以Kripke为基础,既有模糊的原子主张,也有模糊的无障碍关系。 一类扩展配有不知情的信仰操作员,另一类则基于怀疑的新观念。 我们分别用统一的信仰和怀疑的信念来模拟泥沙儿童问题的模糊版本和CPA安全实验。 此外,我们证明这两种信仰的扩展是健全和完整的。