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中文摘要：
引入了MR0代数的概念，讨论了它的一些重要性质，给出了MR0代数的同构定理。其次，构建了模态系统K1，证明了在MR0代数语义下该系统是完备的。最后，通过将Kripke模型中的赋值V模糊化，建立了模态逻辑系统恐，并证明了系统＆是可靠的；通过将Kripke模型中的二元关系R模糊化，建立了模态逻辑系统恐，并证明了系统K是完备的。
英文摘要：
The concept of MR0 algebra was introduced, and some major properties were discussed. Then the isomorphism theorems of MR0 algebra were given. Additionally, the modal logic system Kl was formed, which can be proved to be a complete system under MR0 semantics. Finally, the modal logic system K2 that proved to be soundness was formed through fuzzifying of the evaluation V in the Kripke model, and the modal logic system K3 was formed and proved to be complete through the fuzzifying of the binary relationship R in the Kripke model.
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