Probabilistic fuzzy argumentation frameworks with finite fuzzy statuses

Randomness and fuzziness of argumentation have attracted the interest of many researchers. However, though each of these two properties is discussed in the past, seldom literature considers both of them. The purpose of this paper aims to explore semantics of the argumentation frameworks with these two attributes at the same time. Firstly, we introduce probabilistic-fuzzy matrices to describe the arguments with randomness and fuzziness, and dene the mathematical form of the probabilistic-fuzzy argumentation frameworks. In these frameworks, an argument has nite fuzzy states and each fuzzy state has a probability. This provides a mathematical foundation for the follow-up work. Then, we introduce a method of modifying the probabilities of the fuzzy states, which proposes a feasible way to revise the probabilities. Formally, it is the revision of the probabilistic-fuzzy matrices of arguments. Finally, based on this process, we set up an extension semantics system for probabilistic-fuzzy frameworks. The semantics enriches the theory of argumentation, and propose a way to check the probabilities.