The notion of the fuzzy assertion based on propositional modal logic is introduced and the properties of the fuzzy reasoning based on fuzzy assertions are studied. As an extending of the traditional semantics of modal logics, the fuzzy Kripke semantics is considered and a formal fuzzy reasoning system based on fuzzy constraint is established. In order to decide whether a fuzzy assertion is a logical consequence of a set of fuzzy assertions, the notion of the educed set based on fuzzy constraint is introduced and the relation between the fuzzy reasoning and the satisfiability of the educed set is revealed.
['Zaiyue Zhang', 'Yuefei Sui', 'Cungen Cao']
Further study of the fuzzy reasoning based on propositional modal logic