Fuzzy Communication Reaching Consensus through Robust Messages

We present a fuzzy communication model in multi-agent system. In the model agents have the fuzzy structure induced from an equivalence relation associated with the multi-modal logic S5_n, and he/she obtains the membership value of an event under his/her private information, so each agent considers the event as a fuzzy set. He/she sends not exact information on the membership value but fuzzy information on it. We show that consensus on the fuzzy event among all agents can still be guaranteed in the fuzzy communication according to any a cyclic communication graph; i.e., all the membership values are equal after long running communication. As a consequence we can show that all agents can reach consensus on a sentence phi S5_n through the fuzzy communication.