Fuzzy Signals Fed to Gaussian Channels

We add fuzziness to the signals sent through a continuous Gaussian transmission channel: fuzzy signals are modeled by means of triangular fuzzy numbers. Our approach is mixed, fuzzy/stochastic: below we do not call into question the probabilistic nature of the channel, and fuzziness will concern only the channel inputs. We argue that fuzziness is an adequate choice when one cannot control crisply each signal fed to the channel. Using the fuzzy arithmetic of interactive fuzzy numbers, we explore the impact that a fuzziness constraint has on channel capacity; in our model we are ready to tolerate a given fuzziness error F. We take the chance to put forward a remarkable case of “irrelevance” in fuzzy arithmetic.