Calculation and Display Errors

Abstract

We present fuzzy events within an infinite or finite time space T containing moments t. Moments t are not different from real numbers so from the mathematical point of view T = R. Processing of item A(t) in general can be executed within continuous or discrete time. Processing means adaptation of values of some variable at all moments, of which, in continuous space T there are infinitely many. In fuzzy logic continuous calculation cannot be applied from a practical point of view, as it would last infinitely long. Computer processing or calculation of fuzzy item A(t) has to be done in the shortest possible time. In other spheres of work the situation is probably similar, with the difference that in fuzzy logic we have to deal with discreteness directly, while in other fields of work it is skilfully incorporated in calculation procedures and is in this way implicit for the user or observer. In spite of the wish to have the shortest possible calculation times, it is important not to miss the essence of the fuzzy algorithm to which calculation refers because of approximate results. In this Chapter we are firstly going to observe low-density fuzzy inference processing and its influence on the results. Low-density fuzzy processing can reduce processing time, and thus usually lead to higher performance of the fuzzy system.