Computational Complexity and Feasibility of Fuzzy Data Processing: Why Fuzzy Numbers, Which Fuzzy Numbers, Which Operations with Fuzzy Numbers

In many real-life situations, we cannot directly measure or estimate the desired quantity r. In these situations, we measure or estimate other quantities r 1 ; : : : ; r n related to r, and then reconstruct r from the estimates for r i . This reconstruction is called data processing. Often, we only have fuzzy information about r i . In such cases, we have fuzzy data processing. Fuzzy data means that instead of a single number r i , we have several numbers that describes the fuzzy knowledge about the corresponding quantity. Since we need to process more numbers, the computation time for fuzzy data processing is often much larger than for the usual non-fuzzy one. It is, therefore, desirable to select representations and processing algorithms that minimize this increase and thus, make fuzzy data processing feasible. In this paper, we show that the necessity to minimize computation time explains why we use fuzzy numbers, and describes what operations we should use