Computational Complexity and Feasibility of Fuzzy

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. In many real-life situations, we cannot directly measure or estimate the desired quantity r. For example, we cannot directly measure the distance to a star or the amount of oil in a well. 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. In many real-life applications, we have to deal with quantities r i whose values we do not know precisely, and instead, we only have expert (fuzzy) knowledge about these values. This knowledge is usually described in terms of membership functions i (x) that assign to every real number x the expert's degree of belief i (x) 2 0; 1] that the actual (unknown) value of the quantity r i is equal to x. We want to use the expert (fuzzy) knowledge about the values r 1 ; : : :; r n of some quantities to predict the value of some quantity r that is related to r i. In this paper, we will consider the simplest case when \re-lated" means that we know the exact form of the dependency r = f(r 1 ; : : :; r n) between r i and r, and the only uncertainty in r is caused by the uncertainty in the values of r i. In such situations, we must transform …