A nearly strict fuzzy arithmetic for solving problems with uncertainties

Abstract

Fuzzy arithmetic is a powerful tool to solve engineering problems with uncertain parameters. In doing so, the uncertain parameters in the model equations are expressed by fuzzy numbers, and the problem is solved by using fuzzy arithmetic to carry out the mathematical operations in a generalized form. The practical use of standard fuzzy arithmetic, however turns out to be very problematic, basically because of the overestimation effect which is responsible for a more or less large discrepancy between the proper arithmetical solution of the problem and the calculated one. In this paper a new implementation of fuzzy arithmetic is presented by which those discrepancies in general can be reduced to a slight remainder and in many cases can even be totally avoided. The effectiveness of the method is illustrated by some typical examples.