Interval comparison based on Dempster-Shafer theory of evidence

Abstract

The problem of crisp and fuzzy interval (number) comparison is of perennial interest, because of its direct relevance in practical modeling and optimization of real-world processes under uncertainty. There are many approaches to this problem presented in literature, but in all cases the authors propose the methods which give the result of interval comparison in form of real or Boolean number. On the other hand, it is easy to see that all arithmetic operations on intervals give us intervals. So, it seems quite natural to expect the result of interval comparison as interval as well. Indeed, when comparing intervals, we factually order the sets, and it should be preferable to get the result as the some type of set (interval). To do this, we propose the approach, which can derive us the results of comparison as the probability interval. For this purpose, we use the Dempster-Shafer theory of evidence with its probabilistic interpretation. © Springer-Verlag Berlin Heidelberg 2004.