How to make sure that "/spl ap/100"+1 is /spl ap/100 in fuzzy arithmetic: solution and its (inevitable) drawbacks

Abstract

From the common-sense viewpoint, if a person who weighs around 100 kilograms gains one more kilogram, his weight is still around 100 kilograms. Alas, not so in traditional fuzzy arithmetic. In this paper, we propose a modification of fuzzy arithmetic which does have this property. We gain the desired property, but there is no free lunch - we have to lose two important properties of the traditional fuzzy arithmetic: first, addition is no longer always associative; second, addition is no longer always easily computable.