The addition of fuzzy quantities is undeniably the most important oper
ation in fuzzy arithmetic. In this paper, we consider the general case
of the addition of fuzzy intervals based on a continuous triangular n
orm. We start our discussion with an extensive literature review in wh
ich we recall explicit formulae for the addition based on the stronges
t and the weakest triangular norm, for the addition based on the algeb
raic product, and several recent results for the addition based on a c
ontinuous Archimedean triangular norm, including specific theorems for
strict and nilpotent triangular norms. Subsequently, the addition bas
ed on an ordinal sum is studied, and it is shown how this addition can
be transformed into a series of additions based on the summands of th
is ordinal sum. This important observation implies that the addition b
ased on an arbitrary continuous triangular norm can be practically per
formed, provided the summands of the corresponding ordinal sum represe
ntation and the fuzzy intervals involved fulfil the appropriate condit
ions mentioned in the overview. This is illustrated by means of severa
l examples. (C) 1997 Elsevier Science B.V.