MIN and MAX Operators for Fuzzy Intervals and their Potential Use in Aggregation Operators

Reda Boukezzoula (1) , Sylvie Galichet (1) , Laurent Foulloy (1)

1 LISTIC - Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance

This paper aims at expressing MIN and MAX operations when triangular fuzzy intervals are taken as inputs, that is when Zadeh's extension principle is considered. First presented approach consists in representing fuzzy intervals by means of their profiles. In this context, a computation algorithm can be easily derived for implementing the MIN and MAX operations. Another methodology based on interval relations is then proposed for determining a general analytical expression of the MIN and MAX operations. The potential use of these expressions in the framework of uncertain aggregation operators is illustrated with the two-additive Choquet integral.

Reda Boukezzoula, Sylvie Galichet, Laurent Foulloy. MIN and MAX Operators for Fuzzy Intervals and their Potential Use in Aggregation Operators. IEEE Transactions on Fuzzy Systems, 2007, 15 (6), pp.1135-1144. ⟨10.1109/TFUZZ.2006.890685⟩. ⟨hal-00412992⟩