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

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 algorith...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems 2007-12, Vol.15 (6), p.1135-1144
Main Authors: Boukezzoula, R., Galichet, S., Foulloy, L.
Format: Article
Language:English
Subjects:
Agglomeration
Aggregation operators
Choquet integral
Decision making
Decision theory
Exact solutions
Fuzzy
fuzzy intervals
Fuzzy logic
Fuzzy set theory
Fuzzy sets
Intervals
Lattices
Mathematical analysis
MIN and MAX operators
Operators
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Summary: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.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2006.890685