Characterizing variants of qualitative Sugeno integrals in a totally ordered Heyting algebra
English
Dubois, Didier[Université Paul Sabatier - Toulouse > IRIT]
Rico, Agnès[Université Claude Bernard - Lyon 1 - UCLB > ERIC]
Prade, Henri[Université Paul Sabatier - Toulouse > IRIT]
Teheux, Bruno[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Jul-2015
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
Alonso, José M.
Bustince, Humberto
Reformat, Marek
Atlantic Press
865-875
Yes
No
International
978-94-62520-77-6
IFSA-EUSFLAT 2015
from June 30 2015 to July 3 2015
[en] Sugeno integrals ; Aggregation functions
[en] Sugeno integral is one of the basic aggregation operations on a qualitative scale where only minimum and maximum, as well as order-reversing maps are allowed. Recently some variants of this aggregation operation, named soft and drastic integrals, have been introduced in a previous work by three of the authors. In these operations, importance weights play the role of tolerance thresholds enabling full satisfaction if ratings pass them. These new aggregation operations use residuated implications, hence need a slightly richer structure, and are part of larger family of qualitative aggregations. Based on some properties laid bare in a previous work, this paper proposes characterisation theorems for four variants of Sugeno integrals. These results pave the way to decision-theoretic axiomatizations of these
natural qualitative aggregations.
[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
