Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology

Characterizing variants of qualitative Sugeno integrals in a totally ordered Heyting algebra

Authors
Didier Dubois, Agnès Rico, Bruno Teheux, Henri Prade
Corresponding Author
Didier Dubois
Available Online June 2015.
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.122How to use a DOI?
Keywords
Sugeno integral, residuated implications, multifactorial evaluation.
Abstract

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.

Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
Series
Advances in Intelligent Systems Research
Publication Date
June 2015
ISBN
978-94-62520-77-6
ISSN
1951-6851
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.122How to use a DOI?
Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Didier Dubois
AU  - Agnès Rico
AU  - Bruno Teheux
AU  - Henri Prade
PY  - 2015/06
DA  - 2015/06
TI  - Characterizing variants of qualitative Sugeno integrals in a totally ordered Heyting algebra
BT  - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 865
EP  - 872
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.122
DO  - https://doi.org/10.2991/ifsa-eusflat-15.2015.122
ID  - Dubois2015/06
ER  -