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Conference Papers Year : 2015

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

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.
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Dates and versions

hal-03662609 , version 1 (09-05-2022)

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Didier Dubois, Agnès Rico, Bruno Teheux, Henri Prade. Characterizing variants of qualitative Sugeno integrals in a totally ordered Heyting algebra. 16th International Fuzzy Systems Association World Congress and th Conference of the European Society for Fuzzy Logic and Technology (IFSA - EUSFLAT 2015), Jun 2015, Gijon, Spain. pp.865-872, ⟨10.2991/ifsa-eusflat-15.2015.122⟩. ⟨hal-03662609⟩
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