Canonical form of ordered weighted averaging operators

Discrete Ordered Weighted Averaging (OWA) operators as one of the most representative proposals of Yager (1988) have been widely used and studied in both theoretical and application areas. However, there are no effective and systematic corresponding methods for continuous input functions. In this st...

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Bibliographic Details
Published in:Annals of operations research 2020-12, Vol.295 (2), p.605-631
Main Authors: Jin, LeSheng, Mesiar, Radko, Kalina, Martin, Yager, Ronald R.
Format: Article
Language:English
Subjects:
Algebra
Business and Management
Canonical forms
Combinatorics
Continuity (mathematics)
Integrals
Mathematical research
Operations research
Operations Research/Decision Theory
Operators (mathematics)
Original Research
Permutations
Theory of Computation
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Summary:Discrete Ordered Weighted Averaging (OWA) operators as one of the most representative proposals of Yager (1988) have been widely used and studied in both theoretical and application areas. However, there are no effective and systematic corresponding methods for continuous input functions. In this study, using the language of measure (capacity) space we propose a Canonical Form of OWA operators which yield some common properties like Monotonicity and Idempotency and thus serve as a generalization of Discrete OWA operators. We provide also a representation of the Canonical Form by means of asymmetric Choquet integrals. The Canonical Form of OWA operators can effectively handle some input functions defined on ordered sets.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-020-03802-6