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Constrained ordered weighted averaging aggregation with multiple comonotone constraints

journal contribution
posted on 2020-09-01, 00:00 authored by L Coroianu, R Fullér, Marek Gagolewski, Simon JamesSimon James
The constrained ordered weighted averaging (OWA) aggregation problem arises when we aim to maximize or minimize a convex combination of order statistics under linear inequality constraints that act on the variables with respect to their original sources. The standalone approach to optimizing the OWA under constraints is to consider all permutations of the inputs, which becomes quickly infeasible when there are more than a few variables, however in certain cases we can take advantage of the relationships amongst the constraints and the corresponding solution structures. For example, we can consider a land-use allocation satisfaction problem with an auxiliary aim of balancing land-types, whereby the response curves for each species are non-decreasing with respect to the land-types. This results in comonotone constraints, which allow us to drastically reduce the complexity of the problem. In this paper, we show that if we have an arbitrary number of constraints that are comonotone (i.e., they share the same ordering permutation of the coefficients), then the optimal solution occurs for decreasing components of the solution. After investigating the form of the solution in some special cases and providing theoretical results that shed light on the form of the solution, we detail practical approaches to solving and give real-world examples.

History

Journal

Fuzzy Sets and Systems

Volume

395

Pagination

21 - 39

Publisher

Elsevier

Location

Amsterdam, The Netherlands

ISSN

0165-0114

Language

eng

Publication classification

C1 Refereed article in a scholarly journal