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Axioms 2018, 7(2), 35; https://doi.org/10.3390/axioms7020035

Quantiles in Abstract Convex Structures

Department of Economics, Ca’Foscari University of Venice, Sestiere Cannaregio 873, 30123 Venezia, Italy
Received: 14 May 2018 / Revised: 23 May 2018 / Accepted: 25 May 2018 / Published: 28 May 2018
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
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Abstract

In this short paper, we aim at a qualitative framework for modeling multivariate decision problems where each alternative is characterized by a set of properties. To this extent, we consider convex spaces as underlying universes and make use of lattice operations in convex spaces to formalize the notion of quantiles. We also put in evidence that many important models of decision problems can be viewed as convex spaces-based models. Several properties of aggregation operators are translated into this general setting, and independence and invariance are used to provide axiomatic characterizations of quantiles. View Full-Text
Keywords: convex space; aggregation operator; invariance; independence; quantile convex space; aggregation operator; invariance; independence; quantile
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Cardin, M. Quantiles in Abstract Convex Structures. Axioms 2018, 7, 35.

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