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

Adding feasibility constraints to a ranking rule under a monotonicity constraint

Authors
Raúl Pérez-Fernández, Michael Rademaker, Pedro Alonso, Irene Díaz, Bernard De Baets
Corresponding Author
Raúl Pérez-Fernández
Available Online June 2015.
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.184How to use a DOI?
Keywords
Group Decision Making, Linear Order, Weak Order, Monotonicity, Stochastic Dominance, Integer Linear Programming.
Abstract

We propose a new point of view in the long-standing problem where several voters have expressed a linear order relation (or ranking) over a set of candidates. For a ranking a > b > c to represent a group’s opinion, it would be logical that the strength with which a > c is supported should not be less than the strength with which either a > b or b > c is supported. This intuitive property can be considered a monotonicity constraint, and has been addressed before. We extend previous approaches in the following way: as the voters are expressing linear orders, we can take the number of candidates between two candidates to be a measure of the degree to which one candidate is preferred to the other. In this way, intensity of support is both counted as the number of voters who indicate a > c is true, as well as the distance between a and c in these voters’ rankings. The resulting distributions serve as input for a natural ranking rule that is based on stochastic monotonicity and stochastic dominance. Adapting the previous methodology turns out to be non-trivial once we add some natural feasibility constraints.

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-15.2015.184How 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  - Raúl Pérez-Fernández
AU  - Michael Rademaker
AU  - Pedro Alonso
AU  - Irene Díaz
AU  - Bernard De Baets
PY  - 2015/06
DA  - 2015/06
TI  - Adding feasibility constraints to a ranking rule under a monotonicity constraint
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  - 1302
EP  - 1309
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.184
DO  - https://doi.org/10.2991/ifsa-eusflat-15.2015.184
ID  - Pérez-Fernández2015/06
ER  -