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.
Open Access
This is an open access article distributed under the CC BY-NC license.

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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  -