Monotonicity-based ranking on the basis of multiple partially specified reciprocal relations

The aggregation of rankings is a recurrent task in several fields of application. In a recent work by Rademaker and De Baets, a ranking rule based on a natural monotonicity property was proposed in the context of social choice theory. This rule is built on the premise that, for a ranking a≻b≻c to re...

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Bibliographic Details
Published in:Fuzzy sets and systems 2017-10, Vol.325, p.69-96
Main Authors: Pérez-Fernández, Raúl, Rademaker, Michael, Alonso, Pedro, Díaz, Irene, Montes, Susana, De Baets, Bernard
Format: Article
Language:English
Subjects:
Group decision making
Monometric
Monotonicity
Ranking rule
Reciprocal relation
Social choice
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Summary:The aggregation of rankings is a recurrent task in several fields of application. In a recent work by Rademaker and De Baets, a ranking rule based on a natural monotonicity property was proposed in the context of social choice theory. This rule is built on the premise that, for a ranking a≻b≻c to represent a group's opinion, it would be natural that the strength with which a≻c is supported should not be less than both the strength with which a≻b and the strength with which b≻c are supported. A first approach to this ranking rule considering totally specified monotone reciprocal relations on a bipolar qualitative scale has already been taken. In this paper, a more general setting is considered: each voter is allowed to provide a partially specified reciprocal relation (that may not be monotone) on the unit interval. Additionally, new ways of measuring the cost of imposing monotonicity are introduced.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2016.12.008