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 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.