In this paper, we consider that a group of agents judge a set of alternatives by means of an ordered qualitative scale. The scale is not assumed to be uniform, i.e., the psychological distance between adjacent linguistic terms is not necessarily always the same. In this setting, we propose how to measure the consensus in each subset of at least two agents over each subset of alternatives. We introduce a consensus reaching process where some agents may be invited to change their assessments over some alternatives in order to increase the consensus. All the steps are managed in a purely ordinal way through ordinal proximity measures.
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For instance, Malkevitch (1990) provides an “evil example” where six well-known voting systems generate different outcomes from the same profile of individual preferences.
We have to note that the International Association of Oenologists assigns numbers to these linguistic terms and does manage the assessments in a numerical way.
In Majority Judgment the inputs are arranged in an increasing fashion.
In order to avoid loss of information, we will take into account the two medians in the even case.
This linear order is equivalent to the one provided by Delgado et al. (1998) in the set of trapezoidal fuzzy numbers when it is applied to intervals of real numbers.
For instance, the one introduced by García-Lapresta and Pérez-Román (2015b) in the same setting.
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The authors are grateful to Tomasa Calvo and two anonymous referees for their comments and suggestions. The financial support of the Spanish Ministerio de Economía y Competitividad (project ECO2012-32178) and Consejería de Educación de la Junta de Castilla y León (project VA066U13) are acknowledged.
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García-Lapresta, J.L., Pérez-Román, D. A consensus reaching process in the context of non-uniform ordered qualitative scales. Fuzzy Optim Decis Making 16, 449–461 (2017). https://doi.org/10.1007/s10700-016-9256-6
- Group decision making
- Qualitative scales
- Ordinal proximity measures