Consensus-based clustering under hesitant qualitative assessments

Fuzzy Optim Decis Making

2016

Self Cite

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.

Section: Consensus Measuresmentioning

confidence: 99%

A consensus reaching process in the context of non-uniform ordered qualitative scales

Fuzzy Optim Decis Making

2016

Self Cite

“…As shown in Subsection 2.3, for g = 3, answering a single question is sufficient to assign the corresponding metrizable OPM; for g = 4, the number of questions should be between 2 and 4 (see As further research, the present analyses could be extended to the framework of intervals of linguistic terms, when agents are allowed to assign several consecutive terms of the OQS, if they hesitate (see García-Lapresta and Pérez-Román [12] and García-Lapresta and González del Pozo [10]). …”

Section: Discussionmentioning

confidence: 99%

Metrizable ordinal proximity measures and their aggregation

Pozo

2018

Information Sciences

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Ordered qualitative scales formed by linguistic terms are frequently used for evaluating sets of alternatives in different decision-making problems. These scales are usually implicitly considered as uniform in the sense that the psychological proximity between consecutive terms is perceived as identical. However, sometimes agents can perceive different proximities between the linguistic terms of the scale, and an appropriate method is required for aggregating these perceptions. In this paper we introduce the notion of metrizable ordinal proximity measure, discuss some aggregation procedures and propose a method based on metrics for aggregating experts' opinions on proximities between linguistic terms on ordered qualitative scales.

“…The agglomerative hierarchical clustering procedure we propose has some similarities to the ones provided by García-Lapresta and Pérez-Román [16,17], in different settings. Given an aggregation function F = F (k) k∈N and a profile V = (v a i ), our proposal consists of a sequential process addressed by the following stages:…”

Section: Clusteringmentioning

confidence: 99%

Consensus-Based Agglomerative Hierarchical Clustering

Fuzzy Sets, Rough Sets, Multisets and Clustering

2017

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In this contribution, we consider that a set of agents assess a set of alternatives through numbers in the unit interval. In this setting, we introduce a measure that assigns a degree of consensus to each subset of agents with respect to every subset of alternatives. This consensus measure is defined as 1 minus the outcome generated by a symmetric aggregation function to the distances between the corresponding individual assessments. We establish some properties of the consensus measure, some of them depending on the used aggregation function. We also introduce an agglomerative hierarchical clustering procedure that is generated by similarity functions based on the previous consensus measures.