Consensus measures constructed from aggregation functions and fuzzy implications

Recently accepted article in Knowledge Based Systems for a special issue on Consensus (edited by Enrique Herrera-Viedma). This extends more formally the measure presented at IFSA.  We look at the properties of a measure that should model the concept of consensus for a set of real inputs.  Although this work was mainly motivated by a connection between the form of the Bonferroni mean and the double-fuzzy integrals, I can also see some similarities between properties desired to model Consensus and those to model Evenness in ecology.

Title: Consensus measures constructed from aggregation functions and fuzzy implications

Authors: G. Beliakov, T. Calvo and S. James

Abstract

We focus on the problem of constructing functions that are able to measure the degree of consensus for a set of inputs provided over the unit interval.  When making evaluations based on inputs from multiple criteria, sources or experts, the resulting output can be seen as the value which best represents the individual contributions.   However it may also be desirable to know the extent to which the inputs agree.  Does the representative value reflect a universal opinion?  Or has there been a high degree of tradeoff?  We consider the properties relating to such consensus measures and propose two general models built component-wise from aggregation functions and fuzzy implications.

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