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The precise consistency consensus matrix in a local AHP-group decision making context

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Abstract

A new decisional tool, the consensus consistency matrix (CCM) has recently been proposed for dealing with AHP-group decision making (AHP-GDM) in a local context (a single criterion). Each entry of this matrix, based on the property of consistency, corresponds to the range of values or interval in which all the decision makers are simultaneously consistent in their initial matrices. The main limitation of the CCM is that, on many occasions, it is not possible to obtain a matrix with the minimum \(n-1\) judgments that are required to derive the priorities. In this local AHP context, using the row geometric mean as the prioritisation procedure, this paper presents an extension of the CCM, the precise consensus consistency matrix (PCCM), which significantly mitigates this problem. By identifying precise values in the common consistency intervals, the PCCM automatically allows the number of entries in the CCM to be increased. The PCCM provides more informed and participative GDM and offers more accurate estimations for the group’s priorities. It can also be used as a starting point for posterior negotiation processes between the actors and it can be employed in global AHP-GDM contexts (hierarchies). The new decisional tool has been applied to a real-life experience concerned with the analysis of the integral viability of public investment projects, more specifically, the economic valuation of social aspects.

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Notes

  1. Redundancy in judgments provides more accurate estimations (Saaty 1980).

  2. Defined as the difference between the inconsistency threshold allowed in the problem and the current inconsistency of the pairwise comparison matrix.

  3. If there is no likelihood of confusion, in order to simplify the notation, this interval will be denoted as:\([\underline{a}_{rs} ,\overline{a} _{rs} ]\).

  4. At least the (\(n-1\)) judgments connecting all the nodes are necessary.

  5. PSOE: Partido Socialista Obrero Español; PP: Partido Popular; PAR: Partido Aragonés.

  6. In this first iteration of the algorithm, the maximum variation allowed for the CGI of each of the decision-makers (\(\Delta ^\mathrm{(k)} = \mathrm{{GCI*}}- \mathrm{{GCI}}^\mathrm{(k)})\) is: \(\Delta ^{(1)}\) = 0.227, \(\Delta ^{(2)}\) = 0.067 and \(\Delta ^{(3)}\) = 0.072, respectively .

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Acknowledgments

This paper has been partially funded by the research project “Social Cognocracy Network” (Ref. ECO2011-24181), supported by the Spanish Ministry of Science and Innovation.

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Authors and Affiliations

  1. Grupo Decisión Multicriterio Zaragoza, Facultad de Economía y Empresa, Universidad de Zaragoza, Gran Vía 2, 50005 , Zaragoza, Spain

    Juan Aguarón, María Teresa Escobar & José María Moreno-Jiménez

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  1. Juan Aguarón
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  2. María Teresa Escobar
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  3. José María Moreno-Jiménez
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Correspondence to José María Moreno-Jiménez.

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Aguarón, J., Escobar, M.T. & Moreno-Jiménez, J.M. The precise consistency consensus matrix in a local AHP-group decision making context. Ann Oper Res 245, 245–259 (2016). https://doi.org/10.1007/s10479-014-1576-8

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