*Article* **AHP-Group Decision Making Based on Consistency**

### **Juan Aguarón, María Teresa Escobar, José María Moreno-Jiménez \* and Alberto Turón**

Grupo Decisión Multicriterio Zaragoza (GDMZ), Facultad de Economía y Empresa, Universidad de Zaragoza, Gran Vía 2, 50005 Zaragoza, Spain; aguaron@unizar.es (J.A.); mescobar@unizar.es (M.T.E.); turon@unizar.es (A.T.)

**\*** Correspondence: moreno@unizar.es

Received: 7 February 2019; Accepted: 25 February 2019; Published: 7 March 2019

**Abstract:** The Precise consistency consensus matrix (PCCM) is a consensus matrix for AHP-group decision making in which the value of each entry belongs, simultaneously, to all the individual consistency stability intervals. This new consensus matrix has shown significantly better behaviour with regards to consistency than other group consensus matrices, but it is slightly worse in terms of compatibility, understood as the discrepancy between the individual positions and the collective position that synthesises them. This paper includes an iterative algorithm for improving the compatibility of the PCCM. The sequence followed to modify the judgments of the PCCM is given by the entries that most contribute to the overall compatibility of the group. The procedure is illustrated by means of its application to a real-life situation (a local context) with three decision makers and four alternatives. The paper also offers, for the first time in the scientific literature, a detailed explanation of the process followed to solve the optimisation problem proposed for the consideration of different weights for the decision makers in the calculation of the PCCM.

**Keywords:** Analytic Hierarchy Process (AHP); group decision making; consistency; compatibility
