Consistent clustering of entries in large pairwise comparison matrices

Benítez, Julio; Carpitella, Silvia; Certa, Antonella; Ilaya-Ayza, Amilkar E.; Izquierdo, Joaquín

doi:10.1016/j.cam.2018.04.041

Cited by 11 publications

(4 citation statements)

References 35 publications

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“…Therefore, [22] uses AHP to select information criteria that determine the optimal number of groups in a large data set. They also use cluster techniques within AHP [23] but, in this case, to reduce an excessively high number of alternatives. Other proposals closer to our problem are [24,25], but both are carried out within a deterministic context, so they are not directly comparable with our proposal.…”

Section: Multi-actor Decision Makingmentioning

confidence: 99%

Identification of Homogeneous Groups of Actors in a Local AHP-Multiactor Context with a High Number of Decision-Makers: A Bayesian Stochastic Search

et al. 2022

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The identification of homogeneous groups of actors in a local AHP-multiactor context based on their preferences is an open problem, particularly when the number of decision-makers is high. To solve this problem in the case of using stochastic AHP, this paper proposes a new Bayesian stochastic search methodology for large-scale problems (number of decision-makers greater than 20). The new methodology, based on Bayesian tools for model comparison and selection, takes advantage of the individual preference structures distributions obtained from stochastic AHP to allow the identification of homogeneous groups of actors with a maximum common incompatibility threshold. The methodology offers a heuristic approach with several near-optimal partitions, calculated by the Occam’s window, that capture the uncertainty that is inherent when considering intangible aspects (AHP). This uncertainty is also reflected in the graphs that show the similarities of the decision-maker’s opinions and that can be used to achieve representative collective positions by constructing agreement paths in negotiation processes. If a small number of actors is considered, the proposed algorithm (AHP Bayesian clustering) significantly reduces the computational time of group identification with respect to an exhaustive search method. The methodology is illustrated by a real case of citizen participation based on e-Cognocracy.

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Section: Multi-actor Decision Makingmentioning

confidence: 99%

Identification of Homogeneous Groups of Actors in a Local AHP-Multiactor Context with a High Number of Decision-Makers: A Bayesian Stochastic Search

et al. 2022

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“…Indeed, if judgments were not consistent, this would have a negative impact on the whole quality of final decision. In such a case, experts should be asked to formulate new judgments until the condition of consistency is met [43].…”

Section: Figure 2 Fuzzy Version Of the Saaty Scale [38]mentioning

confidence: 99%

“…In such a case, experts should be asked to formulate new judgments until the condition of consistency is met. 43…”

Section: The Fahp To Calculate Criteria Weightsmentioning

confidence: 99%

District metered area design through multicriteria and multiobjective optimization

Brentan

Carpitella

Izquierdo

et al. 2021

Math Methods in App Sciences

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The design of district metered areas (DMA) in potable water supply systems is of paramount importance for water utilities to properly manage their systems. Concomitant to their main objective, namely deliver quality water to consumers, the benefits include leakage reduction and prompt reaction in cases of natural or malicious contamination events. Given the structure of a water distribution network (WDN), graph theory is the basis for DMA design, and clustering algorithms can be applied to perform the partitioning. However, such sectorization entails a number of network modifications (installing cut-off valves and metering and control devices) involving costs and operation changes, which have to be carefully studied and optimized. Given the complexity of WDNs, optimization is usually performed using metaheuristic algorithms. In turn, optimization may be single or multiple-objective. In this last case, a large number of solutions, frequently integrating the Pareto front, may be produced. The decision maker has eventually to choose one among them, what may be tough task. Multi-criteria decision methods may be applied to support this last step of the decision-making process. In this paper DMA design is addressed by: i) proposing a modified k-means algorithm for partitioning; ii) using a multiobjective particle swarm optimization to suitably place partitioning devices; iii) using fuzzy analytic hierarchy process (FAHP) to weight the four objective functions considered; and iv) using technique for order of preference by similarity to ideal solution (TOPSIS) to rank the Pareto solutions to support the decision. This joint approach is applied in a case of a well-known WDN of the literature, and the results are discussed.

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“…As highlighted by [29], PCMs are a popular tool for weighting criteria and, consequently, evaluating alternatives in relation to a given DM process. However, experts may produce inconsistent judgments [30], especially when comparing a large number of elements [31], due to a natural lack of consistency in human thinking [32]. To help solve this problem, in a previous work [33], the authors developed a linearization process to calculate the closest (synthetic) fully consistent matrix to a given PCM.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%