Understanding the Analytic Hierarchy Process

Kułakowski, Konrad

doi:10.1201/b21817

Cited by 23 publications

(25 citation statements)

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“…Also, in the case of n = 3, priority vectors for both methods coincide even when the PC matrix is inconsistent, see e.g. [5] or [9]. The study [6] established that for not-so-inconsistent matrices, both EVM and GMM produce very similar results, with differences 'small beyond human perception'.…”

Section: Ordinal Rankings' Similarity Of Evm and Gmmmentioning

confidence: 80%

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Some Notes on the Similarity of Priority Vectors Derived by the Eigenvalue Method and the Geometric Mean Method

Mazurek¹,

Kułakowski²,

Ernst³

et al. 2022

Preprint

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The aim of this paper is to examine the differences in ordinal rankings obtained from a pairwise comparison matrix using the eigenvalue method and the geometric mean method. We introduce several propositions on the (dis)similarity of both rankings with respect to the matrix size and its inconsistency expressed by the Koczkodaj's inconsistency index. Further on, we examine the relationship between differences in both rankings and Kendall's rank correlation coefficient τ and Spearman's rank coefficient ρ. Apart from theoretical results, intuitive numerical examples and Monte Carlo simulations are provided as well.

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Section: Ordinal Rankings' Similarity Of Evm and Gmmmentioning

confidence: 80%

“…being compared. Let S be a pairwise comparison scale 1 [9]. Let a ij ⊂ S, a ij > 0 denote the relative importance/preference of an object i over object j, where i, j ∈ {1, .…”

Section: Multiplicative Pairwise Comparisons -Concepts and Notationmentioning

confidence: 99%

Some Notes on the Similarity of Priority Vectors Derived by the Eigenvalue Method and the Geometric Mean Method

Mazurek¹,

Kułakowski²,

Ernst³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Third, the judgments are summed vertically at different levels of the hierarchy. The fourth and final step is to check the consistency of the judgments [9,35]. In the first step, we developed a model for the decision problem by breaking down the criteria into a hierarchy, as shown in Figure 6.…”

Section: Spatial Decision Support Systemmentioning

confidence: 99%

Geospatial Analysis of Solar Energy in Riyadh Using a GIS-AHP-Based Technique

Albraheem

Alabdulkarim

2021

IJGI

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In recent years, spatial multi-criteria decision analysis (MCDA) has been applied to different types of spatial problems, such as solar power site suitability. MCDA can be used to support the process of identifying suitable regions for solar energy projects. To the best of our knowledge, no study has addressed the problem of site evaluation for solar photovoltaic PV systems in the Riyadh region. Therefore, a spatial MCDA framework is proposed to perform a geospatial analysis of solar energy in the Riyadh region, which includes data collection, spatial analysis, a spatial decision support system and visualization. The methodology that was used to solve the site suitability problem is described. It involved the combination of a Geographical Information System (GIS) and the Analytic Hierarchy Process (GIS-AHP). The results show that the most suitable sites are in the north and northwest of the Riyadh region, with an area that represents 16,748 Km2 with an 80% suitability degree. In addition, it was proven that Afif is the largest suitable city. It has high solar radiation, at an average of 2.631687 MWh/m2/year, and low temperatures, at an average of 26.3 °C, as well as having flat areas with a slope under 5°. The results were validated using a sensitivity analysis model and also compared with those for ground-based stations.

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“…Currently, pairwise comparisons are a valuable source of preferential information in many decision-making methods, including TOPSIS [41], PROMETHEE [5], MACBETH [2], BWM [33] or multiple-criteria sorting [18]. One of the best known methods of multiple-criteria decision making based on pairwise comparisons is the Analytic Hierarchy Process (AHP) [37,26]. The method defined by Saaty in 1977 [35] quickly gained popularity.…”

Section: Introductionmentioning

confidence: 99%

Multiple-criteria Heuristic Rating Estimation

Kędzior¹,

Kułakowski²

2022

Preprint

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One of the most widespread multi-criteria decision-making methods is the Analytic Hierarchy Process (AHP). AHP successfully combines the pairwise comparisons method and the hierarchical approach. It allows the decision-maker to set priorities for all ranked alternatives. But what if, for some of them, their ranking value is known (e.g., it can be determined differently)? The Heuristic Rating Estimation (HRE) method proposed in 2014 tried to bring the answer to this question. However, the considerations were limited to a model that did not consider many criteria. In this work, we go a step further and analyze how HRE can be used as part of the AHP hierarchical framework. The theoretical considerations are accompanied by illustrative examples showing HRE as a multiple-criteria decision-making method.

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Understanding the Analytic Hierarchy Process

Cited by 23 publications

References 0 publications

Some Notes on the Similarity of Priority Vectors Derived by the Eigenvalue Method and the Geometric Mean Method

Some Notes on the Similarity of Priority Vectors Derived by the Eigenvalue Method and the Geometric Mean Method

Geospatial Analysis of Solar Energy in Riyadh Using a GIS-AHP-Based Technique

Multiple-criteria Heuristic Rating Estimation

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