A Suite of Distributed Methodologies to Solve the Sparse Analytic Hierarchy Process Problem

Menci, Marta; Oliva, Gabriele; Papi, Marco; Setolal, Roberto; Scala, Antonio

doi:10.23919/ecc.2018.8550604

Cited by 13 publications

(9 citation statements)

References 26 publications

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“…Notice that, in the AHP literature, there is no universal consent on how to estimate the utilities in the presence of perturbations (see for instance the debate in Dyer (1990), Saaty (1990) for the original AHP problem). This is true also in the incomplete information case, see, for instance, Bozóki, Fülöp, and Rónyai (2010), Oliva, Setola, and Scala (2017), Menci et al (2018). While the debate is still open, we point out that the logarithmic least squares approach appears particularly appealing, since it focuses on error minimization.…”

Section: Incomplete Analytic Hierarchy Processmentioning

confidence: 88%

“…For these reasons, in Section 2.5, we review the Incomplete Logarithmic Least Squares (ILLS) Method (Bozóki, Fülöp, and Rónyai 2010;Menci et al 2018), which represents an extension of the classical Logarithmic Least Squares (LLS) Method developed in Crawford (1987), Barzilai, Cook, and Golany (1987) for solving the AHP problem in the complete information case. Moreover, for the sake of completeness, we summarize the main aspects of the Incomplete Direct Least Squares (Section 2.6), the Incomplete Weighted Least Squares (Section 2.7), and the Incomplete Eigenvector Approach (Section 2.8).…”

Section: Incomplete Analytic Hierarchy Processmentioning

confidence: 99%

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Incomplete analytic hierarchy process with minimum weighted ordinal violations

Faramondi

Oliva

Bozóki

2020

International Journal of General Systems

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Incomplete pairwise comparison matrices offer a natural way of expressing preferences in decision-making processes. Although ordinal information is crucial, there is a bias in the literature: cardinal models dominate. Ordinal models usually yield nonunique solutions; therefore, an approach blending ordinal and cardinal information is needed. In this work, we consider two cascading problems: first, we compute ordinal preferences, maximizing an index that combines ordinal and cardinal information; then, we obtain a cardinal ranking by enforcing ordinal constraints. Notably, we provide a sufficient condition (that is likely to be satisfied in practical cases) for the first problem to admit a unique solution and we develop a provably polynomial-time algorithm to compute it. The effectiveness of the proposed method is analyzed and compared with respect to other approaches and criteria at the state of the art.

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Section: Incomplete Analytic Hierarchy Processmentioning

confidence: 88%

Section: Incomplete Analytic Hierarchy Processmentioning

confidence: 99%

Incomplete analytic hierarchy process with minimum weighted ordinal violations

Faramondi

Oliva

Bozóki

2020

International Journal of General Systems

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“…Notice that, in the AHP literature, there is no universal consent on how to estimate the utilities in the presence of perturbations (see for instance the debate in (Dyer 1990;Saaty 1990) for the original AHP problem). This is true also in the incomplete information case, see, for instance, (Bozóki et al 2010;Oliva et al 2017;Menci et al 2018). While the debate is still open, we point out that the logarithmic leasts squares approach appears particularly appealing, since it focuses on error minimization.…”

Section: Incomplete Analytic Hierarchy Processmentioning

confidence: 89%

“…For these reasons, in Section 2.4 we review the Sparse Logarithmic Least Squares (SLLS) Method (Bozóki et al 2010;Menci et al 2018), which represents an extension of the classical Logarithmic Least Squares (LLS) Method developed in (Crawford 1987;Barzilai et al 1987) for solving the AHP problem in the complete information case. Moreover, for the sake of completeness, we summarize the main aspects of the Sparse Direct Least Squares (Section 2.5), the Sparse Weighted Least Squares (Section 2.6), and the Eigenvector Approach (Section 2.7).…”

Section: Incomplete Analytic Hierarchy Processmentioning

confidence: 99%

Incomplete Analytic Hierarchy Process with Minimum Weighted Ordinal Violations

Faramondi,

Oliva,

Bozóki

2019

Preprint

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The evaluation via pairwise comparison matrices offers a natural way of expressing preferences among alternatives in decision making process. Complete and incomplete pairwise comparison matrices have been applied in multi-criteria decision making, as well as in scoring and ranking. Although ordinal information is crucial in both theory and practice, there is a bias in the literature: cardinal models dominate. Purely ordinal models usually lead to non-unique solutions, therefore, a dual approach that takes ordinal and cardinal data into consideration is needed. In this work, we address the problem of identifying a set of weights from pairwise comparison matrices by fusing ordinal information and cardinal information. To this end, the incomplete (sparse) logarithmic least squares method is extended by constraints on ordinal consistency. The effectiveness of the proposed method is analyzed and compared with respect to other approaches and criteria at the state of the art.

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“…There are other papers in AHP literature coping with missing entries of the ratio matrix e.g. Fedrizzi and Giove (2007), Menci et al (2018). The main difference between Sparse and Parsimonious AHP is that the reference points in PAHP are systematically selected and further interactions between the respondents and survey instructors are provided compared to Sparse AHP.…”

Section: Literature Review On Multi-level Criteria Ahp and Public Involvement In Transport Planningmentioning

confidence: 99%

Introduction and comparative analysis of the multi-level parsimonious AHP methodology in a public transport development decision problem

Duleba

2020

Journal of the Operational Research Society

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The methodology of Parsimonious Analytic Hierarchy Process (PAHP) has been originally constructed to unburden the evaluators of an AHP survey from the numerous pairwise comparisons caused by the several alternatives in decision problems. So far, there are very few applications of PAHP and all of them referred to the last level of the decision structure; to the alternatives. This paper aims to demonstrate a multi-level PAHP based model, so how to apply the method on an arbitrary level of the decision structure. Since being a new method, another objective is to conduct a comparative analysis on the correlation of the results between AHP and multi-level PAHP models. Moreover, the new multi-level approach makes it possible to demonstrate an immanent analysis originated from AHP logic to test PAHP results, which is unique in the scientific literature for Parsimonious technique. The created model has been tested in the real-world decision problem of a Turkish big city, Mersin. Based on the test and analysis, the method can be a suitable tool in case of layman evaluations even in case of small number of criteria or alternatives. In the paper, a general application process is also proposed for other future appliers of the method.

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A Suite of Distributed Methodologies to Solve the Sparse Analytic Hierarchy Process Problem

Cited by 13 publications

References 26 publications

Incomplete analytic hierarchy process with minimum weighted ordinal violations

Incomplete analytic hierarchy process with minimum weighted ordinal violations

Incomplete Analytic Hierarchy Process with Minimum Weighted Ordinal Violations

Introduction and comparative analysis of the multi-level parsimonious AHP methodology in a public transport development decision problem

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