Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean

Ramík, Jaroslav; Korviny, Petr

doi:10.1016/j.fss.2009.10.011

Cited by 127 publications

(74 citation statements)

References 11 publications

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“…This consistency check approach, however, has been found to be time-consuming (Ramik, 2009). Hence, in the effort to solve the time related issue, some few researchers has extended and modify the original Saaty's comparison matrix to suit their particular problem and research aim, among them we can mention Ramik (2009), who presented a pair-wise comparison matrix (PCM) with a triangular fuzzy element which uses logarithmic least squares for eliciting associated weights.…”

Section: Fuzzy Analytical Hierarchy Process (Fuzzy-ahp)mentioning

confidence: 99%

“…Hence, in the effort to solve the time related issue, some few researchers has extended and modify the original Saaty's comparison matrix to suit their particular problem and research aim, among them we can mention Ramik (2009), who presented a pair-wise comparison matrix (PCM) with a triangular fuzzy element which uses logarithmic least squares for eliciting associated weights. Turan (2013) presented a pair-wise comparison matrix (PCM) for computing priorities criteria elements in the evaluation of product design at the early stage of product development.…”

Section: Fuzzy Analytical Hierarchy Process (Fuzzy-ahp)mentioning

confidence: 99%

“…Considering the drawback in the fuzzy AHP model as stated above, this study intends to address this issue by extending and improving the evaluation matrix and the priority weight formula in the fuzzy AHP model originally proposed in (Kong & Liu, 2005;Ramik, 2009;Turan, 2013) by employing both a subjective and objective factors/approach for implementing the fuzzy AHP model. In replacing the FCM/PCM in the traditional AHP model with the new evaluation matrix, first a new expert's weighing scale is introduced which is used in balancing and reducing bias in the assessment values given by the experts and a new criteria rating scale (i.e.…”

Section: Subjective and Objective Fuzzy Ahp Modelmentioning

confidence: 99%

“…The new matrix which is an extension of evaluation matrix in the fuzzy AHP model in (Kong & Liu, 2005;Ramik, 2009;Turan, 2013) is implemented using both subjective and objective approach. The subjective aspect of the evaluation is the part where the data are collected from experts in the field, while the objective part is the final weight calculation using the evaluation matrix and the priority weight formula.…”

Section: The Proposed Evaluation Matrixmentioning

confidence: 99%

“…(7-8) below. The matrix which represents the objective aspect of the model can be said different from the traditional and modified FCM/PCM in (Kong & Liu, 2005;Ramik, 2009;Turan, 2013) for the following reasons;…”

Section: The Proposed Evaluation Matrixmentioning

confidence: 99%

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A subjective and objective fuzzy-based analytical hierarchy process model for prioritization of lean product development practices

Aikhuele¹,

Turan²

2017

10.5267/j.msl

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In this paper, a subjective and objective fuzzy-based Analytical Hierarchy Process (AHP) model is proposed. The model which is based on a newly defined evaluation matrix replaces the fuzzy comparison matrix (FCM) in the traditional fuzzy AHP model, which has been found ineffective and time-consuming when criteria/alternatives are increased. The main advantage of the new model is that it is straightforward and completely eliminates the repetitive adjustment of data that is common with the FCM in traditional AHP model. The model reduces the complete dependency on human judgment in prioritization assessment since the weights values are solved automatically using the evaluation matrix and the modified priority weight formula in the proposed model. By virtue of a numerical case study, the model is successfully applied in the determination of the implementation priorities of lean practices for a product development environment and compared with similar computational methods in the literature.

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Section: Fuzzy Analytical Hierarchy Process (Fuzzy-ahp)mentioning

confidence: 99%

Section: Fuzzy Analytical Hierarchy Process (Fuzzy-ahp)mentioning

confidence: 99%

Section: Subjective and Objective Fuzzy Ahp Modelmentioning

confidence: 99%

Section: The Proposed Evaluation Matrixmentioning

confidence: 99%

Section: The Proposed Evaluation Matrixmentioning

confidence: 99%

See 3 more Smart Citations

A subjective and objective fuzzy-based analytical hierarchy process model for prioritization of lean product development practices

Aikhuele¹,

Turan²

2017

10.5267/j.msl

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Incomplete Fuzzy Preference Matrix and Its Application to Ranking of Alternatives

Ramík

2014

Int. J. Intell. Syst.

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A fuzzy preference matrix is the result of pairwise comparison of a powerful method in multicriteria optimization. When comparing two elements, a decision maker assigns the value between 0 and 1 to any pair of alternatives representing the element of the fuzzy preference matrix. Here, we investigate relations between transitivity and consistency of fuzzy preference matrices and multiplicative preference ones. The obtained results are applied to situations where some elements of the fuzzy preference matrix are missing. We propose a new method for completing fuzzy matrix with missing elements called the extension of the fuzzy preference matrix. We investigate some important particular case of the fuzzy preference matrix with missing elements. Consequently, by the eigenvector of the transformed matrix we obtain the corresponding priority vector. Illustrative numerical examples are supplemented. C 2014 Wiley Periodicals, Inc.The DM problem can be formulated as follows: Let X = {x 1 , x 2 , . . . , x n } be a finite set of alternatives. These alternatives have to be classified from best to worst, using the information given by a DM in the form of pairwise comparison matrix.

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Variation of Preference Inconsistency When Applying Ratio and Interval Scale Pairwise Comparisons

Sironen

Leskinen

Kangas

et al. 2013

J. Multi-Crit. Decis. Anal.

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Several studies on numerical rating in discrete choice problems address the tendency of inconsistencies in decision makers' measured preferences. This is partly due to true inconsistencies in preferences or the decision makers' uncertainty on what he or she really wants. This uncertainty may be reflected in the elicited preferences in different ways depending on the questions asked and methods used in deriving the preferences for alternatives. Some part of the inconsistency is due to only having a discrete set of possible judgments. This study examined the variation of preference inconsistency when applying different pairwise preference elicitation techniques in a five-item discrete choice problem. The study data comprised preferences of five career alternatives elicited applying interval scale and numerically and verbally anchored ratio scale pairwise comparisons. Statistical regression technique was used to analyse the differences of inconsistencies between the tested methods. The resulting relative residual variances showed that the interval ratio scale comparison technique provided the greatest variation of inconsistencies between respondents, thus being the most sensitive to inconsistency in preferences. The numeric ratio scale comparison gave the most uniform preferences between the respondents. The verbal ratio scale comparison performed between the latter two when relative residual variances were considered. However, the verbal ratio scale comparison had weaker ability to differentiate the alternatives. The results indicated that the decision recommendation may not be sensitive to the selection between these preference elicitation methods in this kind of five-item discrete choice problem. The numeric ratio scale comparison technique seemed to be the most suitable method to reveal the decision makers' true preferences. However, to confirm this result, more studying will be needed, with an attention paid to users' comprehension and learning in the course of the experiment.

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Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean

Cited by 127 publications

References 11 publications

A subjective and objective fuzzy-based analytical hierarchy process model for prioritization of lean product development practices

A subjective and objective fuzzy-based analytical hierarchy process model for prioritization of lean product development practices

Incomplete Fuzzy Preference Matrix and Its Application to Ranking of Alternatives

Variation of Preference Inconsistency When Applying Ratio and Interval Scale Pairwise Comparisons

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