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How to aggregate expert opinion for Fuzzy AHP methodology?
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Matthew Garrick
How to aggregate expert opinion for Fuzzy AHP methodology?
Dear Nolberto,
You’re right! Tomas Saaty explicitly criticised fuzzifying the AHP method and stated that there is already uncertainty inherent in the nature of the method: i.e. the comparison judgments are already fuzzy because they are allowed to vary over the values of a scale. However, many comparative studies have been made for AHP and FAHP and generally, results indicted that using FAHP leads to better model outcomes than AHP especially when the evaluations made by the decision maker are not much certain.
You’re right! Tomas Saaty explicitly criticised fuzzifying the AHP method and stated that there is already uncertainty inherent in the nature of the method: i.e. the comparison judgments are already fuzzy because they are allowed to vary over the values of a scale. However, many comparative studies have been made for AHP and FAHP and generally, results indicted that using FAHP leads to better model outcomes than AHP especially when the evaluations made by the decision maker are not much certain.
In FAHP, if there is more than one expert involved in the assessment (i.e. group preference), then their judgments (opinions) can be aggregated using weighted averaging method (e.g. establishing weights for experts based on their years of experience). The total of the weights should add up to 1. Then, you multiply each expert's judgment (fuzzy number) by their weight and finally add all resulting judgments fuzzy numbers together in order to get the aggregate one.
In FAHP, if there is more than one expert involved in the assessment (i.e. group preference), then their judgments (opinions) can be aggregated using weighted averaging method (e.g. establishing weights for experts based on their years of experience). The total of the weights should add up to 1. Then, you multiply each expert's judgment (fuzzy number) by their weight and finally add all resulting judgments fuzzy numbers together in order to get the aggregate one.
Dear Batool Years ago, and expert and AHP creator, Dr. Tomas Saaty answered that question, asserting that AHP is already fuzzy and then, no further fuzzy treatment was necessary
Dear Batool Years ago, and expert and AHP creator, Dr. Tomas Saaty answered that question, asserting that AHP is already fuzzy and then, no further fuzzy treatment was necessary
Thank you for your words. I like your explanation about the comparative judgements. It clarifies Saaty comments on that subject.
However, I am curious about how these studies predicted better outcomes using FAHP, considering that they don't know the real result In another words, regarding what yardstick were these comparisons made?
Thank you for your words. I like your explanation about the comparative judgements. It clarifies Saaty comments on that subject.
However, I am curious about how these studies predicted better outcomes using FAHP, considering that they don't know the real result In another words, regarding what yardstick were these comparisons made?
Hi Batool and all the other distinguished researchers.
I have worked exclusively in some of the multi criteria decision making (MCDM) and multi objective decision making methodologies like AHP, TOPSIS, VIKOR, ANP.
I do strongly agree with Prof Nolberto and Prof Nasser on their comments on PROF. TOMAS L SAATY ideas on Analytic Hierarchy Process.
I would like to add my perspective on this question. In AHP, the initial level step involves quantifying the subjective expert opinions (linguistic opinion / inputs). For quantification, many have used traditional triangular fuzzy number and few have incorporated trapezoidal fuzzy numbers.
So, inputs such as linguistic intricacies while performing pairwise comparsion can viewed or quantified with the triangular fuzzy variable.
Also, we can make use of the idea proposed by Prof. Ronald Yager "The Ordered Weighted Averaging (OWA) Operator in Decision Making" in aggregating the linguistic intricacies.
Hi Batool and all the other distinguished researchers.
I have worked exclusively in some of the multi criteria decision making (MCDM) and multi objective decision making methodologies like AHP, TOPSIS, VIKOR, ANP.
I do strongly agree with Prof Nolberto and Prof Nasser on their comments on PROF. TOMAS L SAATY ideas on Analytic Hierarchy Process.
I would like to add my perspective on this question. In AHP, the initial level step involves quantifying the subjective expert opinions (linguistic opinion / inputs). For quantification, many have used traditional triangular fuzzy number and few have incorporated trapezoidal fuzzy numbers.
So, inputs such as linguistic intricacies while performing pairwise comparsion can viewed or quantified with the triangular fuzzy variable.
Also, we can make use of the idea proposed by Prof. Ronald Yager "The Ordered Weighted Averaging (OWA) Operator in Decision Making" in aggregating the linguistic intricacies.
Dear Nolberto,
You’re right! Tomas Saaty explicitly criticised fuzzifying the AHP method and stated that there is already uncertainty inherent in the nature of the method: i.e. the comparison judgments are already fuzzy because they are allowed to vary over the values of a scale. However, many comparative studies have been made for AHP and FAHP and generally, results indicted that using FAHP leads to better model outcomes than AHP especially when the evaluations made by the decision maker are not much certain.
Nasser
Dear Nolberto,
You’re right! Tomas Saaty explicitly criticised fuzzifying the AHP method and stated that there is already uncertainty inherent in the nature of the method: i.e. the comparison judgments are already fuzzy because they are allowed to vary over the values of a scale. However, many comparative studies have been made for AHP and FAHP and generally, results indicted that using FAHP leads to better model outcomes than AHP especially when the evaluations made by the decision maker are not much certain.
Nasser
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Dear Batool,
In FAHP, if there is more than one expert involved in the assessment (i.e. group preference), then their judgments (opinions) can be aggregated using weighted averaging method (e.g. establishing weights for experts based on their years of experience). The total of the weights should add up to 1. Then, you multiply each expert's judgment (fuzzy number) by their weight and finally add all resulting judgments fuzzy numbers together in order to get the aggregate one.
Hope this helps,
Nasser
Dear Batool,
In FAHP, if there is more than one expert involved in the assessment (i.e. group preference), then their judgments (opinions) can be aggregated using weighted averaging method (e.g. establishing weights for experts based on their years of experience). The total of the weights should add up to 1. Then, you multiply each expert's judgment (fuzzy number) by their weight and finally add all resulting judgments fuzzy numbers together in order to get the aggregate one.
Hope this helps,
Nasser
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Dear Batool
Years ago, and expert and AHP creator, Dr. Tomas Saaty answered that question, asserting that AHP is already fuzzy and then, no further fuzzy treatment was necessary
Dear Batool
Years ago, and expert and AHP creator, Dr. Tomas Saaty answered that question, asserting that AHP is already fuzzy and then, no further fuzzy treatment was necessary
More
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Dear Batool Alaoui,
Also i suggest you to see links and attched files on topic.
https://core.ac.uk/download/pdf/6580373.pdf
https://core.ac.uk/download/pdf/33278395.pdf
http://isahp.org/2009Proceedings/Final_Papers/50_Meixner_Fuzzy_AHP_REV_FIN.pdf
Article Evaluating the knowledge, relevance and experience of expert...
Article Group Aggregation Techniques for Analytic Hierarchy Process ...
Best regards
Dear Batool Alaoui,
Also i suggest you to see links and attched files on topic.
https://core.ac.uk/download/pdf/6580373.pdf
https://core.ac.uk/download/pdf/33278395.pdf
http://isahp.org/2009Proceedings/Final_Papers/50_Meixner_Fuzzy_AHP_REV_FIN.pdf
Article Evaluating the knowledge, relevance and experience of expert...
Article Group Aggregation Techniques for Analytic Hierarchy Process ...
Best regards
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Dare Batool, You can follow same steps used in the Normal AHP with take into consideration the fuzzy arithmetic operations.
Dare Batool, You can follow same steps used in the Normal AHP with take into consideration the fuzzy arithmetic operations.
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Dear Nasser
Thank you for your words. I like your explanation about the comparative judgements. It clarifies Saaty comments on that subject.
However, I am curious about how these studies predicted better outcomes using FAHP, considering that they don't know the real result
In another words, regarding what yardstick were these comparisons made?
Dear Nasser
Thank you for your words. I like your explanation about the comparative judgements. It clarifies Saaty comments on that subject.
However, I am curious about how these studies predicted better outcomes using FAHP, considering that they don't know the real result
In another words, regarding what yardstick were these comparisons made?
More
VOTE
The following papers present different cases to aggregated the different point of views:
https://doi.org/10.1016/j.asoc.2020.106920
https://doi.org/10.15388/21-INFOR451
https://doi.org/10.3390/e24030367
https://doi.org/10.3390/su14031881
The following papers present different cases to aggregated the different point of views:
https://doi.org/10.1016/j.asoc.2020.106920
https://doi.org/10.15388/21-INFOR451
https://doi.org/10.3390/e24030367
https://doi.org/10.3390/su14031881
More
VOTE
Hi Batool and all the other distinguished researchers.
I have worked exclusively in some of the multi criteria decision making (MCDM) and multi objective decision making methodologies like AHP, TOPSIS, VIKOR, ANP.
I do strongly agree with Prof Nolberto and Prof Nasser on their comments on PROF. TOMAS L SAATY ideas on Analytic Hierarchy Process.
I would like to add my perspective on this question. In AHP, the initial level step involves quantifying the subjective expert opinions (linguistic opinion / inputs). For quantification, many have used traditional triangular fuzzy number and few have incorporated trapezoidal fuzzy numbers.
So, inputs such as linguistic intricacies while performing pairwise comparsion can viewed or quantified with the triangular fuzzy variable.
Also, we can make use of the idea proposed by Prof. Ronald Yager "The Ordered Weighted Averaging (OWA) Operator in Decision Making" in aggregating the linguistic intricacies.
Thanks - Mike
Hi Batool and all the other distinguished researchers.
I have worked exclusively in some of the multi criteria decision making (MCDM) and multi objective decision making methodologies like AHP, TOPSIS, VIKOR, ANP.
I do strongly agree with Prof Nolberto and Prof Nasser on their comments on PROF. TOMAS L SAATY ideas on Analytic Hierarchy Process.
I would like to add my perspective on this question. In AHP, the initial level step involves quantifying the subjective expert opinions (linguistic opinion / inputs). For quantification, many have used traditional triangular fuzzy number and few have incorporated trapezoidal fuzzy numbers.
So, inputs such as linguistic intricacies while performing pairwise comparsion can viewed or quantified with the triangular fuzzy variable.
Also, we can make use of the idea proposed by Prof. Ronald Yager "The Ordered Weighted Averaging (OWA) Operator in Decision Making" in aggregating the linguistic intricacies.
Thanks - Mike
More
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