AHP-Like Matrices and Structures—Absolute and Relative Preferences
Aggregation functions are extensively used in decision making processes to combine available information. Arithmetic mean and weighted mean are some of the most used ones. In order to use a weighted mean, we need to define its weights. The Analytical Hierarchy Process (AHP) is a well known technique...
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doaj-8cd802c1cf994215a28253877410a7152020-11-25T03:22:05ZengMDPI AGMathematics2227-73902020-05-01881381310.3390/math8050813AHP-Like Matrices and Structures—Absolute and Relative PreferencesDavid Koloseni0Tove Helldin1Vicenç Torra2Department of Mathematics, University of Dar es Salaam, Dar es Salaam 35065, TanzaniaSchool of Informatics, University of Skövde, 54128 Skövde, SwedenSchool of Informatics, University of Skövde, 54128 Skövde, SwedenAggregation functions are extensively used in decision making processes to combine available information. Arithmetic mean and weighted mean are some of the most used ones. In order to use a weighted mean, we need to define its weights. The Analytical Hierarchy Process (AHP) is a well known technique used to obtain weights based on interviews with experts. From the interviews we define a matrix of pairwise comparisons of the importance of the weights. We call these AHP-like matrices absolute preferences of weights. We propose another type of matrix that we call a relative preference matrix. We define this matrix with the same goal—to find the weights for weighted aggregators. We discuss how it can be used for eliciting the weights for the weighted mean and define a similar approach for the Choquet integral.https://www.mdpi.com/2227-7390/8/5/813aggregation functionsweight selectionfuzzy measuresAHP (Analytical Hierarchy Process) |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
David Koloseni Tove Helldin Vicenç Torra |
spellingShingle |
David Koloseni Tove Helldin Vicenç Torra AHP-Like Matrices and Structures—Absolute and Relative Preferences Mathematics aggregation functions weight selection fuzzy measures AHP (Analytical Hierarchy Process) |
author_facet |
David Koloseni Tove Helldin Vicenç Torra |
author_sort |
David Koloseni |
title |
AHP-Like Matrices and Structures—Absolute and Relative Preferences |
title_short |
AHP-Like Matrices and Structures—Absolute and Relative Preferences |
title_full |
AHP-Like Matrices and Structures—Absolute and Relative Preferences |
title_fullStr |
AHP-Like Matrices and Structures—Absolute and Relative Preferences |
title_full_unstemmed |
AHP-Like Matrices and Structures—Absolute and Relative Preferences |
title_sort |
ahp-like matrices and structures—absolute and relative preferences |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2020-05-01 |
description |
Aggregation functions are extensively used in decision making processes to combine available information. Arithmetic mean and weighted mean are some of the most used ones. In order to use a weighted mean, we need to define its weights. The Analytical Hierarchy Process (AHP) is a well known technique used to obtain weights based on interviews with experts. From the interviews we define a matrix of pairwise comparisons of the importance of the weights. We call these AHP-like matrices absolute preferences of weights. We propose another type of matrix that we call a relative preference matrix. We define this matrix with the same goal—to find the weights for weighted aggregators. We discuss how it can be used for eliciting the weights for the weighted mean and define a similar approach for the Choquet integral. |
topic |
aggregation functions weight selection fuzzy measures AHP (Analytical Hierarchy Process) |
url |
https://www.mdpi.com/2227-7390/8/5/813 |
work_keys_str_mv |
AT davidkoloseni ahplikematricesandstructuresabsoluteandrelativepreferences AT tovehelldin ahplikematricesandstructuresabsoluteandrelativepreferences AT vicenctorra ahplikematricesandstructuresabsoluteandrelativepreferences |
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