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PhilipGriffith / AHPy

A Python implementation of the Analytic Hierarchy Process
MIT License
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Thoughts about implementing the "row geometric mean method" in addition to the eigenvalue method? #5

Open dfrankow opened 3 years ago

dfrankow commented 3 years ago

https://www.sciencedirect.com/science/article/pii/S0167923610000643 says :

"When selecting EM as the prioritization method, some researchers have some disputes on the use of the AIJ and the AIP. Ramanathan and Ganesh [35] observe that AIJ violates the Pareto principle of social choice theory [3], and suggest using AIP in AHP group decision making. Forman and Peniwati [23] argue that AIJ and AIP are philosophically different circumstances [8], and whether AIJ or AIP should be used depended on whether the group intends to behave as a synergistic unit or as a collection of individuals. However, when selecting RGMM as the priori- tization method, Barzilai and Golany [4] have shown the equivalence between AIJ and AIP (see Lemma 1)."

"EM" = "eigenvalue method" "RGGM" = "row geometric mean method"

They have equations in the paper. RGGM:

image

I do not yet have an extremely informed opinion about the two, but I wondered if you had any thoughts about implementing RGGM?

PhilipGriffith commented 3 years ago

This has sent me down a long rabbit hole! I haven't surfaced yet, but will let you know when I do. :)

GreenAnalytics commented 2 years ago

AIJ and AIP are aggregation methods for Group decision making (GDM). It is used to aggregate the comparison matrices from different decision makers (DM). The difference is that AIJ aggregates after the judgment matrix, while the AIP aggregate the global weights. It would be very interesting to have GDM implemented!

PhilipGriffith commented 2 years ago

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