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A set theory justification of Garuti's compatibility index
Author(s) -
Garuti Claudio E.
Publication year - 2019
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/mcda.1667
Subject(s) - closeness , compatibility (geochemistry) , jaccard index , mathematics , generalization , sort , computer science , algebra over a field , discrete mathematics , pure mathematics , arithmetic , statistics , cluster analysis , mathematical analysis , geochemistry , geology
This paper is oriented to increase the certainty and reliability of G index through different examples and show that G index expression can be reached by two different paths. The first path is using concepts of vector algebra in a weighted space. The second path is using concepts of set theory. Next, comparing G index with others known compatibility indices, and finally using set theory to show that the G index is a sort of generalization of the Jaccard ( J ) index. The generalization is because G index considers the weights of the elements that belong to different sets. This generalization make G applicable in the decision‐making domain to measure similarity (compatibility or closeness) between priority vectors, between system values and also for patterns recognition, among others important features.