A set theory justification of Garuti's compatibility index

Abstract

AbstractThis 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.