In the context of binary data mining, for unifying view on probabilistic quality measures of association rules, Totohasina’s theory of normalization of quality measures of association rules primarily based on affine homeomorphism presents some drawbacks. Indeed, it cannot normalize some interestingness measures which are explained below. This paper presents an extension of it, as a new normalization method based on proper homographic homeomorphism that appears most consequent.

Regarding the existence of more than sixty interestingness measures proposed in the literature since 1993 till today in the topics of association rules mining and facing the importance these last one, the research on normalization probabilistic quality measures of association rules has already led to many tangible results to consolidate the various existing measures in the literature. This article recommends a simple way to perform this normalization. In the interest of a unified presentation, the article offers also a new concept of normalization function as an effective tool for resolution of the problem of normalization measures that have already their own normalization functions.

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In epidemiology, the rule of association is used to determine the factors at the origin of diseases; implicative statistical analysis is thus a necessary tool in epidemiology too. Epidemiologists have more often chosen the so-called odds ratio measure in their studies of the quantification of the implicit link between an exposure and disease. In order to obtain good results, we need to be sure that the odds ratio measure is really the most relevant measure available. Therefore, it is necessary to study the mathematical properties of the odds ratio. This paper proposes a comparative study of the behaviour and mathematical properties of the odds ratio measure, the measure of Guillaume–Khenchaff (MGK), and the normalised odd-ratio measure. We have chosen the MGK measure because the literature considers it to be a good measure for extracting implicit association rules according to its mathematical properties. The result in this paper concerns only the study of probabilistic data.