On definition and construction of association measures

Abstract

Abstract. The definition and the general methods of construction of non-statistical association measures on different domains are discussed. An association measure is a function of two variables defined on a set X with involutive operation and satisfying the properties similar to the properties of the Pearson's correlation coefficient. Such measure can be used for analysis of the possible positive and negative relationships between variables. The methods of construction of association measures using similarity measures and pseudo-difference operations associated to t-conorms are discussed. The examples of association measures on different domains are considered.

Bipolar Rating Scales: A Survey and Novel Correlation Measures Based on Nonlinear Bipolar Scoring Functions

“…The reasons to use nonlinear bipolar utility functions in correlation measure introduced in the paper are discussed in Section 7. The results on association measures considered in Section 7 are based on the papers [5][6][7]. Here, we use the terms association measure and correlation measure as interchangeable.…”

“…The properties (27)- (29) were used in [7] in the definition of the correlation (association) measures on the set X with involution N. These properties generalize the properties of Pearson's correlation coefficient applied to M-tuples when the negation of M-tuples of real values is defined by N(x) = −x = (−x1, …, −xM). Here we extend the definition of association measures given in [7] on the set of bipolar utility profiles.…”

“…Here we extend the definition of association measures given in [7] on the set of bipolar utility profiles. The properties (30) and (31) are introduced here to avoid the problems with the correlation coefficient defined on bipolar profiles discussed at the beginning of this section.…”

Constructing Correlation Coefficients from Similarity and Dissimilarity Functions

“…Proposition 1 [4]. Let N:V→V be a reflection on a set V, and R:V×V→R be a symmetric real-valued function, i.e.…”

“…The similarity, dissimilarity, and correlation measures are considered as functions satisfying some sets of properties [3,4,8]. This paper introduces a new class of correlation functions, satisfying a weaker set of properties than the previously considered correlation functions (association measures) [4,8] called here strong correlation functions and defined on a set with involution (negation) operation. We discuss the methods of constructing both types of correlation functions using (dis)similarity functions.…”