Association Measures on Sets with Involution and Similarity Measure

On definition and construction of association measures

“…The association measure A on V satisfies for all x, y ∈ V the properties (8), (9) and the following property:…”

“…Consider the methods of construction of association measures using a similarity measure and pseudodifference operation associated with some t-conorm and prove the related results [8,9].…”

“…The examples of association measures on different domains constructed by the methods discussed in the previous section can be found in [7][8][9][10]. The similarity measures satisfying the conditions of Theorems 2 and 3 can be obtained from the distance measures used together with some data transformation [7], from generators of strong negations [3,5,9,10] …”

“…In [8], the methods proposed in [7] have been extended on the general case of functions A : X × X → [−1, 1] defined on a set X with involutive operation N (called reflection) and satisfying the properties similar to the properties of the Pearson's correlation coefficient. The methods of construction of such measures [8,9] use similarity measures and pseudo-difference operations associated with t-conorms [2,15]. In [9], the problems appeared in the definition of the general class of functions similar to the Pearson's correlation coefficient have been discussed.…”

“…The methods of construction of such measures [8,9] use similarity measures and pseudo-difference operations associated with t-conorms [2,15]. In [9], the problems appeared in the definition of the general class of functions similar to the Pearson's correlation coefficient have been discussed. These problems have the different reasons.…”