This paper is a contribution to the theoretical foundations of data mining. More precisely, we contribute to a part of data mining allowing us to search for associations among attributes that can be expressed in the form of natural language sentences. The theoretical background and also a method for mining such associations was published recently in [V. Novák et al., Mining pure linguistic associations from numerical data, Int. Journal of Approximate Reasoning 48 (2008), 4 -- 22]. We elaborated other mathematical representations of the model presented in the mentioned paper in order to extend its applicability.