Fuzzy quantification is a subtopic of fuzzy logic which deals with the modelling of the quantified expressions we can find in natural language. Fuzzy quantifiers have been successfully applied in several fields like fuzzy, control, fuzzy databases, information retrieval, natural language generation, etc. Their ability to model and evaluate linguistic expressions in a mathematical way, makes fuzzy quantifiers very powerful for data analytics and data mining applications. In this paper we will give a general overview of the main applications of fuzzy quantifiers in this field as well as some ideas to use them in new application contexts.

Probabilistic soft logic (PSL) is a probabilistic modeling framework which uses first-order logic and soft truth values in the interval[0;1] for reasoning in relational domains. PSL uses the Łukasiewicz t-norm and t-conorm from fuzzy logic to model respectively conjunction and disjunction. A PSL rule such as Trusts(A;X)^Trusts(X;B)->Trusts(A;B) models that “A trusts B” is true to the degree to which there is a trusted third party X. In the current version of PSL there is no way to express that A should trust B if most trusted friends of A trust B. In this work, we propose an extension of PSL with fuzzy quantifiers to address this limitation.