Different interpretations of fuzzy gradual-inclusion-based IR models

Recently, a theoretical fuzzy IR system, based on gradual inclusion measures, has been proposed [1]. In this model, derived from the division of fuzzy relations, the gradual inclusion of a query in a document is modeled by a fuzzy implication. In previous papers, we have shown that, under some assumptions, this model can be seen as a Vector Space Model. This paper also studies other interpretations of our fuzzy IR models based on gradual inclusions. It is shown that the fuzzy models can be interpreted as language models for IR. The links with logical models to IR are also recalled. More generally, this paper discusses the links between these models, shown from the point of view of our fuzzy models.