Fuzzy relational compositions have been extensively studied by many authors. Especially, we would like to highlight initial studies of the fuzzy relational compositions motivated by their applications to medical diagnosis by Willis Bandler and Ladislav Kohout. We revisit these types of compositions and introduce new definitions that directly employ generalized quantifiers. The motivation for th...

Fuzzy quantifiers (like many, few, ) are an important research topic not only due to their abundance in natural language (NL), but also because an adequate account of these quantifiers would provide a class of powerful yet human-understandable operators for information aggregation and data fusion. We introduce the DFS theory of fuzzy quantification, present a model of the theory, and describe a...

In this paper, we continue the development of a formal theory of intermediate quantifiers (linguistic expressions such as “most”, “many”, “few”, “almost all”, etc.). In previous work, we demonstrated that 105 generalized syllogisms are valid in our theory. We turn our attention to another problem which is the analysis of the generalized Aristotelian square of opposition which, besides the class...

In this paper we introduce ALCQF , a fuzzy description logic with extended qualified quantification. The proposed language allows for the definition of fuzzy quantifiers of the absolute and relative kind by means of piecewise linear functions on N and Q∩ [0, 1] respectively. These quantifiers extends the usual (qualified) ∃, ∀ and number restriction. The semantics of quantified expressions is d...

Fuzzy quantification is a linguistic granulation technique capable of expressing the global characteristics of a collection of individuals, or a relation between individuals, through meaningful linguistic summaries. However, existing approaches to fuzzy quantification fail to provide convincing results in the important case of two-place quantification (e.g. “many blondes are tall”). We develop ...

Fuzzy relational formal concept analysis (FRCA) mines collections of fuzzy lattices from xmlns:xlink="http://www.w3.org/1999/xlink">fuzzy context families , which are special datasets made contexts and relations between objects different types. Mainly, FRCA consists the following procedures...

In a previous paper, we presented an approach to calculate relational division in fuzzy databases, starting with the GEFRED model. This work centered on dealing with fuzzy attributes and fuzzy values and only the universal quantifier was taken into account since it is the inherent quantifier in classical relational division. In this paper, we present an extension of that division to relax the u...

Lindström [11] introduced a very powerful notion of quantifiers, which permits multi-place quantification and the simultaneous binding of several variables. A special case, 'branching' quantifiers, was found to be useful in linguistics, specifically for modelling reciprocal constructions like " Most men and most women admire each other ". Westerståhl [13] showed how to compute the three-place L...