People can refer to quantities in a visual scene by using either exact cardinals (e.g. one, two, three) or natural language quantifiers (e.g. few, most, all). In humans, these two processes underlie fairly different cognitive and neural mechanisms. Inspired by this evidence, the present study proposes two models for learning the objective meaning of cardinals and quantifiers from visual scenes ...

Syllogism is a type of deductive reasoning involving quantified statements. The syllogistic reasoning scheme in the classical Aristotelian framework involves three crisp term sets and four linguistic quantifiers, for which the main support is the linguistic properties of the quantifiers. A number of fuzzy approaches for defining an approximate syllogism have been proposed for which the main sup...

Fuzzy quantifiers like ‘almost all’ and ‘about half’ abound in natural language. They are used for describing uncertain facts, quantitative relations and processes. An implementation of these quantifiers can provide expressive and easy-to-use operators for aggregation and data fusion, but also for steering the fusion process on a higher level through a safe transfer of expert-knowledge expresse...

Interpretation of outputs of fuzzy systems often involves the use of linguistic approximation that assigns a linguistic label to a fuzzy set based on the predefined primary terms, linguistic modifiers and linguistic connectives. More formally linguistic approximation can be considered in the terms of retranslation rules that correspond to the translation rules in explicitation in computing with...

We propose a general scheme of collective choice rule that covers a number of well-known rules. Our point of departure is, first, the set of fuzzy preference relations, and second, the linguistic aggregation rule proposed by Kacprzyk [2-4]. We reconsider this rule on a more abstract level and use the OWA operators instead of Zadeh’s fuzzy linguistic quantifiers. All collective choice rules from...

Recent research on fuzzy quantification for information retrieval has proposed the application of semi-fuzzy quantifiers for improving query languages. Fuzzy quantified sentences are useful as they allow additional restrictions to be imposed on the retrieval process unlike more popular retrieval approaches, which lack the facility to accurately express information needs. For instance, fuzzy qua...

In this paper we introduce reasoning procedures for ALCQF , a fuzzy description logic with extended qualified quantification. The 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. In order to reason about instances, the semantics of quantified expressions is defined based on recently...

Golnoosh Farnadi, Stephen H. Bach, Marie-Francine Moens, Lise Getoor, Martine De Cock Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Belgium, Department of Computer Science, Katholieke Universiteit Leuven, Belgium, Statistical Relational Learning Group, University of Maryland, USA, University of California, Santa Cruz, USA, Center for Data Science, Univers...