We study definability in terms of monotone generalized quantifiers satisfying Isomorphism closure, Conservativity and Extension. Among the quantifiers with the latter three properties — here called CE quantifiers — one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number ...

This paper provides a common framework, a generic model, for Computerized Adaptive Testing (CAT) for different model types. We present question selection methods for CAT for this generic model. We use three different types of models, Item Response Theory, Bayesian Networks, and Neural Networks, that instantiate the generic model. We illustrate the usefulness of a special model condition – the m...

Recently there are several works which analyzed the strategy−proofness of non−resolute social choice rules such as Duggan and Schwartz (2000) and Ching and Zhou (2001). In these analyses it was assumed that individual preferences are linear, that is, they excluded indifference from individual preferences. We present an analysis of the strategy−proofness of non−resolute social choice rules when ...

In this paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and Nuttall Q−functions. More precisely, a simple probabilistic method is firstly given to prove the monotonicity of these two functions. Then, the log-concavity of the generalized Marcum Q−function and its deformations is established with respect to each of the three parameters. Sinc...

In this paper, we firstly propose some generalized prioritized aggregation operators to aggregate the intuitionistic fuzzy values (IFVs), such as the generalized intuitionistic fuzzy prioritized weighted geometric (GIFPWG) operator and the generalized intuitionistic fuzzy prioritized weighted average (GIFPWA) operator. It is shown that some existing intuitionistic fuzzy aggregation operators ar...

Classical quantifiers (e.g., “all”, “some” and “none”) have been extensively studied in logic and psychology. In contrast, generalized quantifiers (e.g., “most”) allow for fine-grained statements about quantities. The discrepancy in the underlying mental representation and its interpretation among interpreters can affect language use and reasoning. We investigated the effect of quantifier type,...

In this paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and Nuttall -functions. More precisely, a simple probabilistic method is first given to prove the monotonicity of these two functions. Then, the log-concavity of the generalized Marcum -function and its deformations is established with respect to each of the three parameters. Since th...