12,614 research outputs found
The probatilistic Quantifier Fuzzification Mechanism FA: A theoretical analysis
The main goal of this work is to analyze the behaviour of the FA quantifier
fuzzification mechanism. As we prove in the paper, this model has a very solid
theorethical behaviour, superior to most of the models defined in the
literature. Moreover, we show that the underlying probabilistic interpretation
has very interesting consequences.Comment: 58 pages, 1 figur
Characterizing Quantifier Fuzzification Mechanisms: a behavioral guide for practical applications
Important advances have been made in the fuzzy quantification field.
Nevertheless, some problems remain when we face the decision of selecting the
most convenient model for a specific application. In the literature, several
desirable adequacy properties have been proposed, but theoretical limits impede
quantification models from simultaneously fulfilling every adequacy property
that has been defined. Besides, the complexity of model definitions and
adequacy properties makes very difficult for real users to understand the
particularities of the different models that have been presented. In this work
we will present several criteria conceived to help in the process of selecting
the most adequate Quantifier Fuzzification Mechanisms for specific practical
applications. In addition, some of the best known well-behaved models will be
compared against this list of criteria. Based on this analysis, some guidance
to choose fuzzy quantification models for practical applications will be
provided.Comment: 28 page
Fuzzy quantification for linguistic data analysis and data mining
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
The FA Quantifier Fuzzification Mechanism: analysis of convergence and efficient implementations
The fuzzy quantification model FA has been identified as one of the best
behaved quantification models in several revisions of the field of fuzzy
quantification. This model is, to our knowledge, the unique one fulfilling the
strict Determiner Fuzzification Scheme axiomatic framework that does not induce
the standard min and max operators. The main contribution of this paper is the
proof of a convergence result that links this quantification model with the
Zadeh's model when the size of the input sets tends to infinite. The
convergence proof is, in any case, more general than the convergence to the
Zadeh's model, being applicable to any quantitative quantifier. In addition,
recent revisions papers have presented some doubts about the existence of
suitable computational implementations to evaluate the FA model in practical
applications. In order to prove that this model is not only a theoretical
approach, we show exact algorithmic solutions for the most common linguistic
quantifiers as well as an approximate implementation by means of Monte Carlo.
Additionally, we will also give a general overview of the main properties
fulfilled by the FA model, as a single compendium integrating the whole set of
properties fulfilled by it has not been previously published.Comment: 22 page
Structural reliability analysis for p-boxes using multi-level meta-models
In modern engineering, computer simulations are a popular tool to analyse,
design, and optimize systems. Furthermore, concepts of uncertainty and the
related reliability analysis and robust design are of increasing importance.
Hence, an efficient quantification of uncertainty is an important aspect of the
engineer's workflow. In this context, the characterization of uncertainty in
the input variables is crucial. In this paper, input variables are modelled by
probability-boxes, which account for both aleatory and epistemic uncertainty.
Two types of probability-boxes are distinguished: free and parametric (also
called distributional) p-boxes. The use of probability-boxes generally
increases the complexity of structural reliability analyses compared to
traditional probabilistic input models. In this paper, the complexity is
handled by two-level approaches which use Kriging meta-models with adaptive
experimental designs at different levels of the structural reliability
analysis. For both types of probability-boxes, the extensive use of meta-models
allows for an efficient estimation of the failure probability at a limited
number of runs of the performance function. The capabilities of the proposed
approaches are illustrated through a benchmark analytical function and two
realistic engineering problems
The Semantic Web Rule Language Expressiveness Extensions-A Survey
The Semantic Web Rule Language (SWRL) is a direct extension of OWL 2 DL with
a subset of RuleML, and it is designed to be the rule language of the Semantic
Web. This paper explores the state-of-the-art of SWRL's expressiveness
extensions proposed over time. As a motivation, the effectiveness of the
SWRL/OWL combination in modeling domain facts is discussed while some of the
common expressive limitations of the combination are also highlighted. The
paper then classifies and presents the relevant language extensions of the SWRL
and their added expressive powers to the original SWRL definition. Furthermore,
it provides a comparative analysis of the syntax and semantics of the proposed
extensions. In conclusion, the decidability requirement and usability of each
expressiveness extension are evaluated towards an efficient inclusion into the
OWL ontologies
On the quantification and efficient propagation of imprecise probabilities with copula dependence
This paper addresses the problem of quantification and propagation of
uncertainties associated with dependence modeling when data for characterizing
probability models are limited. Practically, the system inputs are often
assumed to be mutually independent or correlated by a multivariate Gaussian
distribution. However, this subjective assumption may introduce bias in the
response estimate if the real dependence structure deviates from this
assumption. In this work, we overcome this limitation by introducing a flexible
copula dependence model to capture complex dependencies. A hierarchical
Bayesian multimodel approach is proposed to quantify uncertainty in dependence
model-form and model parameters that result from small data sets. This approach
begins by identifying, through Bayesian multimodel inference, a set of
candidate marginal models and their corresponding model probabilities, and then
estimating the uncertainty in the copula-based dependence structure, which is
conditional on the marginals and their parameters. The overall uncertainties
integrating marginals and copulas are probabilistically represented by an
ensemble of multivariate candidate densities. A novel importance sampling
reweighting approach is proposed to efficiently propagate the overall
uncertainties through a computational model. Through an example studying the
influence of constituent properties on the out-of-plane properties of
transversely isotropic E- glass fiber composites, we show that the composite
property with copula-based dependence model converges to the true estimate as
data set size increases, while an independence or arbitrary Gaussian
correlation assumption leads to a biased estimate.Comment: 41 pages, 16 figure
Fuzzy-Stochastic Partial Differential Equations
We introduce and study a new class of partial differential equations (PDEs)
with hybrid fuzzy-stochastic parameters, coined fuzzy-stochastic PDEs. Compared
to purely stochastic PDEs or purely fuzzy PDEs, fuzzy-stochastic PDEs offer
powerful models for accurate representation and propagation of hybrid
aleatoric-epistemic uncertainties inevitable in many real-world problems. We
will use the level-set representation of fuzzy functions and define the
solution to fuzzy-stochastic PDE problems through a corresponding parametric
problem, and further present theoretical results on the well-posedness and
regularity of such problems. We also propose a numerical strategy for computing
output fuzzy-stochastic quantities, such as fuzzy failure probabilities and
fuzzy probability distributions. We present two numerical examples to compute
various fuzzy-stochastic quantities and to demonstrate the applicability of
fuzzy-stochastic PDEs to complex engineering problems.Comment: 31 page
What are the Goals of Distributional Semantics?
Distributional semantic models have become a mainstay in NLP, providing
useful features for downstream tasks. However, assessing long-term progress
requires explicit long-term goals. In this paper, I take a broad linguistic
perspective, looking at how well current models can deal with various semantic
challenges. Given stark differences between models proposed in different
subfields, a broad perspective is needed to see how we could integrate them. I
conclude that, while linguistic insights can guide the design of model
architectures, future progress will require balancing the often conflicting
demands of linguistic expressiveness and computational tractability.Comment: To be published in Proceedings of the 58th Annual Meeting of the
Association for Computational Linguistics (ACL
On the analysis of set-based fuzzy quantified reasoning using classical syllogistics
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 support is cardinality calculus. In this paper we analyze fuzzy
syllogistic models previously described by Zadeh and Dubois et al. and compare
their behavior with that of the classical Aristotelian framework to check which
of the 24 classical valid syllogistic reasoning patterns or moods are
particular crisp cases of these fuzzy approaches. This allows us to assess to
what extent these approaches can be considered as either plausible extensions
of the classical crisp syllogism or a basis for a general approach to the
problem of approximate syllogism.Comment: 19 pages, 4 figure
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