Non-additive interval-valued F-transform

Strauss, Olivier

doi:10.1016/j.fss.2014.08.006

Cited by 9 publications

(2 citation statements)

References 34 publications

(79 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To do so, we used the so-called imprecise filtering sub-sampling method [10]. It consists of replacing the smoothing anti-aliasing kernel used to transform a high resolution image into a low resolution image by a capacity that represents a convex set of bell-shaped smoothing kernels.…”

Section: Methodsmentioning

confidence: 99%

Comparing Interval-Valued Estimations with Point-Valued Estimations

Saulnier

Strauss

Couso

2016

Communications in Computer and Information Science

View full text Add to dashboard Cite

In the last decade, numerous proposals have been made to deal with imprecision in estimation problems. Those approaches, many of which involve dealing with interval-valued outputs, deal with the subtle difference between uncertainty and imprecision. One of the crucial points − which to our knowledge has never been addressed − is "how to compare an interval-valued method with a precise valued method?"The usual way to compare two estimation methods is to use benchmark data with ground truths and to compute a distance between the estimates of each method and the ground truth. However, most of the mathematical available extensions of distances are either biased in favor of a precise approach or in favor of an imprecise approach.This paper proposes a new tool, the weighted variation of the midpoint distance (WVD), that is more suitable to achieve this kind of comparison, dealing with imprecision with a particular semantic. After reviewing existing distances, we introduce the WVD, first from an intuitive perspective, then from a more mathematical point of view. Its very satisfactory properties are highlighted through an experiment.

show abstract

Section: Methodsmentioning

confidence: 99%

Comparing Interval-Valued Estimations with Point-Valued Estimations

Saulnier

Strauss

Couso

2016

Communications in Computer and Information Science

View full text Add to dashboard Cite

show abstract

“…This technique has been used in [17] under the name of imprecise fuzzy transformation to obtain an interval-valued impulse response [ψ(x), ψ(x)] (x ∈ Z) of all the values that could have been obtained by considering a family of sampling kernels represented by π.…”

Section: Sampling and Fuzzy Transformationmentioning

confidence: 99%

Using Atomic Bounds to Get Sub-modular Approximations

Destercke

Rico²,

Strauss³

2022

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Set functions and inferences over them play an important role in many AI-related problems. They are commonly used in kernel-based methods, game theory, uncertainty representation and preference modelling. Of particular importance are additive set-functions and their associated expectation operator, as well as sub-modular functions. However, specifying precisely and completely such set functions can be a daunting task as well as a lot of data and knowledge. When time or information is missing, it may be handy to have approximating tools of such set-functions, that require less information and possibly enjoy nice mathematical properties. In this paper, we show that if the only information we have are atomic bounds of such functions, we can build conservative approximations that are either sub-or super-modular. We then illustrate the potential use of our approximation on a convolution-based signal processing problem.

show abstract