Piecewise-linear approximation of non-linear models based on probabilistically/possibilistically interpreted intervals’ numbers (INs)

Papadakis, Stelios; Kaburlasos, Vassilis G.

doi:10.1016/j.ins.2010.03.023

Cited by 50 publications

(28 citation statements)

References 61 publications

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“…In fact it is a lattice, as shown by the following well-known theorem. 1 The empty interval may be denoted as [ 1 , 2 ] with any 1 , 2 such that…”

Section: B Intervals' Numbers (Ins)mentioning

confidence: 99%

“…It is well known that a fuzzy subset is fully determined by the family of its ℎ-cuts (i.e., { ℎ } ℎ∈ [0,1] ) as shown next.…”

Section: B Intervals' Numbers (Ins)mentioning

confidence: 99%

“…An Intervals' Number, or IN for short, is a mathematical object that may represent either a fuzzy interval or a distribution of numeric data samples [1]. The space of INs has been studied in the literature.…”

Section: Introductionmentioning

confidence: 99%

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Intervals' Numbers (INs) interpolation/extrapolation

Kaburlasos

Papakostas

Pachidis

et al. 2013

2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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An Intervals' Number (IN) is a mathematical object known to represent either a probability distribution or a possibility distribution. The space of INs has been studied during the last years. After summarizing some instrumental mathematical results, this work demonstrates comparatively novel schemes for tunable fuzzy rule interpolation and extrapolation. Extensions to Type-2 fuzzy sets are straightforward. Finally, this work demonstrates a preliminary application, regarding the reconstruction of partially occluded human facial expressions, based on a neural network that may predict a data distribution from other ones. Far reaching extensions of the proposed techniques are discussed.

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“…In fact it is a lattice, as shown by the following well-known theorem. 1 The empty interval may be denoted as [ 1 , 2 ] with any 1 , 2 such that…”

Section: B Intervals' Numbers (Ins)mentioning

confidence: 99%

“…It is well known that a fuzzy subset is fully determined by the family of its ℎ-cuts (i.e., { ℎ } ℎ∈ [0,1] ) as shown next.…”

Section: B Intervals' Numbers (Ins)mentioning

confidence: 99%

See 1 more Smart Citation

Intervals' Numbers (INs) interpolation/extrapolation

Kaburlasos

Papakostas

Pachidis

et al. 2013

2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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“…In fact, the weak order is actually just the Cartesian product ≤ × ≤ of the natural order ≤ on R, whereas the containment order is defined as ≥ × ≤ (Papadakis et al (2010)). …”

Section: Possible Orders Between Intervals: What Is Knownmentioning

confidence: 99%

Orders on intervals over partially ordered sets: extending Allen’s algebra and interval graph results

et al. 2013

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To make a decision, we need to compare the values of quantities. In many practical situations, we know the values with interval uncertainty. In such situations, we need to compare intervals. Allen's algebra describes all possible relations between intervals on the real line which are generated by the ordering of endpoints; ordering relations between such intervals have also been well studied. In this paper, we extend this description to intervals in an arbitrary partially ordered set (poset). In particular, we explicitly describe ordering relations between intervals that generalize relation between points. As auxiliary results, we provide a logical interpretation of the relation between intervals, and extend the results about interval graphs to intervals over posets.

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“…Clusterwise regression analysis is extensively discussed in the theoretical literature (see, for example, [20][21][22]29,30,60,40,31,32,35,25,41,45,51,55,17,33,61,26,27,42,44,46,47,52,54,62,58]), and furthermore, finds application in several fields, such as market segmentation and business, socio-economics, biology, engineering, and so on (see, for instance [2,20,40,57]). …”

Section: Introductionmentioning

confidence: 99%