Histogram density estimators based upon a fuzzy partition

Loquin, Kevin; Strauss, Olivier

doi:10.1016/j.spl.2008.01.053

Cited by 23 publications

(27 citation statements)

References 5 publications

(5 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1 For our investigation of necessary and sufficient condition of uniform fuzzy partitions, we will consider uniform fuzzy partitions of the real line defined as follows (cf. [2]). Definition 2.2.…”

Section: Necessary and Sufficient Conditions For Uniform Fuzzy Partitmentioning

confidence: 99%

Necessary and sufficient conditions for generalized uniform fuzzy partitions

Holčapek

Perfilieva

Novák

et al. 2015

Fuzzy Sets and Systems

View full text Add to dashboard Cite

The fundamental concept in the theory of fuzzy transform (F-transform) is that of fuzzy partition. The original definition assumes that each two fuzzy subsets overlap in such a way that sum of membership degrees in each point is equal to 1. However, this condition can be generalized to obtain a denser fuzzy partition that leads to improvement of approximation properties of Ftransform. However, a problem arises how one can effectively construct such type of fuzzy partitions. We use a generating function having special properties and it is not immediately clear whether it really defines a general uniform fuzzy partition. In this paper, we provide necessary and sufficient condition using which we can solve this task so that optimal generalized uniform fuzzy partition can be designed more easily. This is important in various practical applications of the F-transform, for example in image processing, time series analysis, solving differential equations with boundary conditions, and other ones.

show abstract

Section: Necessary and Sufficient Conditions For Uniform Fuzzy Partitmentioning

confidence: 99%

Necessary and sufficient conditions for generalized uniform fuzzy partitions

Holčapek

Perfilieva

Novák

et al. 2015

Fuzzy Sets and Systems

View full text Add to dashboard Cite

show abstract

“…It consists of transferring the value of a k to W proportionally to the coverage of W and C k . A similar counting transfer has been used to prove the convergence of fpbh in mean squared error [21] and integrated mean square error [47].…”

Section: Precise Pignistic Counting Transfermentioning

confidence: 99%

“…which is the interpolating method proposed in [20,21,32,35,44]. Note that using the precise pignistic transfer to estimate the votes purporting a crisp subset W of coincides with estimating these votes via a Parzen-Rosenblatt kernel density estimation.…”

Section: Article In Pressmentioning

confidence: 99%

“…Then we estimate the number of observations purporting each crisp interval W i by different transfer methods (see Section 4). This estimation is then normalized by using expressions (20) and (21). In this experiment, the different summative kernels were adapted to the partition granularity [19].…”

Section: Counting Transfer and Density Estimationmentioning

confidence: 99%

“…Convergence of such fuzzy-partition-based histograms (fpbh) to the underlying pdf has been proved in mean squared error [21] and integrated mean square error [47]. The reduced sensitivity to the choice of partition compared to the crisp case was shown in [20].…”

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

Quasi-continuous histograms

Strauss

2009

Fuzzy Sets and Systems

Self Cite

View full text Add to dashboard Cite

Histograms are very useful for summarizing statistical information associated with a set of observed data. They are one of the most frequently used density estimators due to their ease of implementation and interpretation. However, histograms suffer from a high sensitivity to the choice of both reference interval and bin width. This paper addresses this difficulty by means of a fuzzy partition. We propose a new density estimator based on transferring the counts associated with each cell of the fuzzy partition to any subset of the reference interval. We introduce three different methods of achieving this transfer. The properties of each method are illustrated with a classic real observation set. The density estimator obtained relates to the Parzen-Rosenblatt kernel density estimation technique. In this paper, we only consider the monovariate case with precise and imprecise observations.

show abstract

Fuzzy Relational Models

Dexter

2012

Monitoring and Control of Information‐Poor Systems

View full text Add to dashboard Cite

Histogram density estimators based upon a fuzzy partition

Cited by 23 publications

References 5 publications

Necessary and sufficient conditions for generalized uniform fuzzy partitions

Necessary and sufficient conditions for generalized uniform fuzzy partitions

Quasi-continuous histograms

Fuzzy Relational Models

Contact Info

Product

Resources

About