Completable fuzzy metric spaces

Gregori, Valentı́n; Miñana, Juan-José; Sapena, Almanzor

doi:10.1016/j.topol.2017.04.016

Cited by 8 publications

(3 citation statements)

References 22 publications

(17 reference statements)

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“…where F σ represents a parameter which will be analyzed in Section 3, and · is the Euclidean norm. This function was selected because it can be considered a fuzzy metric in consonance with the notion given in [36] and it has been proven to be adequate in the context of fuzzy image denoising [10,14,37]. This similarity function ρ is valued within [0, 1] and verifies ρ(x 0 ,…”

Section: Gaussian Noise Reductionmentioning

confidence: 99%

Hybrid Filter Based on Fuzzy Techniques for Mixed Noise Reduction in Color Images

Arnal

Súcar

2019

Applied Sciences

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To decrease contamination from a mixed combination of impulse and Gaussian noise on color digital images, a novel hybrid filter is proposed. The new technique is composed of two stages. A filter based on a fuzzy metric is used for the reduction of impulse noise at the first stage. At the second stage, to remove Gaussian noise, a fuzzy peer group method is applied on the image generated from the previous stage. The performance of the introduced algorithm was evaluated on standard test images employing widely used objective quality metrics. The new approach can efficiently reduce both impulse and Gaussian noise, as much as mixed noise. The proposed filtering method was compared to the state-of-the-art methodologies: adaptive nearest neighbor filter, alternating projections filter, color block-matching 3D filter, fuzzy peer group averaging filter, partition-based trimmed vector median filter, trilateral filter, fuzzy wavelet shrinkage denoising filter, graph regularization filter, iterative peer group switching vector filter, peer group method, and the fuzzy vector median method. The experiments demonstrated that the introduced noise reduction technique outperforms those state-of-the-art filters with respect to the metrics peak signal to noise ratio (PSNR), the mean absolute error (MAE), and the normalized color difference (NCD).

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Section: Gaussian Noise Reductionmentioning

confidence: 99%

Hybrid Filter Based on Fuzzy Techniques for Mixed Noise Reduction in Color Images

Arnal

Súcar

2019

Applied Sciences

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“…In Equation ( 4), F σ is a parameter studied in Section 3. This function has been selected in view of the fact that it is a fuzzy metric according to definition presented in [39], and it has been shown to be convenient in the topic of fuzzy image filtering [9,20,40]. This similarity function ρ takes values in the interval [0, 1] and fulfills ρ(x 0 , x i ) = 1 for x 0 = x (i) .…”

Section: Gaussian Noise Removalmentioning

confidence: 99%

Fast Method Based on Fuzzy Logic for Gaussian-Impulsive Noise Reduction in CT Medical Images

Arnal

Súcar

2022

Mathematics

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To remove Gaussian-impulsive mixed noise in CT medical images, a parallel filter based on fuzzy logic is applied. The used methodology is structured in two steps. A method based on a fuzzy metric is applied to remove the impulsive noise at the first step. To reduce Gaussian noise, at the second step, a fuzzy peer group filter is used on the filtered image obtained at the first step. A comparative analysis with state-of-the-art methods is performed on CT medical images using qualitative and quantitative measures evidencing the effectiveness of the proposed algorithm. The parallel method is parallelized on shared memory multiprocessors. After applying parallel computing strategies, the obtained computing times indicate that the introduced filter enables to reduce Gaussian-impulse mixed noise on CT medical images in real-time.

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“…Explanatory 1. The problem of finding fuzzy metrics satisfying condition (c2) was approached in [25]. There, a family of fuzzy metrics was found, called stratified, that satisfy (c2).…”

Section: Examplementioning

confidence: 99%

On Principal Fuzzy Metric Spaces

et al. 2022

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In this paper, we deal with the notion of fuzzy metric space (X,M,∗), or simply X, due to George and Veeramani. It is well known that such fuzzy metric spaces, in general, are not completable and also that there exist p-Cauchy sequences which are not Cauchy. We prove that if every p-Cauchy sequence in X is Cauchy, then X is principal, and we observe that the converse is false, in general. Hence, we introduce and study a stronger concept than principal, called strongly principal. Moreover, X is called weak p-complete if every p-Cauchy sequence is p-convergent. We prove that if X is strongly principal (or weak p-complete principal), then the family of p-Cauchy sequences agrees with the family of Cauchy sequences. Among other results related to completeness, we prove that every strongly principal fuzzy metric space where M is strong with respect to an integral (positive) t-norm ∗ admits completion.

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Completable fuzzy metric spaces

Cited by 8 publications

References 22 publications

Hybrid Filter Based on Fuzzy Techniques for Mixed Noise Reduction in Color Images

Hybrid Filter Based on Fuzzy Techniques for Mixed Noise Reduction in Color Images

Fast Method Based on Fuzzy Logic for Gaussian-Impulsive Noise Reduction in CT Medical Images

On Principal Fuzzy Metric Spaces

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