Results 11 to 20 of about 1,470 (111)
On completable fuzzy metric spaces [PDF]
Fuzzy Sets and Systems, 2015 In this paper we construct a non-completable fuzzy metric space in the sense of George and Veeramani which allows to answer an open question related to continuity on the real parameter t. In addition, the constructed space is not strong (non-Archimedean).
Valentin Gregori +2 more
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On Principal Fuzzy Metric Spaces
Mathematics, 2022 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 ...
Valentín Gregori +3 more
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An identification theorem for the completion of the Hausdorff fuzzy metric [PDF]
Fuzzy Sets and Systems, 2013 We prove that given a fuzzy metric space (in the sense of Kramosil and Michalek), the completion of its Hausdorff fuzzy metric space is isometric to the Hausdorff fuzzy metric space of its completion, when the Hausdorff fuzzy metrics are defined on the respective collections of non-empty closed subsets.
Javier Gutierrez Garcia +2 more
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On the Axiomatic of GV-Fuzzy Metric Spaces and Its Completion
AxiomsThe concept of fuzzy metric space introduced by Kramosil and Michalek was later slightly modified by George and Veeramani who imposed three additional restrictions on it.
Valentín Gregori +3 more
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On completion of fuzzy quasi-metric spaces
Topology and Its Applications, 2005 A sequence \(\{x_n\}\) in a fuzzy quasi-metric space \((X,M)\) is called a Cauchy sequence if there exists a sequence \(\{y_m\}\) such that \(\lim_{m,n}M(y_m,x_n,t)=1\) for all \(t>0\). By means of the above notion, the authors introduce the completion of a fuzzy quasi-metric space, and investigate its properties.
Valentin Gregori, Almanzor Sapena
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The completion of fuzzy metric spaces
Journal of Mathematical Analysis and Applications, 1985 In a previous paper [Fuzzy Sets Syst. 12, 215-229 (1984; Zbl 0558.54003)], the author jointly with \textit{S. Seikkala} introduced the notion of a fuzzy metric spaces. Now he discusses the completion of such space. For some type of fuzzy metric spaces, the author proves that there is a completion which is unique up to isometry.
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On weak G-completeness for fuzzy metric spaces [PDF]
Soft Computing, 2022 In this paper, we provide equivalent characterizations of weak $G$-complete fuzzy metric spaces. Since such spaces are complete, we also characterize fuzzy metric spaces that have weak $G$-complete fuzzy metric completions. Moreover we establish analogous results for classical metric spaces.
Sugata Adhya, A. Deb Ray
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Adaptive kernel fuzzy clustering for missing data
PLoS ONE, 2021 Many machine learning procedures, including clustering analysis are often affected by missing values. This work aims to propose and evaluate a Kernel Fuzzy C-means clustering algorithm considering the kernelization of the metric with local adaptive ...
Anny K. G. Rodrigues +2 more
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A characterization of p-complete fuzzy metric spaces
Fuzzy Sets and Systems, 2022 [EN] George and Veeramani characterized complete fuzzy metric spaces ¿ by means of nested sequences of closed sets of X which have fuzzy diameter zero. According to the concept of p-convergence due to D. Mihet, an appropriate concept of p-Cauchy sequence was given. In this paper we introduce for a concept of p-fuzzy diameter zero, which is according to
Valentín Gregori +3 more
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COMPLETE INVARIANT FUZZY METRICS ON SEMIGROUPS AND GROUPS
Journal of Applied Analysis & Computation, 2021 Summary: In this paper, we study the Raǐkov completion of invariant fuzzy metric groups and complete fuzzy metric semigroups (in the sense of Kramosil and Michael). We establish that: (1) if \((G, M,\ast)\) is a fuzzy metric group such that \((M,\ast)\) is invariant, then the Raǐkov completion \(\varrho G\) of \((G,\tau_M)\) is a fuzzy metric group \((\
Tu, Jin-Ji, Xie, Li-Hong
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