Displaying similar documents to “Approximate quantities, hyperspaces and metric completeness”

Partial Fuzzy Metric Space and Some Fixed Point Results

Shaban Sedghi, Nabi Shobkolaei, Ishak Altun (2015)

Communications in Mathematics

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In this paper, we introduce the concept of partial fuzzy metric on a nonempty set X and give the topological structure and some properties of partial fuzzy metric space. Then some fixed point results are provided.

Note on the Wijsman hyperspaces of completely metrizable spaces

J. Chaber, R. Pol (2002)

Bollettino dell'Unione Matematica Italiana

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We consider the hyperspace C ⁢ L ⁢ X of nonempty closed subsets of completely metrizable space X endowed with the Wijsman topologies τ W d . If X is separable and d , e are two metrics generating the topology of X , every countable set closed in C ⁢ L ⁢ X , τ W e has isolated points in C ⁢ L ⁢ X , τ W d . For d = e , this implies a theorem of Costantini on topological completeness of C ⁢ L ⁢ X , τ W d . We show that for nonseparable X the hyperspace C ⁢ L ⁢ X , τ W d may contain a closed copy of the rationals. This answers a question of Zsilinszky.

On generalizations of fuzzy metric spaces

Yi Shi, Wei Yao (2023)

Kybernetika

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The aim of the paper is to present three-variable generalizations of fuzzy metric spaces in sense of George and Veeramani from functional and topological points of view, respectively. From the viewpoint of functional generalization, we introduce a notion of generalized fuzzy 2-metric spaces, study their topological properties, and point out that it is also a common generalization of both tripled fuzzy metric spaces proposed by Tian et al. and ℳ -fuzzy metric spaces proposed by Sedghi...

Preservation of properties of fuzzy relations during aggregation processes

Józef Drewniak, Urszula Dudziak (2007)

Kybernetika

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Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by n -ary operations is considered. Namely, with the use of fuzzy relations R 1 , ... , R n and n -argument operation F on the interval [ 0 , 1 ] , a new fuzzy relation R F = F ( R 1 , ... , R n ) is created....