Some Properties of Fuzzy Hilbert Spaces

Daraby, Bayaz; Solimani, Zahra; Rahimi, Asghar

doi:10.1007/s11785-016-0581-0

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Cited by 8 publications

(4 citation statements)

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“…al. ([3,4]) redefined the idea of Felbin's [8] definition of fuzzy norm and studied various properties of its topological structure. Das [5] constructed a fuzzy topology generated by fuzzy norm and studied some properties of this topology.…”

Section: Introductionmentioning

confidence: 99%

Weak fuzzy topology on vector spaces

Daraby

Khosravi

Rahimi

2021

Filomat

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In this paper, we study the concept of weak linear fuzzy topology on a fuzzy topological vector space as a generalization of usual weak topology. We prove that this fuzzy topology consists of all weakly lower semi-continuous fuzzy sets on a given vector space when K (R or C) endowed with its usual fuzzy topology. In the case that the fuzzy topology of K is different from the usual fuzzy topology, we show that the weak fuzzy topology is not equivalent with the fuzzy topology of weakly lower semi-continuous fuzzy sets.

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Section: Introductionmentioning

confidence: 99%

Weak fuzzy topology on vector spaces

Daraby

Khosravi

Rahimi

2021

Filomat

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“…In 2015, Saheli conducted a comparative study of the relationship between Goudarzia's definition and Hasankhani's definition for a fuzzy inner product (see [9][10][11]). In 2017, Daraby et al [12] conducted a study about topological properties of fuzzy inner product spaces in Hasankhani's contexts. In 2019, J. M. Kim and K. Y. Lee [13] consider approximation properties in Felbin fuzzy normed spaces.…”

Section: Introductionmentioning

confidence: 99%

Absence of Non-Trivial Fuzzy Inner Product Spaces and the Cauchy–Schwartz Inequality

Byun

Lee

2020

Mathematics

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“…al. [5,6], redefined the notion of Felbin's [10] definition of fuzzy norm. Das [7] introduced a fuzzy topology generated by fuzzy norm and studied some properties of this topology.…”

Section: Introductionmentioning

confidence: 99%