A note on fuzzy Hilbert spaces

Daraby, Bayaz; Solimani, Zahra; Rahimi, Asghar

doi:10.3233/ifs-162143

Cited by 7 publications

(4 citation statements)

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“…The set of all fuzzy real numbers is denoted by F(R). If η ∈ F(R) and η(t) = 0 whenever t < 0, then η is called a non-negative fuzzy real number and F * (R) denotes the set of all non-negative fuzzy real numbers [3]. Definition 2.10.…”

Section: Definition 25 ([6]mentioning

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: Definition 25 ([6]mentioning

confidence: 99%

Weak fuzzy topology on vector spaces

Daraby

Khosravi

Rahimi

2021

Filomat

Self Cite

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“…The set of all fuzzy real numbers (fuzzy intervals) is denoted by F (R). If η ∈ F (R) and η(t) = 0 whenever t < 0, then η is called a non-negative fuzzy real number and F * (R) denotes the set of all non-negative fuzzy real numbers [3]. Definition 2.9.…”

Section: Preliminariesmentioning

confidence: 99%

Weak fuzzy topology on fuzzy topological vector spaces

Daraby,

Khosravi,

Rahimi

2019

Preprint

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

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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%