Generalized quasi-proximities

Yue, Yueli; Shi, Fu-Gui

doi:10.1016/j.fss.2006.09.008

Cited by 6 publications

(5 citation statements)

References 21 publications

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“…e (A) = e ≤B δ(B , A) for the given L-fuzzy quasi-proximity δ, see [15]. In fact, we can also prove the following similarly results.…”

Section: L-fuzzy Proximitysupporting

confidence: 69%

“…Subsequently, Liu [10], Artico and Moresco [2] extended it into L-fuzzy set theory. In [15], Yue extended the proximity theory in L-topology to L-fuzzy topology. see [15].…”

Section: Introductionmentioning

confidence: 99%

“…In [15], Yue extended the proximity theory in L-topology to L-fuzzy topology. see [15]. Motivated by that, in this paper we make a further research on the relationship between L-fuzzy topological spaces and L-fuzzy quasi-proximity spaces.…”

Section: Introductionmentioning

confidence: 99%

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L-Fuzzy Topological Spaces and L-Fuzzy Quasi-Proximity Spaces

Kim¹,

Ahn²,

Park³

2011

Honam Mathematical Journal

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“…e (A) = e ≤B δ(B , A) for the given L-fuzzy quasi-proximity δ, see [15]. In fact, we can also prove the following similarly results.…”

Section: L-fuzzy Proximitysupporting

confidence: 69%

“…Subsequently, Liu [10], Artico and Moresco [2] extended it into L-fuzzy set theory. In [15], Yue extended the proximity theory in L-topology to L-fuzzy topology. see [15].…”

Section: Introductionmentioning

confidence: 99%

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L-Fuzzy Topological Spaces and L-Fuzzy Quasi-Proximity Spaces

Kim¹,

Ahn²,

Park³

2011

Honam Mathematical Journal

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“…(1) ⊤ → x = x , x → ⊤ = ⊤ and ⊥ → x = ⊤, (2) If y ≤ z , then x → y ≤ x → z and z → x ≤ y → x, (3) x ≤ y iff x → y = ⊤ and x ∧ y ≤ z iff x ≤ y → z for x, y, z ∈ L, (4) x → (y ∧ z) = (x → y) ∧ (x → z) and (x ∨ y) → z = (x → z) ∧ (y → z), (5) (x ∧ y) → z = x → (y → z) = y → (x → z), (6) x ∧ (x → y) ≤ y and y ≤ x → (x ∧ y) and (x → y) → y ≥ x, (7) (x → ⊥) → (y → ⊥) = y → x, (8) x ∧ y = (x → (y → ⊥)) → ⊥, and x ∨ y = (x → ⊥) → y.…”

Section: Preliminariesmentioning

confidence: 99%

L-fuzzy pre-proximities, L-fuzzy filters and L-fuzzy grills

2020

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This article gives results on fixed complete lattice L-fuzzy pre-proximities, L-fuzzy grills and L-fuzzy filters. Moreover, we investigate the relations among the L-fuzzy pre-proximities , L-fuzzy grills and L-fuzzy filters. We show that there is a Galois correspondence between the category of separated L-fuzzy grill spaces and that of separated L-fuzzy pre-proximity spaces. We introduced the local function associated with L-fuzzy grill and L-fuzzy topology and studied some of its properties. Finally, we build an L-fuzzy topology for the corresponding L-fuzzy grill by using local function.

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“…The I-fuzzy proximity is defined on X I by [32] and it is generalized to the L-fuzzy proximity on X L [19].…”

Section: Induced Proximity In Fuzzy Spaces 121mentioning

confidence: 99%