Intuitionistic Fuzzy Sublattices and Ideals

Thomas, K. V.; Nair, Latha S.

doi:10.1007/s12543-011-0086-5

Cited by 6 publications

(4 citation statements)

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“…The concept of intuitionistic fuzzy lattice was introduced by Thomas and Nair [30] as an intuitionistic fuzzy set on a crisp lattice stable by the supremum and the infimum of the binary operations ⊓ and ⊔. For further details on intuitionistic fuzzy lattices, we refer to [24,29,30].…”

Section: Intuitionistic Fuzzy Latticesmentioning

confidence: 99%

“…Qin and Liu [21,26] introduced and investigated the properties of intuitionistic fuzzy filters on a residuated lattice. Thomas and Nair [29,30] studied intuitionistic fuzzy sublattices, intuitionistic fuzzy ideals and intuitionistic fuzzy filters on a lattice. In [35], Xu introduced the notion of interval valued intuitionistic (T, S)-fuzzy filter on a lattice implication algebra and some basic properties of it were obtained.…”

Section: Introductionmentioning

confidence: 99%

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Characterizations of intuitionistic fuzzy ideals and filters based on lattice operations

Milles¹,

Zedam²,

Rak³

2017

Journal of Fuzzy Set Valued Analysis

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In a recent paper, Thomas and Nair have introduced the notions of intuitionistic fuzzy ideal and intuitionistic fuzzy filter on a lattice and some basic properties were proved. In this paper, we characterize these notions in terms of the lattice operations and in terms of their associated crisp sets. We introduce the notions of prime intuitionistic fuzzy ideal and filter as interesting kinds, and then we investigate their various characterizations and different properties.

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Section: Intuitionistic Fuzzy Latticesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Characterizations of intuitionistic fuzzy ideals and filters based on lattice operations

Milles¹,

Zedam²,

Rak³

2017

Journal of Fuzzy Set Valued Analysis

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“…Definition 4 (see [11]). An IFS A of L is called an intuitionistic fuzzy ideal (IFI) of L if the following conditions are satisfied.…”

Section: Preliminariesmentioning

confidence: 99%

Quotient of Ideals of an Intuitionistic Fuzzy Lattice

Thomas

Nair

2010

Advances in Fuzzy Systems

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“…Later, Ajmal and Thomas [5] specifically applied the concept of FSs in lattice theory and developed the theory of fuzzy sublattices (FSLs). Thereafter, Thomas and Nair [3] introduced the concept of intuitionistic fuzzy sublattices (IFSLs) in 2011. Characterization of intuitionistic fuzzy ideals and filters based on lattice operations were studied by Milles [11] in 2017.…”

Section: Introductionmentioning

confidence: 99%