L-E-Fuzzy Lattices

Šešelja, Branimir; Tepavčević, Andreja

doi:10.1007/s40815-015-0057-9

Cited by 8 publications

(3 citation statements)

References 19 publications

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“…Among all the existing extensions, two of them are considered to be the main ones. On the one hand, some authors define a fuzzy lattice as a fuzzy subset of a (classical) lattice that is compatible with the lattice structure in one way or another [23,24]. This particular extension could be called that of fuzzy sublattices.…”

Section: Introductionmentioning

confidence: 99%

Characterizing closure systems in the graded setting - CMMSE

Ojeda-Hernandez,

Cabrera,

Cordero

et al. 2024

Preprint

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Closure systems play a major role in both pure and applied mathematics. This paperpresents an extension of the notion of closure system, which is done adapting theidea of meet-subsemilattice to a complete fuzzy lattice. This extension is carried outon two levels, first as crisp sets and then as fuzzy sets. In both cases, the one-to-onerelations between closure operators and closure systems that hold in the classicalcase are extended properly to this framework. Furthermore, a novel characterizationfor a closure system is established.

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Section: Introductionmentioning

confidence: 99%

Characterizing closure systems in the graded setting - CMMSE

Ojeda-Hernandez,

Cabrera,

Cordero

et al. 2024

Preprint

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“…On the one hand, some authors define a fuzzy lattice as a fuzzy subset of a (classical) lattice L that is compatible with the structure of the lattice in some manner [21,23]. This particular extension could be called that of fuzzy sublattices.…”

Section: Introductionmentioning

confidence: 99%

Closure Systems as a Fuzzy Extension of Meet-subsemilattices

Ojeda-Hernández¹,

Cabrera²,

Muñoz‐Velasco³

2021

Atlantis Studies in Uncertainty Modelling

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An extension of the notion of closure system is studied adapting the idea of meetsubsemilattice to a complete fuzzy lattice. Results relating closure operators and closure systems in the classical case are extended properly to this framework. This definition is proved to be equivalent to the most used definition given by Bělohlávek on the fuzzy powerset lattice. A definition of fuzzy closure system is presented and related to closure systems. Atlantis Studies in Uncertainty Modelling, volume 3Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)

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“…Of the three research areas mentioned, order theory undoubtedly is the youngest. In recent years, as order and partial ordered set theory were widely applied in the combinatorics [1,9,13,37,43], fuzzy mathematics [7,32,40,42,44], computer science [2,39], and even in the social science [14,15] etc.…”

Section: Introductionmentioning

confidence: 99%

A new view of relationship between atomic posets and complete (algebraic) lattices

2017

Open Mathematics

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L-E-Fuzzy Lattices

Cited by 8 publications

References 19 publications

Characterizing closure systems in the graded setting - CMMSE

Characterizing closure systems in the graded setting - CMMSE

Closure Systems as a Fuzzy Extension of Meet-subsemilattices

A new view of relationship between atomic posets and complete (algebraic) lattices

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