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Embedding Theorem
Existence Theorem
Fuzzy Set
Modular Lattice
Relation Algebra
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REDUCING FUZZY ALGEBRA TO CLASSICAL ALGEBRA
REDUCING FUZZY ALGEBRA TO CLASSICAL ALGEBRA,ARTHUR WEINBERGER
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REDUCING FUZZY ALGEBRA TO CLASSICAL ALGEBRA
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Citations: 3
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ARTHUR WEINBERGER
This paper presents three main ideas. They are the Metatheorem, the lattice embedding for sets, and the lattice embedding for algebras.The Metatheorem allows you to convert existing theorems about classical subsets into corresponding theorem about fuzzy subsets. The concept of a fuzzyfiable operation on a powerset is defined. The main result states that any implication or identity which can be stated using fuzzyfiable operations is true about fuzzy subsets if and only if it is true about classical subsets.The lattice
embedding theorem
for sets shows that for any set X, there is a set Y such that the lattice of fuzzy subsets of X is isomorphic to a sublattice of the classical subsets of Y. In fact it is further proved that if X is infinite, then we can choose Y = X and get the surprising result that the lattice of fuzzy subsets of X is isomorphic to a sublattice of the classical subsets of X itself. The idea is illustrated with an example explicitly showing how the lattice of fuzzy subsets of the closed unit interval 𝕀 = [0,1] embeds into the lattice of classical subsets of 𝕀.The lattice
embedding theorem
for algebras shows that under certain circumstances the lattice of fuzzy subalgebras of an algebra A embeds into the lattice of classical subalgebras of a closely related algebra A′. The following sample use of this embeding theorem is given. It is a well known fact that the lattice of normal subgroups of a group is a modular lattice. The embeding theorem is used here to conclude that lattice of fuzzy normal subgroups of a group is a
modular lattice
too.
Published in 2005.
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References
(9)
The Lattice of Fuzzy Normal Subgroups in Modular
(
Citations: 10
)
Naseem Ajmal
Journal:
Information Sciences  ISCI
, vol. 83, no. 3&4, pp. 199209, 1995
Embedding lattices of fuzzy subgroups into lattices of crisp subgroups
(
Citations: 1
)
T. Head
Conference:
Conference of the North American Fuzzy Information Processing Society  NAFIPS
, 1996
A metatheorem for deriving fuzzy theorems from crisp versions
(
Citations: 6
)
Tom Head
Journal:
Fuzzy Sets and Systems  FSS
, vol. 73, no. 3, pp. 349358, 1995
The Lattices of Fuzzy Subgroups and Fuzzy Normal Subgroups
(
Citations: 15
)
Naseem Ajmal
,
K. V. Thomas
Journal:
Information Sciences  ISCI
, vol. 76, no. 12, pp. 111, 1994
Modularity of the QuasiHamiltonian Fuzzy Subgroups
(
Citations: 8
)
K. C. Gupta
,
Suryansu Ray
Journal:
Information Sciences  ISCI
, vol. 79, no. 34, pp. 233250, 1994
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Citations
(3)
Distributivity in lattices of fuzzy subgroups
(
Citations: 3
)
Marius Tarnauceanu
Journal:
Information Sciences  ISCI
, vol. 179, no. 8, pp. 11631168, 2009
On the number of fuzzy subgroups of finite abelian groups
(
Citations: 4
)
Marius Tarnauceanu
,
Lucian Bentea
Journal:
Fuzzy Sets and Systems  FSS
, vol. 159, no. 9, pp. 10841096, 2008
General form of latticevalued fuzzy sets under the cutworthy approach
(
Citations: 3
)
Marijana Gorjanacranitovic
,
Andreja Tepavcevic
Journal:
Fuzzy Sets and Systems  FSS
, vol. 158, no. 11, pp. 12131216, 2007