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Lattice valued intuitionistic fuzzy sets

100%
Gerstenkorn T., Tepavĉević A.
Open Mathematics
|
2004
|
tom 2
|
nr 3
388-398
EN
In this paper a new definition of a lattice valued intuitionistic fuzzy set (LIFS) is introduced, in an attempt to overcome the disadvantages of earlier definitions. Some properties of this kind of fuzzy sets and their basic operations are given. The theorem of synthesis is proved: For every two families of subsets of a set satisfying certain conditions, there is an lattice valued intuitionistic fuzzy set for which these are families of level sets.
2
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Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras

84%
Cabrer L., Celani S.
Open Mathematics
|
2006
|
tom 4
|
nr 4
600-623
EN
In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 604). These dualities are obtained by restricting the duality given by the second author for DLFI-algebras by means of Priestley spaces with ternary relations (see [2]). We translate the equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space.
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