Displaying similar documents to “Some operations on lattice implication algebras.”

Lattices of fuzzy objects.

Sangalli, Arturo A.L. (1996)

International Journal of Mathematics and Mathematical Sciences

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The embedding of the formal concept analysis into the L-Fuzzy concept theory.

Ana Burusco Juandeaburre, Ramón Fuentes-González (1998)

Mathware and Soft Computing

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In this work, we study the relation between the concept lattice of Wille ([5], [6]) and the L-Fuzzy concept lattice ([2]) developed by us. To do it, we have defined an application g that associates to each concept of Wille an L-Fuzzy concept. The main point of this work is to prove that if we are working with a crisp relation between an object set and an attribute set, the concept lattice of Wille is a sublattice of the L-Fuzzy concept lattice. At the end, we show a typical example in...

Fuzzy sets (in)equations with a complete codomain lattice

Vanja Stepanović, Andreja Tepavčević (2022)

Kybernetika

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The paper applies some properties of the monotonous operators on the complete lattices to problems of the existence and the construction of the solutions to some fuzzy relational equations, inequations, and their systems, taking a complete lattice for the codomain lattice. The existing solutions are extremal - the least or the greatest, thus we prove some extremal problems related to fuzzy sets (in)equations. Also, some properties of upper-continuous lattices are proved and applied to...

Classes of fuzzy filters of residuated lattice ordered monoids

Jiří Rachůnek, Dana Šalounová (2010)

Mathematica Bohemica

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The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (monoids) are common generalizations of BL -algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain information, sets of provable formulas in inference systems could be described by fuzzy filters...

The study of the L-fuzzy concept lattice.

Ana Burusco Juandeaburre, Ramón Fuentes-González (1994)

Mathware and Soft Computing

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The L-Fuzzy concept theory that we have developed sets up classifications from the objects and attributes of a context through L-Fuzzy relations. This theory generalizes the formal concept theory of R. Wille. In this paper we begin with the L-Fuzzy concept definition that generalizes the definitions of the formal concept theory, and we study the lattice structure of the L-Fuzzy concept set, giving a constructive method for calculating this lattice. At the end, we apply this constructive...

Lattice valued intuitionistic fuzzy sets

Tadeusz Gerstenkorn, Andreja Tepavĉević (2004)

Open Mathematics

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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.

Fuzzy n-fold integral filters in BL-algebras

Rajab Ali Borzooei, Akbar Paad (2013)

Discussiones Mathematicae - General Algebra and Applications

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In this paper, we introduce the notion of fuzzy n-fold integral filter in BL-algebras and we state and prove several properties of fuzzy n-fold integral filters. Using a level subset of a fuzzy set in a BL-algebra, we give a characterization of fuzzy n-fold integral filters. Also, we prove that the homomorphic image and preimage of fuzzy n-fold integral filters are also fuzzy n-fold integral filters. Finally, we study the relationship among fuzzy n-fold obstinate filters, fuzzy n-fold...