Results 181 to 190 of about 224 (217)

Double Approximation and Complete Lattices

Fundamenta Informaticae, 2009
We explore lattice theoretic aspects in rough set theory in terms of the duality between algebra and representation. Approximation spaces are dual to complete atomic Boolean algebras in the sense that there is an adjunction between corresponding suitable categories.
Taichi Haruna, Yukio-Pegio Gunji
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A COMPLETENESS THEOREM FOR CORRELATION LATTICES

Mathematical Logic Quarterly, 1983
In this paper the authors study the varieties \(A_ n\), n fixed odd, of all Boolean correlation lattices. They obtain a characterization of simple algebras and prove that they are functionally complete; they also show that the variety \(A_ n\) is arithmetical.
Dietmar Schweigert, Magdalena Szymanska
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Completeness in Semi-Lattices

Canadian Journal of Mathematics, 1957
Let (X, ≤) be a partially ordered set, that is, X is a set and ≤ is a reflexive, anti-symmetric, transitive, binary relation on X.We write,for each x ∈ X. If, moreover,exists for each x and y in X, then (X, ≤) is said to be a semi-lattice.
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The Complete Congruence Lattice of a Complete Lattice

1990
G. Birkhoff [1] raised the following question in 1945: Is every complete lattice isomorphic to the lattice of congruence relations of a suitable (infinitary) algebra? In 1948, Birkhoff restated this question in the Second Edition of his Lattice Theory [2]; however, “(infinitary)” was dropped from the question. This was intentional; G. Birkhoff referred
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Decompositions in Complete Lattices

Algebra and Logic, 2001
A series of results on the existence of various kinds of decompositions in upper continuous lattices, lower continuous lattices, and some other types of lattices are proven.
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On Convergence of Sequences in Complete Lattices

Order, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Characterizations of Complete Sublattices of a Given Complete Lattice

Southeast Asian Bulletin of Mathematics, 2001
Let \(L\) be a complete lattice. A mapping \(\varphi\) of \(L\) into itself is called a closure operator if \(\varphi (x)\geq x\) and \(\varphi (\varphi ( x))=\varphi (x)\) for all \(x\in X\) and \(\varphi (x)\leq\varphi (y)\) whenever \(x\leq y\) for all \(x,y\in L\). The dual notion is that one of a kernel operator.
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OWA Operators on Complete Lattices

IEEE Transactions on Fuzzy Systems, 2018
Considering some aggregation functions, we define ${\bf B}$ - $ A$ -weighting vectors. Then, a definition for ordered weighted average (OWA) operators is given based on ${\bf B}$ - $ A$ -weighting vectors. Moreover, we show that our proposed definition for OWA operators over complete lattices is a generalization of the given definition by ...
Radko Mesiar, Fateme Kouchakinejad, Alexandra Siposová, Mashaallah Mashinchi   +3 more
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Logical operators on complete lattices

Information Sciences, 1991
A concept of consistency among logical operators is given with a criterion to decide whether a group of logical operators is suitable for fuzzy reasoning. Also, a necessary and sufficient condition for a kind of logical operators on \([0,1]\) is obtained.
Ma Zherui, Wu Wangming
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Complete lattices

2020
The theory of complete lattices is described in the language of set theory. The use of Hasse diagrams to represent finite lattices is described. Boolean lattices are defined and de Morgan's Laws are introduced. Regular closed sets are studied as an example of such lattices. Boolean functions and their representations are defined.
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