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Additive closure operators on abelian unital l -groups

Filip Švrček (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In the paper an additive closure operator on an abelian unital l -group ( G , u ) is introduced and one studies the mutual relation of such operators and of additive closure ones on the M V -algebra Γ ( G , u ) .

Adjoint Semilattice and Minimal Brouwerian Extensions of a Hilbert Algebra

Jānis Cīrulis (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Let A : = ( A , → , 1 ) be a Hilbert algebra. The monoid of all unary operations on A generated by operations α p : x ↦ ( p → x ) , which is actually an upper semilattice w.r.t. the pointwise ordering, is called the adjoint semilattice of A . This semilattice is isomorphic to the semilattice of finitely generated filters of A , it is subtractive (i.e., dually implicative), and its ideal lattice is isomorphic to the filter lattice of A . Moreover, the order dual of the adjoint semilattice is a minimal Brouwerian extension of A , and the...

Aggregation operators on partially ordered sets and their categorical foundations

Mustafa Demirci (2006)

Kybernetika

In spite of increasing studies and investigations in the field of aggregation operators, there are two fundamental problems remaining unsolved: aggregation of L -fuzzy set-theoretic notions and their justification. In order to solve these problems, we will formulate aggregation operators and their special types on partially ordered sets with universal bounds, and introduce their categories. Furthermore, we will show that there exists a strong connection between the category of aggregation operators...

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