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Fixed points theorems of non-expanding fuzzy multifunctions

Abdelkader Stouti (2005)

Archivum Mathematicum

We prove the existence of a fixed point of non-expanding fuzzy multifunctions in α -fuzzy preordered sets. Furthermore, we establish the existence of least and minimal fixed points of non-expanding fuzzy multifunctions in α -fuzzy ordered sets.

Fixed points with respect to the L-slice homomorphism σ a

K.S. Sabna, N.R. Mangalambal (2019)

Archivum Mathematicum

Given a locale L and a join semilattice J with bottom element 0 J , a new concept ( σ , J ) called L -slice is defined,where σ is as an action of the locale L on the join semilattice J . The L -slice ( σ , J ) adopts topological properties of the locale L through the action σ . It is shown that for each a ∈ L , σ a is an interior operator on ( σ , J ) .The collection M = { σ a ; a ∈ L } is a Priestly space and a subslice of L - Hom ( J , J ) . If the locale L is spatial we establish an isomorphism between the L -slices ( σ , L ) and ( δ , M ) . We have shown that the fixed set of σ a ,...

Flocks in universal and Boolean algebras

Gabriele Ricci (2010)

Discussiones Mathematicae - General Algebra and Applications

We propose the notion of flocks, which formerly were introduced only in based algebras, for any universal algebra. This generalization keeps the main properties we know from vector spaces, e.g. a closure system that extends the subalgebra one. It comes from the idempotent elementary functions, we call "interpolators", that in case of vector spaces merely are linear functions with normalized coefficients. The main example, we consider outside vector spaces, concerns Boolean algebras,...

Folding theory applied to BL-algebras

Young Jun, Jung Ko (2004)

Open Mathematics

The notion of n-fold grisly deductive systems is introduced. Some conditions for a deductive system to be an n-fold grisly deductive system are provided. Extension property for n-fold grisly deductive system is established.

Foldness of Commutative Ideals in BCK-algebras

Celestin Lele, Salissou Moutari (2006)

Discussiones Mathematicae - General Algebra and Applications

This paper deals with some properties of n-fold commutative ideals and n-fold weak commutative ideals in BCK-algebras. Afterwards, we construct some algorithms for studying foldness theory of commutative ideals in BCK-algebras.

Forcing for hL and hd

Andrzej Rosłanowski, Saharon Shelah (2001)

Colloquium Mathematicae

The present paper addresses the problem of attainment of the supremums in various equivalent definitions of the hereditary density hd and hereditary Lindelöf degree hL of Boolean algebras. We partially answer two problems of J. Donald Monk [13, Problems 50, 54], showing consistency of different attainment behaviour and proving that (for the variants considered) this is the best result we can expect.

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