In this paper, we investigate two L-neighborhood systems induced by an Lfuzzy topology in a complete residuated lattice L. We study the relationships among L-fuzzy topology, L-topologies and L-neighborhood systems. Finally, we give their examples. AMS Subject Classification: 03E72, 06A15, 06F07, 54A05

This paper is an extended abstract of my paper [12] published in Fuzzy Set and Systems. We start from a residuated lattice L and a monoid M , and we define a Galois connection from the lattice of the compatible L-preorders in M and the lattice of L-submonoids of M . Given a set S we define a Galois connection between the lattice of the L-preorders in S and the lattice of L-submonoids of the mon...

In this paper, we investigate the properties of join (meet) preserving and meet-join (join-meet) maps in complete residuated lattices. Mathematics Subject Classification: 03E72, 03G10, 06A15, 06F07

It is proved that the variety of representable idempotent commutative residuated lattices is locally finite. The n-generated subdirectly irreducible algebras in this variety are shown to have at most 3n+1 elements each. A constructive characterization of the subdirectly irreducible algebras is provided, with some applications. The main result implies that every finitely based extension of posit...

The “representation problem” in abstract algebraic logic is that of finding necessary and sufficient conditions for a structure, on a well defined abstract framework, to have the following property: that for every structural closure operator on it, every structural embedding of the expanded lattice of its closed sets into that of the closed sets of another structural closure operator on another...

In this paper, a theorem on the existence of complete embedding of partially ordered monoids into complete residuated lattices is shown. From this, many interesting results on residuated lattices and substructural logics follows, including various types of completeness theorems of substructural logics.

for all x, y, z ∈ L. (So we do not require the dual arrow nor the associativity of .) In other words, the actions − y, y ( − : L→ L, for any fixed y ∈ L, provide a Galois connection on L. The Galois connection is also completely determined by the partial isomorphism between fixpoints of closure mapping y ( (− y) and coclosure mapping (y ( −) y. Thus we can restrict ,( to partial operations ·,→ ...

ACKNOWLEDGMENTS This thesis wouldn't have been possible without the help and support of certain people. I could not possibly itemize my gratitude in detail, but I would like to mention some of the most important names. First and foremost, I would like to thank my advisor, Constantine Tsinakis, for introducing me to the subject of residuated lattices, and for his guidance and advice. Despite his...

D. Buşneag 1 defined pseudo valuation on a Hilbert algebra and proved that every pseudo valuation induces a pseudometric on a Hilbert algebra. Also, D. Buşneag 2 provided several theorems on extensions of pseudo valuations. C. Buşneag 3 introduced the notions of pseudo valuations valuations on residuated lattices, and proved some theorems of extension for these using the model of Hilbert algebr...

In this paper, we introduced two types of fuzzy stabilizers St R (F) and St ⊕ R (F) of a fuzzy set F and the stabilizer St ∨(F, G) of F with respect to G in IMTL-algebras. We proved that St R (F), St ⊕ R (F) and St ∨(F, G) are fuzzy filters of M. We investigated some properties of the stabilizers. By introducing the ⊗̃ operation of two fuzzy filters, we prove that ⊗̃ and St∨(·, ·) form an adjoint...