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Filters of residuated lattices and triangle algebras

B. Van Gasse, G. Deschrijver, C. Cornelis, E.E. Kerre
2010 Information Sciences  
An important concept in the theory of residuated lattices and other algebraic structures used for formal fuzzy logic, is that of a filter.  ...  In this paper, we define several different filters of residuated lattices and triangle algebras and examine their mutual dependencies and connections.  ...  To be more precise, there will be only one residuated lattice: the Boolean algebra. The proof of this property is very short.  ... 
doi:10.1016/j.ins.2010.04.010 fatcat:6tcu6ftuqjhofcrp2rpmekksnm

Increasing The Performance Of The Lms Algorithm Using An Adaptive Preconditioner

J.G. McWhirter, I.K. Proudler, I.D. Skidmore
1996 Zenodo  
C l e a r l y , a n o p t i m u m p r e c o n d i t i o n e r i s a transformation that results in a new data matrix that has an eigenvalue spread of unity i.e. produces an orthonormal matrix.  ...  F i g u r e 5 s h o w s t h e p e r f o r m a n c e o f t h e preconditioned LMS algorithm (with and without normalisation) when the order of the AR (M) process is known a-priori.  ... 
doi:10.5281/zenodo.36421 fatcat:ci7ynqhsxnfjtfa4v62sim6vq4

A new approach to filters in triangle algebras

Saeide Zahiri, Arsham Saeid, Esfandiar Eslami
2017 Publications de l'Institut Mathématique (Beograd)  
We develop the filter theory in triangle algebras. We define several interval valued residuated lattice-filters (IVRL-filters for short) in triangle algebras.  ...  We investigate the relationships among these types of IVRL-filters. Also, some special triangle algebras are introduced and studied in details.  ...  The authors are extremely grateful to the reviewers for their valuable comments and helpful suggestions.  ... 
doi:10.2298/pim1715267z fatcat:zolzwfrtrvghxfvnzvtsussaim

Pitch prediction filters in speech coding

R.P. Ramachandran, P. Kabal
1989 IEEE Transactions on Acoustics Speech and Signal Processing  
Furthermore, new methods to estimate the appropriate pitch lag for a pitch filter are proposed for both transversal and lattice structures.  ...  Prediction error filters which combine short-time prediction (formant prediction) with long-time prediction (pitch prediction) in a cascade connection are examined.  ...  THREE NUMBERS I N A N ENTRY REFER TO ONE-,TWO-, A N D THREE-TAP PITCH PREDICTORS. THE PREDICTOR G A I N IS THE GAIN BEFORE S T A B~L~Z A T~O N .  ... 
doi:10.1109/29.17527 fatcat:nisjxum5qvhffhbm5v6tlwukhq

Commutative integral bounded residuated lattices with an added involution

Roberto Cignoli, Francesc Esteva
2009 Annals of Pure and Applied Logic  
A symmetric residuated lattice is an algebra A = (A, ∨, ∧, * , →, ∼, 1, 0) such that (A, ∨, ∧, * , →, 1, 0) is a commutative integral bounded residuated lattice and the equations ∼∼ x = x and ∼ (x ∨ y)  ...  In particular we consider the chain of varieties of symmetric residuated lattices such that the n iteration of ε is a boolean interior operator.  ...  Acknowledgement The research communicated in this paper was partially supported by a bilateral Argentinean-Spanish project CONICET-CSIC.  ... 
doi:10.1016/j.apal.2009.05.008 fatcat:i4yxfu54sfgltgorrokwtsfok4

Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics over FL

Nikolaos Galatos, Hiroakira Ono
2006 Studia Logica: An International Journal for Symbolic Logic  
We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized  ...  Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.  ...  We would like to thank Josep Maria Font and James Raftery for reading through our draft and for their helpful suggestions.  ... 
doi:10.1007/s11225-006-8305-5 fatcat:jfwnjin2kra3dixd5zqf2uwtfm

On the structure of generalized BL-algebras

P. Jipsen, F. Montagna
2006 Algebra Universalis  
A generalized BL-algebra (or GBL-algebra for short) is a residuated lattice that satisfies the identities x ∧ y = ((x ∧ y)/y)y = y(y\(x ∧ y)).  ...  The construction provides a new way of order-embedding the lattice of -group varieties into the lattice of varieties of integral GBL-algebras.  ...  Note that if a residuated lattice has a top element and is either cancellative or a GBL-algebra, then it is in fact integral.  ... 
doi:10.1007/s00012-006-1960-6 fatcat:cmqb2eeq4nfqfiyoapqwmkosu4

The pseudo-linear semantics of interval-valued fuzzy logics

B VANGASSE, C CORNELIS, G DESCHRIJVER, E KERRE
2009 Information Sciences  
It is known that there is a one-to-one correspondence between triangle algebras and couples (L, α), in which L is a residuated lattice and α an element in that residuated lattice.  ...  Triangle algebras are equationally defined structures that are equivalent with certain residuated lattices on a set of intervals, which are called interval-valued residuated lattices (IVRLs).  ...  ., w.r.t. the triangle algebras on L I ), similarly as MTL being complete w.r.t. residuated lattices on ([0, 1], min, max). This is a topic for further research.  ... 
doi:10.1016/j.ins.2008.11.005 fatcat:bodpu7lnljbkzh4dddx5gh3efy

Regularizing phase-based stereo

T. Frohlinghaus, J.M. Buhmann
1996 Proceedings of 13th International Conference on Pattern Recognition  
In the spirit of Markov random f ields, we propose a probabilistic lattice model which describes the complete disparity distribution instead of representing only a single conf iguration.  ...  The complex-valued Gabor f ilter responses reduce the ambiguity of raw image intensities, and their phase differences between left and right image provide a direct measure for the disparities.  ...  Note that even though this is a continuous output, the internal lattice structure bases completely on a discrete model.  ... 
doi:10.1109/icpr.1996.546067 dblp:conf/icpr/FrohlinghausB96 fatcat:j4z4tbolebgatcpqjoxmrl626a

The order topology in a bicompactly generated lattice

D. C. Kent, C. R. Atherton
1968 Journal of the Australian Mathematical Society  
Our first example is very short and simple; it shows that the conclusion of Theorem 2b cannot be extended to an arbitrary complete bicompactly generated lattice. EXAMPLE 1.  ...  Let L be a lattice, x e L, A C L and J 5 " a filter on L; then x* = {y\y 2: x), A* = {y\y ^ x, all x in A), 3F* = u {F*\F e =F}.  ... 
doi:10.1017/s1446788700005401 fatcat:zc6qv25ea5bf7fmf5hd6eqpdwe

The Distributive Full Lambek Calculus with Modal Operators [article]

Daniel Rogozin
2020 arXiv   pre-print
In this paper, we study logics of bounded distributive residuated lattices with modal operators considering and in a noncommutative setting.  ...  After that, we establish a Priestley-style duality between residuated distributive modal algebras and topological Kripke structures based on Priestley spaces.  ...  exist finite subsets S ′ ⊆ S and T ′ ⊆ T such that S ′ ≤ T ′ .  ... 
arXiv:2003.09975v3 fatcat:rbrz2afsw5fxrifkghudzr3fti

A categorical equivalence for Stonean residuated lattices [article]

Manuela Busaniche, Roberto Cignoli, Miguel Marcos
2017 arXiv   pre-print
Given a Stonean residuated lattice, we consider the triple formed by its Boolean skeleton, its algebra of dense elements and a connecting map.  ...  We define a category whose objects are these triples and suitably defined morphisms, and prove that we have a categorical equivalence between this category and that of Stonean residuated lattices.  ...  By an implicative filter or i-filter of a residuated lattice A we mean a subset F ⊆ A satisfying that ⊤ ∈ F and if x, x → y are in F , then y ∈ F.  ... 
arXiv:1706.06332v2 fatcat:s3zpkv4brjh5llev3moph4e4fy

Performance Analysis of Multichannel Lattice Equalization in Coherent Underwater Communications

Joao Gomes, Antonio Silva, Sergio Jesus
2007 OCEANS 2007  
This work examines the numerical fixed-point performance of a new multichannel lattice RLS filtering algorithm using data from two underwater acoustic communication experiments.  ...  The algorithm may be an appealing choice for underwater equalization due to its robust numerical behavior and linear scaling of the computational complexity with filter order.  ...  This vector is assumed to be updated up to time n in channels 1, . . . i, but only up to time n − 1 in the remaining ones, u i,0 (n) = u (1) T (n) . . . u (i) T (n) u (i+1) T (n − 1) . . . u (L) T (n −  ... 
doi:10.1109/oceans.2007.4449374 fatcat:jaojgu7py5adxnpxtn6bqmfo2y

A decomposition theorem for maxitive measures

Paul Poncet
2011 Linear Algebra and its Applications  
We show that maxitive measures can be decomposed as the supremum of a maxitive measure with density, and a residual maxitive measure that is null on compact sets under specific conditions.  ...  A maxitive measure is the analogue of a finitely additive measure or charge, in which the usual addition is replaced by the supremum operation.  ...  Acknowledgements I would like to thank Marianne Akian for her valuable comments and suggestions.  ... 
doi:10.1016/j.laa.2010.03.004 fatcat:7c5bx46w2nhvzpyzdsuqhbkisq

Logics preserving degrees of truth from varieties of residuated lattices [article]

F. Bou, F. Esteva, J. M. Font, A. Gil, L. Godo, A. Torrens, V. Verdú
2009 arXiv   pre-print
Let K be a variety of (commutative, integral) residuated lattices.  ...  We also characterize the new logic in three ways: by a Hilbert style axiomatic system, by a Gentzen style sequent calculus, and by a set of conditions on its closure operator.  ...  If T ∈ C then from T3 it follows that T /≡ C is a lattice filter. Moreover, by 1, T /≡ C ⊆ T ′ /≡ C if and only if TT ′ . This also implies that the mapping is one-to-one.  ... 
arXiv:0803.1648v2 fatcat:ysxryn6yjva3bgkjjst5vkjkgy
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