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## Filters

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Filters of residuated lattices and triangle algebras

2010
*
Information Sciences
*

An important concept in the theory of

doi:10.1016/j.ins.2010.04.010
fatcat:6tcu6ftuqjhofcrp2rpmekksnm
*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*. ...##
###
Increasing The Performance Of The Lms Algorithm Using An Adaptive Preconditioner

1996
*
Zenodo
*

C l e

doi:10.5281/zenodo.36421
fatcat:ci7ynqhsxnfjtfa4v62sim6vq4
*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. ...##
###
A new approach to filters in triangle algebras

2017
*
Publications de l'Institut Mathématique (Beograd)
*

We develop the

doi:10.2298/pim1715267z
fatcat:zolzwfrtrvghxfvnzvtsussaim
*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. ...##
###
Pitch prediction filters in speech coding

1989
*
IEEE Transactions on Acoustics Speech and Signal Processing
*

Furthermore, new methods to estimate the appropriate pitch lag for

doi:10.1109/29.17527
fatcat:nisjxum5qvhffhbm5v6tlwukhq
*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 . ...##
###
Commutative integral bounded residuated lattices with an added involution

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. ...

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

2006
*
Studia Logica: An International Journal for Symbolic Logic
*

We discuss the algebraization of substructural logics over the full Lambek calculus

doi:10.1007/s11225-006-8305-5
fatcat:jfwnjin2kra3dixd5zqf2uwtfm
*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. ...##
###
On the structure of generalized BL-algebras

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. ...

##
###
The pseudo-linear semantics of interval-valued fuzzy logics

2009
*
Information Sciences
*

It is known that there is

doi:10.1016/j.ins.2008.11.005
fatcat:bodpu7lnljbkzh4dddx5gh3efy
*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. ...##
###
Regularizing phase-based stereo

1996
*
Proceedings of 13th International Conference on Pattern Recognition
*

In the spirit of Markov random f ields, we propose

doi:10.1109/icpr.1996.546067
dblp:conf/icpr/FrohlinghausB96
fatcat:j4z4tbolebgatcpqjoxmrl626a
*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. ...##
###
The order topology in a bicompactly generated lattice

1968
*
Journal of the Australian Mathematical Society
*

Our first example is very

doi:10.1017/s1446788700005401
fatcat:zc6qv25ea5bf7fmf5hd6eqpdwe
*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}. ...##
###
The Distributive Full Lambek Calculus with Modal Operators
[article]

2020
*
arXiv
*
pre-print

In this paper, we study logics of bounded distributive

arXiv:2003.09975v3
fatcat:rbrz2afsw5fxrifkghudzr3fti
*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*′ . ...##
###
A categorical equivalence for Stonean residuated lattices
[article]

2017
*
arXiv
*
pre-print

Given

arXiv:1706.06332v2
fatcat:s3zpkv4brjh5llev3moph4e4fy
*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. ...##
###
Performance Analysis of Multichannel Lattice Equalization in Coherent Underwater Communications

2007
*
OCEANS 2007
*

This work examines the numerical fixed-point performance of

doi:10.1109/oceans.2007.4449374
fatcat:jaojgu7py5adxnpxtn6bqmfo2y
*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 − ...##
###
A decomposition theorem for maxitive measures

2011
*
Linear Algebra and its Applications
*

We show that maxitive measures can be decomposed as the supremum of

doi:10.1016/j.laa.2010.03.004
fatcat:7c5bx46w2nhvzpyzdsuqhbkisq
*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. ...##
###
Logics preserving degrees of truth from varieties of residuated lattices
[article]

2009
*
arXiv
*
pre-print

Let K be

arXiv:0803.1648v2
fatcat:ysxryn6yjva3bgkjjst5vkjkgy
*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*T*⊆*T*′ . This also implies that the mapping is*one*-to-*one*. ...
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