the aim of this paper is to extend results established by h. onoand t. kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. the main theorem states that a residuatedlattice a is directly indecomposable if and only if its boolean center b(a)is {0, 1}. we also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...

This paper presents a simple uni ed graphical ap proach to designs implemented with multiplexers and to the decomposition of Boolean functions In doing so de signs composed of both completely and incompletely spec i ed Boolean functions are presented and illustrated using the numerical method as well as an applicable computer program

November 16, 2009 Type Package Title Generation, reconstruction, simulation and analysis of Boolean networks Version 1.3 Date 2009-10-02 Author Christoph Muessel, Dao Zhou, Hans Kestler Maintainer Hans Kestler Suggests igraph Description Provides methods to reconstruct and generate Boolean networks, and to analyze and visualize attractors in Boolean networks License Ar...

The authors regret that there is a correction needed to Reference [29] and apologize for any inconvenience caused. Reference [29] should read ‘‘N. Çağman, S. Enginoğlu, Soft set theory and uni-int decision making, European Journal of Operational Research 207 (2010) 848–855’’ instead of ‘‘N. Çağman, S. Enginoğlu, Soft set theory and uni-int decisionmaking, European Journal of Operational Researc...

At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that fil...

We further study the filter theory of pseudo-BL algebras.We give some equivalent conditions of filter, normal filter and Boolean filter. We introduce the notion of pseudo MV-filter, pseudo-G filter and characterize Boolean algebras, pseudo-MV algebras and pseudo Gödel algebras (i.e. Gödel algebras) in pseudo-BL algebras. We establish the connections between BCC-algebras, pseudo-BCK algebras, ps...

In [1] and [2] we have discussed the problem of existence of an independent set of generators for a countably generated filter in an atomless Boolean algebra and for any filter in a free Boolean algebra. In particular, we have proved that if F is a filter in a free Boolean algebra then F is freely generated provided the minimal cardinality of the set of generators of F is not a singular cardina...

An impressive variety of multirate lter banks evolved during the past twenty years. We present an algebraic approach that subsumes many concepts developed so far (e. g. multi lters, nonseparable multidimensional lter banks, cyclic lter banks, lter banks with values in nite elds, etc.). In our approach the signals and lters are viewed as elements of a group ring. We give necessary and su cient c...