We propose assertion-consistency (AC) semi-lattices as suitable orders for the analysis of partial models. Such orders express semantic entailment, multiple-viewpoint and multiple-valued analysis, maintain internal consistency of reasoning, and subsume finite De Morgan lattices. We classify those orders that are finite and distributive and apply them to design an efficient algorithm for multipl...

In this paper, a double-layer modificatory linguistic truth-value lattice-valued evaluation method is presented. Its logic basic is based on modificatory linguistic truth-value lattice-valued proposition logic system MLTVLP(X) and operator modificatory linguistic truth-value lattice-valued proposition logic OMLTVLP(X). MLTVLP(X) and OMLTVLP(X) are similar to LTVLP(X) and MLTVLP(X), which have b...

A formalism is proposed for representing uncertain information on set-valued variables using the formalism of belief functions. A set-valued variableX on a domain Ω is a variable taking zero, one or several values in Ω. While defining mass functions on the frame 22 Ω is usually not feasible because of the double-exponential complexity involved, we propose an approach based on a definition of a ...

This article gives results on fixed basis frame valued neighborhood topological groups and stratified neighborhood topological groups, includes some characterization theorems, and presents the uniformizability of stratified neighborhood topological groups within the unified approach of Gutiérrez García, DePrada Vicente, and Šostak. It is shown that for a frame L, the category L-NGrp is topologi...

We present multiresolution spaces of complex rotation-covariant functions, deployed on the 2-D hexagonal lattice. The designed wavelets, which are complex-valued, provide an important phase information for image analysis, which is missing in the discrete wavelet transform with real wavelets. Moreover, the hexagonal lattice allows to build wavelets having a more isotropic magnitude than on the C...

Multiple-valued logics can be effectively used to reason about incomplete and/or inconsistent systems, e.g. during early software requirements or as the systems evolve. We specify multiple-valued logics using finite lattices. In this paper, we use lattice representation theory to cast the multiple-valued modelchecking problem in terms of symbolic operations on classical sets of states, provided...

We consider the lattice-reduction-aided detection scheme for 2×2 channels recently proposed by Yao and Wornell [11]. Using an equivalent real-valued substitute MIMO channel model their lattice reduction algorithm can be replaced by the well-known LLL algorithm, which enables the application to MIMO systems with arbitrary numbers of dimensions. We show how lattice reduction can also be favourabl...

Relations between halfand full-lattice CMV operators with scalarand matrix-valued Verblunsky coefficients are investigated. In particular, the decoupling of full-lattice CMV operators into a direct sum of two half-lattice CMV operators by a perturbation of minimal rank is studied. Contrary to the Jacobi case, decoupling a full-lattice CMV matrix by changing one of the Verblunsky coefficients re...

In this paper we introduce the notion of additive and multiplicative generators on the lattice L , which is the underlying lattice of interval-valued fuzzy set theory (which is equivalent to intuitionistic fuzzy set theory in the sense of Atanassov). We study the properties of these operators, some of which are similar to well-known results on ([0, 1],≤).