The Interval Constructor on classes of ML-algebras

Monoidal logic, ML for short, which formalized the fuzzy logics of continuous t-norms and their residua, has arisen great interest, since it has been applied to fuzzy mathematics, artificial intelligence, and other areas. It is clear that fuzzy logics basically try to represent imperfect or fuzzy information aiming to model the natural human reasoning. On the other hand, in order to deal with imprecision in the computational representation of real numbers, the use of intervals have been proposed, as it can guarantee that the results of numerical computation are in a bounded interval, controlling, in this way, the numerical errors produced by successive roundings. There are several ways to connect both areas; the most usual one is to consider interval membership degrees. The algebraic counterpart of ML is ML-algebra, an interesting structure due to the fact that by adding some properties it is possible to reach different classes of residuated lattices. We propose to apply an interval constructor to ML-algebras and some of their subclasses, to verify some properties within these algebras, in addition to the analysis of the algebraic aspects of them

Em direção a uma representação para equações algébricas :uma lógica equacional local

The intervalar arithmetic well-known as arithmetic of Moore, doesn't possess the same properties of the real numbers, and for this reason, it is confronted with a problem of operative nature, when we want to solve intervalar equations as extension of real equations by the usual equality and of the intervalar arithmetic, for this not to possess the inverse addictive, as well as, the property of the distributivity of the multiplication for the sum doesn t be valid for any triplet of intervals. The lack of those properties disables the use of equacional logic, so much for the resolution of an intervalar equation using the same, as for a representation of a real equation, and still, for the algebraic verification of properties of a computational system, whose data are real numbers represented by intervals. However, with the notion of order of information and of approach on intervals, introduced by Acióly[6] in 1991, the idea of an intervalar equation appears to represent a real equation satisfactorily, since the terms of the intervalar equation carry the information about the solution of the real equation. In 1999, Santiago proposed the notion of simple equality and, later on, local equality for intervals [8] and [33]. Based on that idea, this dissertation extends Santiago's local groups for local algebras, following the idea of Σ-algebras according to (Hennessy[31], 1988) and (Santiago[7], 1995). One of the contributions of this dissertation, is the theorem 5.1.3.2 that it guarantees that, when deducing a local Σ-equation E t t in the proposed system SDedLoc(E), the interpretations of t and t' will be locally the same in any local Σ-algebra that satisfies the group of fixed equations local E, whenever t and t have meaning in A. This assures to a kind of safety between the local equacional logic and the local algebras

Especificação do tipo intervalar parametrizado em CASL

The interval datatype applications in several areas is important to construct a interval type reusable, i.e., a interval constructor can be applied to any datatype and get intervals this datatype. Since the interval is, of certain form, a set of elements limited for two bounds, left and right, with a order notions, then it s reasonable that interval constructor enclose datatypes with partial order. On the order hand, what we want is work with interval of any datatype like this we work with this datatype then. it s important to guarantee the properties of the datatype when maps to interval of this datatype. Thus, the interval constructor get a theory to parametrized interval type, i.e., a interval with generics parameters (for example rational, real, complex). Sometimes, the interval application in some algebras doesn t guarantee the mainutenance of their properties, for example, when we use interval of real, that satisfies the field properties, it doesn t guarantee the distributivity propertie. A form to surpass this problem Santiago introduced the local equality theory that weakened the notion of strong equality, and thus, allowing some properties are local keeped, what can be discard before. The interval arithmetic generalization aim to apply the interval constructor on ordered algebras weakened for local equality with the purpose of the keep their properties. How the intervals are important in applications with continuous data, it s interesting specify that theory using a specification language that supply a system development using intervals of form disciplined, trustworth and safe. Currently, the algebraic specification language, based in math models, have been use to that intention often. We choose CASL (Common Algebraic Specification Language) among others languages because CASL has several characteristics excellent to parametrized interval type, such as, provide parcialiy and parametrization

Detecção de áreas degradadas na sub-bacia hidrográfica do rio taperoá/pb, utilizando parâmetros físicos dos sensores modis/terra e tm/landsat

This study includes the results of the analysis of areas susceptible to degradation by remote sensing in semi-arid region, which is a matter of concern and affects the whole population and the catalyst of this process occurs by the deforestation of the savanna and improper practices by the use of soil. The objective of this research is to use biophysical parameters of the MODIS / Terra and images TM/Landsat-5 to determine areas susceptible to degradation in semi-arid Paraiba. The study area is located in the central interior of Paraíba, in the sub-basin of the River Taperoá, with average annual rainfall below 400 mm and average annual temperature of 28 ° C. To draw up the map of vegetation were used TM/Landsat-5 images, specifically, the composition 5R4G3B colored, commonly used for mapping land use. This map was produced by unsupervised classification by maximum likelihood. The legend corresponds to the following targets: savanna vegetation sparse and dense, riparian vegetation and exposed soil. The biophysical parameters used in the MODIS were emissivity, albedo and vegetation index for NDVI (NDVI). The GIS computer programs used were Modis Reprojections Tools and System Information Processing Georeferenced (SPRING), which was set up and worked the bank of information from sensors MODIS and TM and ArcGIS software for making maps more customizable. Initially, we evaluated the behavior of the vegetation emissivity by adapting equation Bastiaanssen on NDVI for spatialize emissivity and observe changes during the year 2006. The albedo was used to view your percentage of increase in the periods December 2003 and 2004. The image sensor of Landsat TM were used for the month of December 2005, according to the availability of images and in periods of low emissivity. For these applications were made in language programs for GIS Algebraic Space (LEGAL), which is a routine programming SPRING, which allows you to perform various types of algebras of spatial data and maps. For the detection of areas susceptible to environmental degradation took into account the behavior of the emissivity of the savanna that showed seasonal coinciding with the rainy season, reaching a maximum emissivity in the months April to July and in the remaining months of a low emissivity . With the images of the albedo of December 2003 and 2004, it was verified the percentage increase, which allowed the generation of two distinct classes: areas with increased variation percentage of 1 to 11.6% and the percentage change in areas with less than 1 % albedo. It was then possible to generate the map of susceptibility to environmental degradation, with the intersection of the class of exposed soil with varying percentage of the albedo, resulting in classes susceptibility to environmental degradation