DIRECT AND SUPPLEMENTARY SHADOWS IN THE TASK OF THE EFFICIENT DESCRIPTION OF CLASSES

One of the best techniques of feature efficiency estimation is based on the application of composition of the binary relations, i.e. direct shadows of fuzzy sets. Furthermore, the analysis of the binary relations yields a significant increase in the efficiency of the method operation, and also a detailed understanding of the processes occurring during the process of composition under various conditions.Since the composition of the binary relations is exploited to estimate the efficiency of attributes by means of direct shadows of fuzzy sets, a question appears: what volume of the information regarding the efficiency of attributes can supplementary shadows of fuzzy sets bear ? The use of supplementary shadows along with the analysis of direct shadows of fuzzy sets will presumably give a more complete representation about the efficiency of features of classes.The experiments performed on solving tasks by means of the composition of direct and supplementary shadows have shown that imder certain conditions supplementary shadows can give some auxiliary estimation of the attributes efficiency. It was then decided to continue some of experiments to reveal the valid behavior of supplementary shadows under various statements of the task and various samples, and also provided that the quantity of classes and the degree of their participation in space were changed.In this paper, an example is considered where three classes participate on a three-dimensional space of attributes. The convolution of composition realization results, degrees of reduction, is also proposed to estimate the attributes available

Fuzzy Soft Shadow in Augmented Reality Systems

Realistic soft shadows in Augmented Reality (AR) is a fascinating topic in computer graphics. Many researchers are involved to have a significant improvement on this demand. In this paper, we have presented a new technique to produce soft shadows using one of the well-known methods in mathematics called Fuzzy Logic. Fuzzy logic is taken into account to generate the realistic soft shadows in AR. The wide light source is split into some parts that each of them plays the rule of a single light source. The desired soft shadow is generated by splitting the wide light source into multiple parts and considering each part as a single light source. The method which we called Fuzzy Soft Shadow is employed in AR to enhance the quality of semi-soft shadows and soft shadows

Geometric reconstruction methods for electron tomography

Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and nonlinear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full $180^\circ$ tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce and discuss several algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire

Fuzzy spectral and spatial feature integration for classification of nonferrous materials in hyperspectral data

Hyperspectral data allows the construction of more elaborate models to sample the properties of the nonferrous materials than the standard RGB color representation. In this paper, the nonferrous waste materials are studied as they cannot be sorted by classical procedures due to their color, weight and shape similarities. The experimental results presented in this paper reveal that factors such as the various levels of oxidization of the waste materials and the slight differences in their chemical composition preclude the use of the spectral features in a simplistic manner for robust material classification. To address these problems, the proposed FUSSER (fuzzy spectral and spatial classifier) algorithm detailed in this paper merges the spectral and spatial features to obtain a combined feature vector that is able to better sample the properties of the nonferrous materials than the single pixel spectral features when applied to the construction of multivariate Gaussian distributions. This approach allows the implementation of statistical region merging techniques in order to increase the performance of the classification process. To achieve an efficient implementation, the dimensionality of the hyperspectral data is reduced by constructing bio-inspired spectral fuzzy sets that minimize the amount of redundant information contained in adjacent hyperspectral bands. The experimental results indicate that the proposed algorithm increased the overall classification rate from 44% using RGB data up to 98% when the spectral-spatial features are used for nonferrous material classification

FUZZY IMPLICATIVE FILTERS OF BE-ALGEBRAS BASED ON THE THEORY OF FALLING SHADOWS

Based on the idea of falling shadows and fuzzy sets, the notion of a falling fuzzy implicative filter of a BE-algebra is introduced. Relations between fuzzy implicative filters and falling fuzzy implicative filters are provided

A pure probabilistic interpretation of possibilistic expected value, variance, covariance and correlation

In this work we shall give a pure probabilistic interpretation of possibilistic expected value, variance, covariance and correlation