A temporal semantics for Nilpotent Minimum logic

In [Ban97] a connection among rough sets (in particular, pre-rough algebras) and three-valued {\L}ukasiewicz logic {\L}3 is pointed out. In this paper we present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95, EG01]), in which the logic of every instant is given by {\L}3: a completeness theorem will be shown. This is the prosecution of the work initiated in [AGM08] and [ABM09], in which the authors construct a temporal semantics for the many-valued logics of G\"odel ([G\"od32], [Dum59]) and Basic Logic ([H\'aj98]).Comment: 19 pages, 2 table

Neutrosophic Hough Transform

Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image processing, a dozen of applications can be handled with HT, such as lane detection for autonomous cars, blood cell detection in microscope images, and so on. As HT is a straight forward shape detector in a given image, its shape detection ability is low in noisy images. To alleviate its weakness on noisy images and improve its shape detection performance, in this paper, we proposed neutrosophic Hough transform (NHT). As it was proved earlier, neutrosophy theory based image processing applications were successful in noisy environments. To this end, the Hough space is initially transferred into the NS domain by calculating the NS membership triples (T, I, and F). An indeterminacy filtering is constructed where the neighborhood information is used in order to remove the indeterminacy in the spatial neighborhood of neutrosophic Hough space. The potential peaks are detected based on thresholding on the neutrosophic Hough space, and these peak locations are then used to detect the lines in the image domain. Extensive experiments on noisy and noise-free images are performed in order to show the efficiency of the proposed NHT algorithm. We also compared our proposed NHT with traditional HT and fuzzy HT methods on variety of images. The obtained results showed the efficiency of the proposed NHT on noisy images

Clustering stock price volatility using intuitionistic fuzzy sets

Clustering involves gathering a collection of objects into homogeneous groups or clusters, such that objects in the same cluster are more similar when compared to objects present in other groups. Clustering algorithms that generate a tree of clusters called dendrogram which can be either divisive or agglomerative. The partitional clustering gives a single partition of objects, with a predefined K number of clusters. The most popular partition clustering approaches are: k-means and fuzzy C-means (FCM). In k-means clustering, data are divided into a number of clusters where data elements belong to exactly one cluster. The k-means clustering works well when data elements are well separable. To overcome the problem of non-seprability, FCM and IFCM clustering algorithm were proposed. Here we review the use of FCM/IFCM with reference to the problem of market volatility

Interim research assessment 2003-2005 - Computer Science

This report primarily serves as a source of information for the 2007 Interim Research Assessment Committee for Computer Science at the three technical universities in the Netherlands. The report also provides information for others interested in our research activities

Extended Nonstandard Neutrosophic Logic, Set, and Probability Based on Extended Nonstandard Analysis

We extend for the second time the nonstandard analysis by adding the left monad closed to the right, and right monad closed to the left, while besides the pierced binad (we introduced in 1998) we add now the unpierced binad—all these in order to close the newly extended nonstandard space under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations

Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists

This book introduces the concept of fuzzy super matrices and operations on them. This book will be highly useful to social scientists who wish to work with multi-expert models. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy Relational Maps, Bidirectional Associative Memories and Fuzzy Associative Memories are defined here. The authors introduce 13 multi-expert models using the notion of fuzzy supermatrices. These models are described with illustrative examples. This book has three chapters. In the first chaper, the basic concepts about super matrices and fuzzy super matrices are recalled. Chapter two introduces the notion of fuzzy super matrices adn their properties. The final chapter introduces many super fuzzy multi expert models.Comment: 280 page

A Research Platform for Artificial Neural Networks with Applications in Pediatric Epilepsy

This dissertation established a state-of-the-art programming tool for designing and training artificial neural networks (ANNs) and showed its applicability to brain research. The developed tool, called NeuralStudio, allows users without programming skills to conduct studies based on ANNs in a powerful and very user friendly interface. A series of unique features has been implemented in NeuralStudio, such as ROC analysis, cross-validation, network averaging, topology optimization, and optimization of the activation function’s slopes. It also included a Support Vector Machines module for comparison purposes. Once the tool was fully developed, it was applied to two studies in brain research. In the first study, the goal was to create and train an ANN to detect epileptic seizures from subdural EEG. This analysis involved extracting features from the spectral power in the gamma frequencies. In the second application, a unique method was devised to link EEG recordings to epileptic and non-epileptic subjects. The contribution of this method consisted of developing a descriptor matrix that can be used to represent any EEG file regarding its duration and the number of electrodes. The first study showed that the inter-electrode mean of the spectral power in the gamma frequencies and its duration above a specific threshold performs better than the other frequencies in seizure detection, exhibiting an accuracy of 95.90%, a sensitivity of 92.59%, and a specificity of 96.84%. The second study yielded that Hjorth’s parameter activity is sufficient to accurately relate EEG to epileptic and non-epileptic subjects. After testing, accuracy, sensitivity and specificity of the classifier were all above 0.9667. Statistical tests measured the superiority of activity at over 99.99 % certainty. It was demonstrated that 1) the spectral power in the gamma frequencies is highly effective in locating seizures from EEG and 2) activity can be used to link EEG recordings to epileptic and non-epileptic subjects. These two studies required high computational load and could be addressed thanks to NeuralStudio. From a medical perspective, both methods proved the merits of NeuralStudio in brain research applications. For its outstanding features, NeuralStudio has been recently awarded a patent (US patent No. 7502763)

A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers

The objective of this paper is to introduce a distance measure for intuitionistic fuzzy numbers. Firstly the existing distance measures for intuitionistic fuzzy sets are analyzed and compared with the help of some examples. Then the new distance measure for intuitionistic fuzzy numbers is proposed based on interval difference. Also in particular the type of distance measure for triangle intuitionistic fuzzy numbers is described. The metric properties of the proposed measure are also studied. Some numerical examples are considered for applying the proposed measure and finally the result is compared with the existing ones