Biplots of fuzzy coded data

A biplot, which is the multivariate generalization of the two-variable scatterplot, can be used to visualize the results of many multivariate techniques, especially those that are based on the singular value decomposition. We consider data sets consisting of continuous-scale measurements, their fuzzy coding and the biplots that visualize them, using a fuzzy version of multiple correspondence analysis. Of special interest is the way quality of fit of the biplot is measured, since it is well-known that regular (i.e., crisp) multiple correspondence analysis seriously under-estimates this measure. We show how the results of fuzzy multiple correspondence analysis can be defuzzified to obtain estimated values of the original data, and prove that this implies an orthogonal decomposition of variance. This permits a measure of fit to be calculated in the familiar form of a percentage of explained variance, which is directly comparable to the corresponding fit measure used in principal component analysis of the original data. The approach is motivated initially by its application to a simulated data set, showing how the fuzzy approach can lead to diagnosing nonlinear relationships, and finally it is applied to a real set of meteorological data.defuzzification, fuzzy coding, indicator matrix, measure of fit, multivariate data, multiple correspondence analysis, principal component analysis.

A Fuzzy Logic Based Algorithm for Finding Astronomical Objects in Wide-Angle Frames

Accurate automatic identification of astronomical objects in an imperfect world of non-linear wide-angle optics, imperfect optics, inaccurately pointed telescopes, and defect-ridden cameras is not always a trivial first step. In the past few years, this problem has been exacerbated by the rise of digital imaging, providing vast digital streams of astronomical images and data. In the modern age of increasing bandwidth, human identifications are many times impracticably slow. In order to perform an automatic computer-based analysis of astronomical frames, a quick and accurate identification of astronomical objects is required. Such identification must follow a rigorous transformation from topocentric celestial coordinates into image coordinates on a CCD frame. This paper presents a fuzzy logic based algorithm that estimates needed coordinate transformations in a practical setting. Using a training set of reference stars, the algorithm statically builds a fuzzy logic model. At runtime, the algorithm uses this model to associate stellar objects visible in the frames to known-catalogued objects, and generates files that contain photometry information of objects visible in the frame. Use of this algorithm facilitates real-time monitoring of stars and bright transients, allowing identifications and alerts to be issued more reliably. The algorithm is being implemented by the Night Sky Live all-sky monitoring global network and has shown itself significantly more reliable than the previously used non-fuzzy logic algorithm.Comment: Accepted for publication in PAS

Fuzzy geometry, entropy, and image information

Presented here are various uncertainty measures arising from grayness ambiguity and spatial ambiguity in an image, and their possible applications as image information measures. Definitions are given of an image in the light of fuzzy set theory, and of information measures and tools relevant for processing/analysis e.g., fuzzy geometrical properties, correlation, bound functions and entropy measures. Also given is a formulation of algorithms along with management of uncertainties for segmentation and object extraction, and edge detection. The output obtained here is both fuzzy and nonfuzzy. Ambiguity in evaluation and assessment of membership function are also described

Improving activity recognition using a wearable barometric pressure sensor in mobility-impaired stroke patients.

© 2015 Massé et al.Background: Stroke survivors often suffer from mobility deficits. Current clinical evaluation methods, including questionnaires and motor function tests, cannot provide an objective measure of the patients mobility in daily life. Physical activity performance in daily-life can be assessed using unobtrusive monitoring, for example with a single sensor module fixed on the trunk. Existing approaches based on inertial sensors have limited performance, particularly in detecting transitions between different activities and postures, due to the inherent inter-patient variability of kinematic patterns. To overcome these limitations, one possibility is to use additional information from a barometric pressure (BP) sensor. Methods: Our study aims at integrating BP and inertial sensor data into an activity classifier in order to improve the activity (sitting, standing, walking, lying) recognition and the corresponding body elevation (during climbing stairs or when taking an elevator). Taking into account the trunk elevation changes during postural transitions (sit-to-stand, stand-to-sit), we devised an event-driven activity classifier based on fuzzy-logic. Data were acquired from 12 stroke patients with impaired mobility, using a trunk-worn inertial and BP sensor. Events, including walking and lying periods and potential postural transitions, were first extracted. These events were then fed into a double-stage hierarchical Fuzzy Inference System (H-FIS). The first stage processed the events to infer activities and the second stage improved activity recognition by applying behavioral constraints. Finally, the body elevation was estimated using a pattern-enhancing algorithm applied on BP. The patients were videotaped for reference. The performance of the algorithm was estimated using the Correct Classification Rate (CCR) and F-score. The BP-based classification approach was benchmarked against a previously-published fuzzy-logic classifier (FIS-IMU) and a conventional epoch-based classifier (EPOCH). Results: The algorithm performance for posture/activity detection, in terms of CCR was 90.4 %, with 3.3 % and 5.6 % improvements against FIS-IMU and EPOCH, respectively. The proposed classifier essentially benefits from a better recognition of standing activity (70.3 % versus 61.5 % [FIS-IMU] and 42.5 % [EPOCH]) with 98.2 % CCR for body elevation estimation. Conclusion: The monitoring and recognition of daily activities in mobility-impaired stoke patients can be significantly improved using a trunk-fixed sensor that integrates BP, inertial sensors, and an event-based activity classifier

Application of an iterative method and an evolutionary algorithm in fuzzy optimization

This work develops two approaches based on the fuzzy set theory to solve a class of fuzzy mathematical optimization problems with uncertainties in the objective function and in the set of constraints. The first approach is an adaptation of an iterative method that obtains cut levels and later maximizes the membership function of fuzzy decision making using the bound search method. The second one is a metaheuristic approach that adapts a standard genetic algorithm to use fuzzy numbers. Both approaches use a decision criterion called satisfaction level that reaches the best solution in the uncertain environment. Selected examples from the literature are presented to compare and to validate the efficiency of the methods addressed, emphasizing the fuzzy optimization problem in some import-export companies in the south of Spain.Federal University of São Paulo Institute of Science and TechnologySão Paulo State University Environmental Engineering DepartmentUNICAMP School of Electrical and Computer Engineering Department of TelematicsUNIFESP, Institute of Science and TechnologySciEL