Generalized Fuzzy Entropy Optimization Methods for Fuzzy Data Analysis

This paper presents a work about palm print recognition using fuzzy entropy. A number of schemes have been proposed to combine the fuzzy set theory and its application to the entropy concept for modelling a palm print recognition system. The measure of uncertainty is adopted as a measure of information. Hence, the measures of fuzziness are known as fuzzy information measures. The measure of information is used to measure the uncertainty. Hence, fuzzy information measures are used to measure the fuzziness. The measure of a quantity of fuzzy information obtained from a fuzzy set or fuzzy system is known as fuzzy entropy. Since no probabilistic concept is needed to define fuzzy entropy, classical Shannon entropy is quite different from it. Further, Shannon entropy contains the randomness uncertainty (probabilistic) whereas fuzzy entropy contains vagueness and ambiguity uncertainties. The concept of membership function is used to define fuzzy entropy. The properties of fuzzy entropy have become popular and are being used very frequently to define any new fuzzy entropy. The fuzzy entropy function used in this paper is defined using the new random membership function μ. Previous works in palm print recognition use standard methods for feature extraction. By using standard techniques, the recognition rate was not as expected. Incorporating fuzzy concept to derive the features of palm print is the motivation for this work. The proposed work uses fuzzy membership function to extract the maximum information out of palm print as it contains lot of uncertainties. The fuzzy membership function developed in the proposed work is applied in the fuzzy entropy function to generate the new entropy information features which when tested with the standard classifier using support vector machine gives the encouraging result in terms of recognition rate. The proposed work was done using COEP (College of Engineering, Pune) database. It can be noted that palm print recognition is an important modality in biometrics for security purposes, as its use in practical life cannot be avoided. The palm print image contains lot of undefined and vague information and the best method to take out the maximum information out of the palm print image is the use of fuzzy logic concepts. This feature also motivated us for the proposed work.

Minimum Cross Entropy and Informational Approaches for Spectrum Estimation

This paper presents an efficient fuzzy classifier with the ability of feature selection based on a fuzzy entropy measure. Fuzzy entropy is employed to evaluate the information of pattern distribution in the pattern space. With this information, we can partition the pattern space into nonoverlapping decision regions for pattern classification. Since the decision regions do not overlap, both the complexity and computational load of the classifier are reduced and thus the training time and classification time are extremely short. Although the decision regions are partitioned into nonoverlapping subspaces, we can achieve good classification performance since the decision regions can be correctly determined via our proposed fuzzy entropy measure. In addition, we also investigate the use of fuzzy entropy to select relevant features. The feature selection procedure not only reduces the dimensionality of a problem but also discards noise-corrupted, redundant and unimportant features. Finally, we apply the proposed classifier to the Iris database and Wisconsin breast cancer database to evaluate the classification performance. Both of the results show that the proposed classifier can work well for the pattern classification application.

This study introduced entropy measures to analyze the heart sound signals of people with and without pulmonary hypertension (PH). The lead II Electrocardiography (ECG) signal and heart sound signal were simultaneously collected from 104 subjects aged between 22 and 89. Fifty of them were PH patients and 54 were healthy. Eleven heart sound features were extracted and three entropy measures, namely sample entropy (SampEn), fuzzy entropy (FuzzyEn) and fuzzy measure entropy (FuzzyMEn) of the feature sequences were calculated. The Mann–Whitney U test was used to study the feature significance between the patient and health group. To reduce the age confounding factor, nine entropy measures were selected based on correlation analysis. Further, the probability density function (pdf) of a single selected entropy measure of both groups was constructed by kernel density estimation, as well as the joint pdf of any two and multiple selected entropy measures. Therefore, a patient or a healthy subject can be classified using his/her entropy measure probability based on Bayes’ decision rule. The results showed that the best identification performance by a single selected measure had sensitivity of 0.720 and specificity of 0.648. The identification performance was improved to 0.680, 0.796 by the joint pdf of two measures and 0.740, 0.870 by the joint pdf of multiple measures. This study showed that entropy measures could be a powerful tool for early screening of PH patients.

We survey the relation of fuzzy entropy measure and similarity measure. Each measure represents features of data uncertainty and certainty between comparative data group. With the help of one-to-one correspondence characteristics, distance measure and similarity measure have been expressed by the complementary characteristics. We construct similarity measure using distance measure, and verification of usefulness is proved. Furthermore analysis of similarity measure from fuzzy entropy measure is also discussed.

Spasticity is a major contributor to pain, disabilities and many secondary complications after stroke. Investigating the effect of spasticity on neuromuscular function in stroke patients may facilitate the development of its clinical treatment, while the underlying mechanism of spasticity still remains unclear. The aim of this study is to explore the difference in the neuromuscular response to passive stretch between healthy subjects and stroke patients with spasticity. Five healthy subjects and three stroke patients with spastic elbow flexor were recruited to complete the passive stretch at four angular velocities (10°/s, 60°/s, 120°/s, and 180°/s) performed by an isokinetic dynamometer. Meanwhile, the 64-channel electromyography (EMG) signals from biceps brachii muscle were recorded. The root mean square (RMS) and fuzzy entropy (FuzzyEn) of EMG recordings of each channel were calculated, and the relationship between the average value of RMS and FuzzyEn over 64-channel was examined. The two groups showed similar performance from results that RMS increased and FuzzyEn decreased with the increment of stretch velocity, and the RMS was negatively correlated with FuzzyEn. The difference is that stroke patients showed higher RMS and lower FuzzyEn during quick stretch than the healthy group. Furthermore, compared with the healthy group, distinct variations of spatial distribution within the spastic muscle were found in the EMG activity of stroke patients. These results suggested that a large number of motor units were recruited synchronously in the presence of spasticity, and this recruitment pattern was non-uniform in the whole muscle. Using a combination of RMS and FuzzyEn calculated from high-density EMG (HD-EMG) recordings can provide an innovative insight into the physiological mechanism underlying spasticity, and FuzzyEn could potentially be used as a new indicator for spasticity, which would be beneficial to clinical intervention and further research on spasticity.

Validity analysis of maximum entropy distribution based on different moment constraints for wind energy assessment

The fuzzy entropy designed for multiple facts selection has been carried out in this work. The entropy for the fuzzy data with respect to a specified fact is designed through a distance measure method. The obtained fuzzy entropy is then applied for the selection from multiple facts. From the relevant fuzzy entropy, it is concluded that data uncertainty information is limited by the total fact of n-1. The bounded calculation of data uncertainty to each fact is proven for multiple facts, and the decision of fuzzy data to the certain fact among multiple facts has been considered with the assistance of fuzzy entropy calculation. To cite this document: Sanghyuk Lee and T.O. Ting, "Uncertainty evaluation via fuzzy entropy for multiple facts", International Journal of Electronic Commerce Studies, Vol.4, No.2, pp. 313-322, 2013. Permanent link to this document: http://dx.doi.org/10.7903/ijecs.1124

Considering the nature and characteristics of construction waste piles, this paper analyzed the factors affecting the stability of the slope of construction waste piles, and established the system of the assessment indexes for the slope failure risks of construction waste piles. Based on the basic principles and methods of fuzzy mathematics, the factor set and the remark set were established. The membership grade of continuous factor indexes is determined using the “ridge row distribution” function, while that for the discrete factor indexes was determined by the Delphi Method. For the weight of factors, the subjective weight was determined by the Analytic Hierarchy Process (AHP) and objective weight by the entropy weight method. And the distance function was introduced to determine the combination coefficient. This paper established a fuzzy comprehensive assessment model of slope failure risks of construction waste piles, and assessed pile slopes in the two dimensions of hazard and vulnerability. The root mean square of the hazard assessment result and vulnerability assessment result was the final assessment result. The paper then used a certain construction waste pile slope as the example for analysis, assessed the risks of the four stages of a landfill, verified the assessment model and analyzed the slope’s failure risks and preventive measures against a slide.

Anomaly detection of rolling elements using fuzzy entropy and similarity measures

Fuzzy partitioning of continuous attributes through discretization methods to construct fuzzy decision tree classifiers

In numerous data clustering problems, the main priority remains a constant demand on development of new improved algorithmic schemes capable of robust and correct data handling. This requirement has been recently boosted by emerging new technologies in data acquisition area. In image processing and image analysis procedures, the image segmentation procedures have the most important impact on the image analysis results. In data analysis methods, in order to improve understanding and description of data structures, many innovative approaches have been introduced. Data analysis methods always strongly depend upon revealing inherent data structure. In the paper, a new algorithmic Rough Entropy Framework - (REF, in short) has been applied in the probabilistic setting. Crisp and Fuzzy RECA measures (Rough Entropy Clustering Algorithm) introduced in [5] are extended into probability area. The basic rough entropy notions, the procedure of rough (entropy) measure calculations and examples of probabilistic approximations have been presented and supported by comparison to crisp and fuzzy rough entropy measures. In this way, uncertainty measures have been combined with probabilistic procedures in order to obtain better insight into data internal structure.

A method is presented for three-level image segmentation through maximizing the fuzzy partition entropy of two-dimensional histogram. Two groups, each including three member functions, namely Z-function, Π-function and S-function, are used for fuzzy division of two-dimensional histogram to get nine fuzzy sets. And the nine fuzzy sets are classified to three parts, corresponding to dark, gray and white part of the image, respectively, while a fuzzy partition is obtained for the two-dimensional space. Then a fuzzy partition entropy is defined based on multi-dimensional fuzzy partition and entropy theory. The parameters of the six membership functions can be determined by maximizing fuzzy partition entropy of two-dimensional histogram and the procedure for finding the optimal combination of all the fuzzy parameters is implemented by quantum genetic algorithm with an appropriate coding method. The experiment results show that the proposed method gives better performance than onedimensional three-level thresholding method under noise case.KeywordsImage segmentationFuzzy partitionQuantum genetic algorithm

This paper deals with the divergence of fuzzy variables from a priori one. Within the framework of credibility theory, a fuzzy cross-entropy is defined to measure the divergence, and some mathematical properties are investigated. Furthermore, a minimum cross-entropy principle is proposed, which tells us that out of all membership functions satisfying given moment constraints, we should choose the one that is closest to the given a priori membership function.

The diagnosis of social anxiety disorder (SAD) is of great consequence not only due to its impacts on the individual and society but also the expenditures to the national health systems. There is yet a deficiency of objective neurophysiological information to assist the present clinical SAD diagnosis. The main objective of this study is to analyze the electroencephalogram (EEG) complexity of 88 SAD subjects, subdivided into 4 balanced groups (22 severe, 22 moderate, 22 mild, and 22 healthy controls (HCs) using Fuzzy Entropy measure (FE) and machine learning algorithms. In addition, this study aimed at designing a computer-aided diagnosis system to identify the severity of SAD (severe, moderate, mild, and HC) in different EEG frequency bands (delta, theta, alpha, and beta). The experimental results showed that among the HC and the three considered levels of SAD, SAD patients in fast-waves exhibited significantly less FE values in resting-state compared with HCs (p <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\leq0.05$ </tex-math></inline-formula> ). The EEG complexity analysis showed a discriminatory neuronal activity over the frontoparietal and occipital regions between SAD patients and HCs. Additionally, the FE values measured in the resting-state were positively correlated with Social Interaction Anxiety Scale (SIAS) scores in fast-waves (beta and alpha), indicating that the regional FE measures are putative biomarkers in assessing the clinical symptoms of SAD. Also, the classification results demonstrated that the proposed method outperformed the state of the art methods with an accuracy of 86.93 %, sensitivity of 92.46%, and specificity of 95.32% with the Naive Bayes (NB) classifier. This study emphasizes the viability of quantitative FE measures and the specific combinations involving the chosen classifiers could be considered as an alternative biomarker for future clinical SAD recognition.