Fuzzy entropy from weak fuzzy subsethood measures

In this paper, we propose a new construction method for fuzzy and weak fuzzy subsethood measures based on the aggregation of implication operators. We study the desired properties of the implication operators in order to construct these measures. We also show the relationship between fuzzy entropy and weak fuzzy subsethood measures constructed by our method

Detection of Epileptic Seizures on EEG Signals Using ANFIS Classifier, Autoencoders and Fuzzy Entropies

Epileptic seizures are one of the most crucial neurological disorders, and their early diagnosis will help the clinicians to provide accurate treatment for the patients. The electroencephalogram (EEG) signals are widely used for epileptic seizures detection, which provides specialists with substantial information about the functioning of the brain. In this paper, a novel diagnostic procedure using fuzzy theory and deep learning techniques is introduced. The proposed method is evaluated on the Bonn University dataset with six classification combinations and also on the Freiburg dataset. The tunable- Q wavelet transform (TQWT) is employed to decompose the EEG signals into different sub-bands. In the feature extraction step, 13 different fuzzy entropies are calculated from different sub-bands of TQWT, and their computational complexities are calculated to help researchers choose the best set for various tasks. In the following, an autoencoder (AE) with six layers is employed for dimensionality reduction. Finally, the standard adaptive neuro-fuzzy inference system (ANFIS), and also its variants with grasshopper optimization algorithm (ANFIS-GOA), particle swarm optimization (ANFIS-PSO), and breeding swarm optimization (ANFIS-BS) methods are used for classification. Using our proposed method, ANFIS-BS method has obtained an accuracy of 99.7

Modeling and Evaluation of Single Machine Flexibility Using Fuzzy Entropy and Genetic Algorithm Based Approach

International audienceFlexibility has long been recognized as a manufacturing capability that has the potential to impact mainly the competitive position of an organization. The entropy approach, which was extended from information theory, fell in handling problems with incomplete and uncertain data, because it depicts only the stochastic aspects included with measured observations. In order to get a global view, this work proposes a new approach based on fuzzy entropy concept. The development of the fuzzy model results in a set of nonlinear constrained problems to be solved using a metaheuristics method. The applicability of our approach is illustrated through a flexible manufacturing cell. By adopting such framework, both dimensions of uncertainty in system modeling, expressed by stochastic variability and imprecision, can be taken into consideration

Identification of the General Anesthesia Induced Loss of Consciousness by Cross Fuzzy Entropy-Based Brain Network.

Although the spatiotemporal complexity and network connectivity are clarified to be disrupted during the general anesthesia (GA) induced unconsciousness, it remains to be difficult to exactly monitor the fluctuation of consciousness clinically. In this study, to track the loss of consciousness (LOC) induced by GA, we first developed the multi-channel cross fuzzy entropy method to construct the time-varying networks, whose temporal fluctuations were then explored and quantitatively evaluated. Thereafter, an algorithm was further proposed to detect the time onset at which patients lost their consciousness. The results clarified during the resting state, relatively stable fuzzy fluctuations in multi-channel network architectures and properties were found; by contrast, during the LOC period, the disrupted frontal-occipital connectivity occurred at the early stage, while at the later stage, the inner-frontal connectivity was identified. When specifically exploring the early LOC stage, the uphill of the clustering coefficients and the downhill of the characteristic path length were found, which might help resolve the propofol-induced consciousness fluctuation in patients. Moreover, the developed detection algorithm was validated to have great capacity in exactly capturing the time point (in seconds) at which patients lost consciousness. The findings demonstrated that the time-varying cross-fuzzy networks help decode the GA and are of great significance for developing anesthesia depth monitoring technology clinically

A Fuzzy Entropy-Based Thematic Classification Method Aimed at Improving the Reliability of Thematic Maps in GIS Environments

Thematic maps of spatial data are constructed by using standard thematic classification methods that do not allow management of the uncertainty of classification and, consequently, eval uation of the reliability of the resulting thematic map. We propose a novel fuzzy-based thematic classification method applied to construct thematic maps in Geographical Information Systems. An initial fuzzy partition of the domain of the features of the spatial dataset is constructed using triangular fuzzy numbers; our method finds an optimal fuzzy partition evaluating the fuzziness of the fuzzy sets by using a fuzzy entropy measure. An assessment of the reliability of the final thematic map is performed according to the fuzziness of the fuzzy sets. We implement our method on a GIS framework, testing it on various vector and image spatial datasets. The results of these tests confirm that our thematic classification method provide thematic maps with a higher reliability with respect to that obtained through fuzzy partitions constructed by expert users

Type-2 Fuzzy Entropy-Sets

The final goal of this study is to adapt the concept of fuzzy entropy of De Luca and Termini to deal with Type-2 Fuzzy Sets. We denote this concept Type-2 Fuzzy Entropy-Set. However, the construction of the notion of entropy measure on an infinite set, such us [0, 1], is not effortless. For this reason, we first introduce the concept of quasi-entropy of a Fuzzy Set on the universe [0, 1]. Furthermore, whenever the membership function of the considered Fuzzy Set in the universe [0, 1] is continuous, we prove that the quasi-entropy of that set is a fuzzy entropy in the sense of De Luca y Termini. Finally, we present an illustrative example where we use Type-2 Fuzzy Entropy-Sets instead of fuzzy entropies in a classical fuzzy algorithm

Fault Diagnosis of Planetary Gear Based on Fuzzy Entropy of CEEMDAN and MLP Neural Network by Using Vibration Signal

A method of planetary gear fault diagnosis based on the fuzzy entropy of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and multi-layer perceptron (MLP) neural network is proposed. The vibration signal is decomposed into multiple intrinsic mode functions (IMFs) by CEEMDAN, and the fuzzy entropy that combines the fuzzy function and sample entropy is proposed and used to extract the feature information contained in each IMF. The fuzzy entropies of each IMF are defined as the input of the MLP neural network, and the planetary gear status can be recognized by the output. The experiments prove the proposed method is effective