# Redefining fuzzy entropy with a general framework

TL;DR: The existing fuzzy entropy functions are redefined and extended to the probabilistic-fuzzy domain and the usefulness of the work is shown in a real world case-study.

Abstract: A general entropy framework is proposed, which could lead to intuitive, interpretable and comparable entropy functions in both probabilistic or fuzzy domain, alike. Based on the proposed general entropy framework, the existing fuzzy entropy functions are redefined. The proposed entropy functions are also extended to the probabilistic-fuzzy domain. The usefulness of the work is shown in a real world case-study.

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TL;DR: This model combines the principle of deep learning algorithm and the improved BP neural network to deal with nonlinear wind speed prediction and shows that this model can achieve the best performance and obtain higher prediction accuracy.

Abstract: Accurate and reasonable wind speed prediction system has a significant impact on the utilization of wind energy. A novel combination forecasting model based on Long Short-Term Memory (LSTM) network and BP neural network is designed in this paper. This model combines the principle of deep learning algorithm and the improved BP neural network to deal with nonlinear wind speed prediction. Before the prediction, singular spectrum analysis (ssa) and complete ensemble empirical model decomposition adaptive noise (CEEMDAN) are selected as the data pretreatment part to de-noise the original wind speed data and decompose it into multiple components. This part is conducive to improving the signal-to-noise ratio (SNR) of wind speed data and simplifying the characteristics of wind speed data. Then, in order to reduce the error accumulation and computation redundancy, fuzzy entropy (FE) is used to calculate the time complexity of each component, according to the Spearman correlation, the inherent mode function (IMF) components are recombined to form a new subsequence. Experimental results show that the error accumulation can be reduced by 48.65% for dataset 1 and 29.53% for dataset 2, and the operation time can be reduced by about 50% for two datasets. To avoid the limitation of a single model, introducing the LSTM and improved BPNN which improved by sparrow search algorithm (SSA) two different prediction models are used to predict the sub sequences with high complexity and the low complexity subsequences, respectively. Finally, the predicted values of the models are superimposed to get the final values. In order to verify the validity of the proposed model, the final predictions, compared with six different prediction models, show that this model can achieve the best performance and obtain higher prediction accuracy. Such as the performance evaluation indexes (RMSE = 0.051, MAPE = 0.929%) are smallest obtained from dataset1 by one-step prediction, and (RMSE = 0.086, MAPE = 0.966%) are smallest obtained from dataset2 by one-step prediction. In addition, the Pearson correlation between the predicted value and the true wind speed value obtained by the prediction model applied to the two data sets is the highest 99.17% and 98.73%, respectively.

55 citations

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TL;DR: In this paper , a combination forecasting model based on Long Short-Term Memory (LSTM) network and BP neural network is designed to deal with nonlinear wind speed prediction.

Abstract: Accurate and reasonable wind speed prediction system has a significant impact on the utilization of wind energy. A novel combination forecasting model based on Long Short-Term Memory (LSTM) network and BP neural network is designed in this paper. This model combines the principle of deep learning algorithm and the improved BP neural network to deal with nonlinear wind speed prediction. Before the prediction, singular spectrum analysis (ssa) and complete ensemble empirical model decomposition adaptive noise (CEEMDAN) are selected as the data pretreatment part to de-noise the original wind speed data and decompose it into multiple components. This part is conducive to improving the signal-to-noise ratio (SNR) of wind speed data and simplifying the characteristics of wind speed data. Then, in order to reduce the error accumulation and computation redundancy, fuzzy entropy (FE) is used to calculate the time complexity of each component, according to the Spearman correlation, the inherent mode function (IMF) components are recombined to form a new subsequence. Experimental results show that the error accumulation can be reduced by 48.65% for dataset 1 and 29.53% for dataset 2, and the operation time can be reduced by about 50% for two datasets. To avoid the limitation of a single model, introducing the LSTM and improved BPNN which improved by sparrow search algorithm (SSA) two different prediction models are used to predict the sub sequences with high complexity and the low complexity subsequences, respectively. Finally, the predicted values of the models are superimposed to get the final values. In order to verify the validity of the proposed model, the final predictions, compared with six different prediction models, show that this model can achieve the best performance and obtain higher prediction accuracy. Such as the performance evaluation indexes (RMSE = 0.051, MAPE = 0.929%) are smallest obtained from dataset1 by one-step prediction, and (RMSE = 0.086, MAPE = 0.966%) are smallest obtained from dataset2 by one-step prediction. In addition, the Pearson correlation between the predicted value and the true wind speed value obtained by the prediction model applied to the two data sets is the highest 99.17% and 98.73%, respectively.

52 citations

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01 Mar 2018

TL;DR: In this article, a new normalized projection as a separation measure, along with TOPSIS (technique for order preference by similarity to ideal solution) technique, is used for current decision model.

Abstract: Abstract The weights of decision makers play an important role in group decision-making problems. Entropy is a very important measure in information science. This work models an approach to determine the weights of decision makers by using an entropy measure. A new normalized projection as a separation measure, along with TOPSIS (technique for order preference by similarity to ideal solution) technique, is used for current decision model. The attribute values in current model are characterized by exact values and intervals. A comparison and experimental analysis show the applicability, feasibility, effectiveness and advantages of the proposed method.

45 citations

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TL;DR: A hybrid approach combining information entropy and an evolutionary algorithm to optimize a geodetic network's measurement structure to determine an engineering object's horizontal displacements and it was noticed that the application of the hybrid approach allowed the selection of only those observations with the highest information content.

Abstract: The article aims to present a hybrid approach combining information entropy and an evolutionary algorithm to optimize a geodetic network's measurement structure to determine an engineering object's horizontal displacements. The objective function was defined, which in the case under consideration was the information entropy of the geodetic observation system in terms of the parameter vector's entropy with the true values. The optimal number of observations in the geodetic network depended on the observation system's increase in information. During the research, it was noticed that the application of the hybrid approach allowed the selection of only those observations with the highest information content. It shortened the measurement time without reducing the accuracy of the displacements obtained. The obtained results of numerical analyses showed the proposed solution's effectiveness for optimizing the geodetic network structure.

11 citations

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TL;DR: The authors formulate a bi-objective distribution model for urban trips constrained by origins and destinations while maximizing entropy, and develop a flexible and consistent approach in which the estimatio- gatio-...

Abstract: We formulate a bi-objective distribution model for urban trips constrained by origins and destinations while maximizing entropy. We develop a flexible and consistent approach in which the estimatio...

5 citations

##### References

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TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.

Abstract: In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a considerable extent the continuous case can be obtained through a limiting process from the discrete case by dividing the continuum of messages and signals into a large but finite number of small regions and calculating the various parameters involved on a discrete basis. As the size of the regions is decreased these parameters in general approach as limits the proper values for the continuous case. There are, however, a few new effects that appear and also a general change of emphasis in the direction of specialization of the general results to particular cases.

65,425 citations

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TL;DR: A functional defined on the class of generalized characteristic functions (fuzzy sets), called “entropy≓, is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets.

Abstract: A functional defined on the class of generalized characteristic functions (fuzzy sets), called “entropy≓, is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets. This “entropy≓ may be regarded as a measure of a quantity of information which is not necessarily related to random experiments. Some mathematical properties of this functional are analyzed and some considerations on its applicability to pattern analysis are made.

2,024 citations

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TL;DR: It is shown that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of F ∩ F c and F ∪ F c .

Abstract: A non-probabilistic-type entropy measure for intuitionistic fuzzy sets is proposed. It is a result of a geometric interpretation of intuitionistic fuzzy sets and uses a ratio of distances between them proposed in Szmidt and Kacprzyk (to appear). It is also shown that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of F ∩ F c and F ∪ F c .

829 citations

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TL;DR: The distance measure between intuitionistic fuzzy sets is defined and an axiom definition of intuitionist fuzzy entropy is given and a theorem which characterizes it is studied.

Abstract: We recall the definitions of intuitionistic fuzzy sets and interval-valued fuzzy sets with the relation between these sets established by K. Atanassov. We define the distance measure between intuitionistic fuzzy sets and we give an axiom definition of intuitionistic fuzzy entropy and a theorem which characterizes it. Finally, we study a very special entropy and recall that all we have done for intuitionistic fuzzy sets is also good for interval-valued fuzzy sets.

684 citations