Attribute Reduction of Hybrid Decision Information Systems Based on Fuzzy Conditional Information Entropy

The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

Novel detection method for infrared small targets using weighted information entropy

This paper presents a method for detecting the small infrared target under complex background. An algorithm, named local mutation weighted information entropy （LMWIE）, is proposed to suppress background. Then, the grey value of targets is enhanced by calculating the local energy. Image segmentation based on the adaptive threshold is used to solve the problems that the grey value of noise is enhanced with the grey value improvement of targets. Experimental results show that compared with the adaptive Butterworth high-pass filter method, the proposed algorithm is more effective and faster for the infrared small target detection.

Integrating unascertained measurement and information entropy theory to assess blastability of rock mass

Due to the complex features of rock mass blastability assessment systems, an evaluation model of rock mass blastability was established on the basis of the unascertained measurement （UM） theory and the actual characteristics of the project. Considering a comprehensive range of intact rock properties and discontinuous structures of rock mass, twelve main factors influencing the evaluation blastability of rock mass were taken into account in the UM model, and the blastability evaluation index system of rock mass was constructed. The unascertained evaluation indices corresponding to the selected factors for the actual situation were solved both qualitatively and quantitatively. Then, the UM function of each evaluation index was obtained based on the initial data for the analysis of the blastability of six rock mass at a highway improvement cutting site in North Wales. The index weights of the factors were calculated by entropy theory, and credible degree identification （CDI） criteria were established according to the UM theory. The results of rock mass blastability evaluation were obtained by the CDI criteria. The results show that the UM model assessment results agree well with the actual records, and are consistent with those of the fuzzy sets evaluation method. Meanwhile, the unascertained superiority degree of rock mass blastability of samples S1-$6 which can be calculated by scoring criteria are 3.428 5, 3.453 3, 4.058 7, 3.675 9, 3.516 7 and 3.289 7, respectively. Furthermore, the proposed method can take into account large amount of uncertain information in blastability evaluation, which can provide an effective, credible and feasible way for estimating the blastability of rock mass. Engineering practices show that it can complete the blastability assessment systematically and scientifically without any assumption by the proposed model, which can be applied to practical engineering.

Determination of neutron-skin thickness using configurational information entropy

Configurational information entropy(CIE)theory was employed to determine the neutron-skin thickness of neutron-rich calcium isotopes.The nuclear density distributions and fragment cross sections in 350 MeV/u ^(40-60)Ca+^(9)Be projectile fragmentation reactions were calculated using a modified statistical abrasion-ablation model.CIE quantities were determined from the nuclear density,isotopic,mass,and charge distributions.The linear correlations between the CIE determined using the isotopic,mass,and charge distributions and the neutron-skin thickness of the projectile nucleus show that CIE provides new methods to extract the neutron-skin thickness of neutron-rich nuclei.

An Intelligent Fault Diagnosis Method of Multi-Scale Deep Feature Fusion Based on Information Entropy

For a single-structure deep learning fault diagnosis model,its disadvantages are an insufficient feature extraction and weak fault classification capability.This paper proposes a multi-scale deep feature fusion intelligent fault diagnosis method based on information entropy.First,a normal autoencoder,denoising autoencoder,sparse autoencoder,and contractive autoencoder are used in parallel to construct a multi-scale deep neural network feature extraction structure.A deep feature fusion strategy based on information entropy is proposed to obtain low-dimensional features and ensure the robustness of the model and the quality of deep features.Finally,the advantage of the deep belief network probability model is used as the fault classifier to identify the faults.The effectiveness of the proposed method was verified by a gearbox test-bed.Experimental results show that,compared with traditional and existing intelligent fault diagnosis methods,the proposed method can obtain representative information and features from the raw data with higher classification accuracy.

Fuzzy entropy design for non convex fuzzy set and application to mutual information

Fuzzy entropy was designed for non convex fuzzy membership function using well known Hamming distance measure.The proposed fuzzy entropy had the same structure as that of convex fuzzy membership case.Design procedure of fuzzy entropy was proposed by considering fuzzy membership through distance measure,and the obtained results contained more flexibility than the general fuzzy membership function.Furthermore,characteristic analyses for non convex function were also illustrated.Analyses on the mutual information were carried out through the proposed fuzzy entropy and similarity measure,which was also dual structure of fuzzy entropy.By the illustrative example,mutual information was discussed.

Relativistic Information Entropy on Uncertainty Analysis

in this paper, a new approach to relativistic information entropy is used to assess some relative uncertainties in structural reliability assessment. This approach is composed of the information theory and the relativistic theory, and can be used to measure the relativity of parameter uncertainty and system uncertainty in structural reliability theory based on the same generalized relativistic reference system. Therefore, the structural reliability assessment can be assessed reasonably by the approach.

A framework of force of information influence and application for C4KISR system

The subversive nature of information war lies not only in the information itself, but also in the circulation and application of information. It has always been a challenge to quantitatively analyze the function and effect of information flow through command, control, communications, computer, kill, intelligence,surveillance, reconnaissance (C4KISR) system. In this work, we propose a framework of force of information influence and the methods for calculating the force of information influence between C4KISR nodes of sensing, intelligence processing,decision making and fire attack. Specifically, the basic concept of force of information influence between nodes in C4KISR system is formally proposed and its mathematical definition is provided. Then, based on the information entropy theory, the model of force of information influence between C4KISR system nodes is constructed. Finally, the simulation experiments have been performed under an air defense and attack scenario. The experimental results show that, with the proposed force of information influence framework, we can effectively evaluate the contribution of information circulation through different C4KISR system nodes to the corresponding tasks. Our framework of force of information influence can also serve as an effective tool for the design and dynamic reconfiguration of C4KISR system architecture.

Quantum information entropies of the eigenstates for the Pschl-Teller-like potential

Shannon entropy for lower position and momentum eigenstates of Ptschl-Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position information entropy density p （x） moves right when the potential parameter V1 increases and its amplitude decreases. However, its wave through moves left with the increase in the potential parameter 丨V2丨. Concerning the momentum information entropy density p（p）, we observe that its amplitude increases with increasing potential parameter V1, but its amplitude decreases with increasing丨V2丨. The Bialynicki-Birula-Mycielski （BBM） inequality has also been tested for a number of states. Moreover, there exist eigenstates that exhibit squeezing in the momentum information entropy. Finally, we note that position information entropy increases with V1, but decreases with 丨V2丨, However, the variation of momentum information entropy is contrary to that of the position information entropy.

Multi-objectives fuzzy optimization model for ship form demonstration based on information entropy

Selecting optimization ship form scheme is an important content in the process of concept design of ship. Multi-objective fuzzy decision-making model for ship form demonstration is set up according to the fuzzy pattern-recognition theory. Weight coefficients of each target of ship form scheme are determined by information entropy and individual subjective partiality. This model is used to select the optimal ship form scheme, the example shows that the model is exact and the resuh is credible. It can provide a reference for choosing the optimization scheme of ship form.

Configurational information entropy analysis of fragment mass cross distributions to determine the neutron skin thickness of projectile nuclei

Configurational information entropy(CIE)analysis has been shown to be applicable for determining the neutron skin thickness(δnp)of neutron-rich nuclei from fragment production in projectile fragmentation reactions.The BNN+FRACS machine learning model was adopted to predict the fragment mass cross-sections(σ_(A))of the projectile fragmentation reactions induced by calcium isotopes from ^(36)Ca to ^(56)Ca on a ^(9)Be target at 140MeV/u.The fast Fourier transform was adopted to decompose the possible information compositions inσA distributions and determine the quantity of CIE(S_(A)[f]).It was found that the range of fragments significantly influences the quantity of S_(A)[f],which results in different trends of S_(A)[f]~δnp correlation.The linear S_(A)[f]~δnp correlation in a previous study[Nucl.Sci.Tech.33,6(2022)]could be reproduced using fragments with relatively large mass fragments,which verifies that S_(A)[f]determined from fragmentσAis sensitive to the neutron skin thickness of neutron-rich isotopes.

Information Entropy Squeezing for a Atom in Mode-Mode Competition System

The entropy squeezing properties for a two-level atom interacting with a two-mode field via two differentcompeting transitions are investigated from a quantum information point of view.The influences of the initial state of thesystem and the relative coupling strength between the atom and the field on the atomic information entropy squeezingare discussed.Our results show that the squeezed direction and the frequency of the information entropy squeezing canbe controlled by choosing the phase of the atom dipole and the relative competing strength of atom-field,respectively.We find that,under the same condition,no atomic variance squeezing is predicted from the HUR while optimal entropysqueezing is obtained from the EUR,so the quantum information entropy is a remarkable precision measure for theatomic squeezing in the considered system.

A Heuristic Clustering Algorithm forIntrusion Detection Based on Information Entropy

This paper studied on the clustering problem for intrusion detection with the theory of information entropy, it was put forward that the clustering problem for exact intrusion detection based on information entropy is NP complete, therefore, the heuristic algorithm to solve the clustering problem for intrusion detection was designed, this algorithm has the characteristic of incremental development, it can deal with the database with large connection records from the internet.

The Emergence of Time from Quantum Information Dynamics

This paper presents a novel framework for understanding time as an emergent phenomenon arising from quantum information dynamics. We propose that the flow of time and its directional arrow are intrinsically linked to the growth of quantum complexity and the evolution of entanglement entropy in physical systems. By integrating principles from quantum mechanics, information theory, and holography, we develop a comprehensive theory that explains how time can emerge from timeless quantum processes. Our approach unifies concepts from quantum mechanics, general relativity, and thermodynamics, providing new perspectives on longstanding puzzles such as the black hole information paradox and the arrow of time. We derive modified Friedmann equations that incorporate quantum information measures, offering novel insights into cosmic evolution and the nature of dark energy. The paper presents a series of experimental proposals to test key aspects of this theory, ranging from quantum simulations to cosmological observations. Our framework suggests a deeply information-theoretic view of the universe, challenging our understanding of the nature of reality and opening new avenues for technological applications in quantum computing and sensing. This work contributes to the ongoing quest for a unified theory of quantum gravity and information, potentially with far-reaching implications for our understanding of space, time, and the fundamental structure of the cosmos.

Time evolution of information entropy for a stochastic system with double singularities driven by quasimonochromatic noise

This paper deals with the time evolution of information entropy for a stochastic system with double singularities driven by quasimonochromatic noise. The dimension of the Fokker Planck equation is reduced by the linear transfor- mation. The exact expression of the time dependence of information entropy is obtained based on the definition of Shannon＇s information entropy. The relationships between the properties of dissipative parameters, system singularity strength parameter, quasimonochromatic noise, and their effects on information entropy are discussed.

Mutual Information and Relative Entropy of Sequential Effect Algebras

In this paper,we introduce and investigate the mutual information and relative entropy on the sequentialeffect algebra,we also give a comparison of these mutual information and relative entropy with the classical ones by thevenn diagrams.Finally,a nice example shows that the entropies of sequential effect algebra depend extremely on theorder of its sequential product.

Target Ship Identification Algorithm Based on Comprehensive Correlation Discriminant and Information Entropy

Ship type identification is an important part of electronic reconnaissance. However, in the existing methods, such as statistical-based methods and fuzzy-mathematics-based methods, the information acquired by the passive sensor is not fully utilized, and there is a certain ambiguity in the assignment relationship of the emitters-ship. They can’t conclude the accurate and reliable assignment relationship of the emitters-ship. Therefore, this paper proposes a comprehensive correlation discriminant method to obtain a more reliable and comprehensive emitters-ship assignment, and then uses information entropy method to identify the type of the target ship on the basis of this association and assign the credibility. The simulation results show that this algorithm can effectively solve the problem of target ship type identification using the information of multi-passive sensors.

An outlier recognition approach in surveying data based on information entropy

A novel outlier recognition method in surveying data is presented based on Shannon information entropy. The probability distribution of surveying data does not need to be known or hypothesized in this method, and it is not only accurate but also convenient to calculate in this method compared with statistical recognition method.

k-NN Based Bypass Entropy and Mutual Information Estimation for Incremental Remote-Sensing Image Compressibility Evaluation

Incremental image compression techniques using priori information are of significance to deal with the explosively increasing remote-sensing image data. However, the potential benefi ts of priori information are still to be evaluated quantitatively for effi cient compression scheme designing. In this paper, we present a k-nearest neighbor(k-NN) based bypass image entropy estimation scheme, together with the corresponding mutual information estimation method. Firstly, we apply the k-NN entropy estimation theory to split image blocks, describing block-wise intra-frame spatial correlation while avoiding the curse of dimensionality. Secondly, we propose the corresponding mutual information estimator based on feature-based image calibration and straight-forward correlation enhancement. The estimator is designed to evaluate the compression performance gain of using priori information. Numerical results on natural and remote-sensing images show that the proposed scheme obtains an estimation accuracy gain by 10% compared with conventional image entropy estimators. Furthermore, experimental results demonstrate both the effectiveness of the proposed mutual information evaluation scheme, and the quantitative incremental compressibility by using the priori remote-sensing frames.

A Method of Using Information Entropy of an Image as an Effective Feature for Com-puter-Aided Diagnostic Applications

Computer-aided detection and diagnosis (CAD) systems are increasingly being used as an aid by clinicians for detection and interpretation of diseases. In general, a CAD system employs a classifier to detect or distinguish between abnormal and normal tissues on images. In the phase of classification, a set of image features and/or texture features extracted from the images are commonly used. In this article, we investigated the characteristic of the output entropy of an image and demonstrated the usefulness of the output entropy acting as a texture feature in CAD systems. In order to validate the effectiveness and superiority of the output-entropy-based texture feature, two well-known texture features, i.e., mean and standard deviation were used for comparison. The database used in this study comprised 50 CT images obtained from 10 patients with pulmonary nodules, and 50 CT images obtained from 5 normal subjects. We used a support vector machine for classification. A leave-one-out method was employed for training and classification. Three combinations of texture features, i.e., mean and entropy, standard deviation and entropy, and standard deviation and mean were used as the inputs to the classifier. Three different regions of interest (ROI) sizes, i.e., 11 × 11, 9 × 9 and 7 × 7 pixels from the database were selected for computation of the feature values. Our experimental results show that the combination of entropy and standard deviation is significantly better than both the combination of mean and entropy and that of standard deviation and mean in the case of the ROI size of 11 × 11 pixels (p < 0.05). These results suggest that information entropy of an image can be used as an effective feature for CAD applications.