Maximum Entropy Value Research Articles

Structure, Electronic, Optical, Magnetic and Magnetocaloric Properties of Sm2CuMnO6 Double Perovskite Nanomaterial

This study explores the structural, microstructural, optical, and magnetic characteristics of double perovskite oxide Sm2CuMnO6. The sample is prepared in the monoclinic phase with space group P21/n using the auto-combustion method. The crystal structure exhibits distortion and tilting. First-principles calculations are conducted using the density-functional theory framework, focusing on electronic structures and density of states. The average crystallite size, particle size and grain size of the sintered sample are 34.42 nm, 36.15 nm and 475 nm respectively. The sample exhibits a direct band gap energy of 1.96 eV. Analysis of the X-ray photoelectron spectra indicates the presence of Sm3+, Cu2+, and Mn3+/Mn4+ ions in the sample. The DC magnetization study reveals a Curie temperature (Tc) of 50 K for the sample. A non-metallic state resembling a spin glass is detected below 15 K, arising from the competition between antiferromagnetic and ferromagnetic interactions. The maximum value of isothermal magnetic entropy, the relative cooling power and heat capacity are 1.4 J.kg–1.K–1, 100.2 J.kg–1, and 1.35 J.kg–1.K–1 at a field change of 70 kOe respectively. The value of Temperature Averaged Entropy Change is 1.36 J.kg−1.K−1 and 1.29 J.kg−1.K−1 for a temperature span of 10 K and 40 K at a field change of 70 kOe.

Defining urban boundaries through DBSCAN and Shannon's entropy: The case of the Mexican National Urban System

A novel method is proposed to define cities' boundaries within a given national urban system. Point Volunteered Geographic Information, such as the OpenStreetMap road network nodes, together with national geospatial information, like economic units, are recursively clustered using DBSCAN at different distance thresholds; clusters smaller than a threshold reflecting the rural settlements pattern are filtered, and then Shannon's entropy for the entire system is calculated. The system of percolated nodes obtained when this entropy reaches its maximum is compared against the current definition of what is officially urban. It is found to be very similar to the actual urban-nonurban classification, and also to have a very high correspondence with the current classification of the Mexican National Urban System (SUN). An additional finding is that the percolated system at the maximum entropy value has a very high correspondence with Zipf's law, while the current Mexican SUN does not.

Practical Teaching and Intellectualization of University Courses Based on the Maximum Information Entropy Model

Abstract Traditional teaching has become a thing of the past, the integration of technology and the classroom has brought about significant changes in education, and the role of information entropy in teaching has gradually manifested itself. In this paper, the behavioral time occupancy of the teaching process of university courses is viewed as a probability distribution event combined with the Lagrange multiplier method to solve the maximum entropy value in the distribution of practical teaching behavior. The practice depth value of classroom behavior can be calculated using the interaction behavior coefficient and interaction behavior entropy. Apply the information entropy to the practical teaching analysis of university courses, verify the practical effect of university courses from different sides, and carry out intelligent course construction according to the current situation of students’ learning behavior. The results show that the average score of class 3 in the practical analysis ability assessment is 4.021, which indicates that the practical analysis ability of students in the class meets the standard, and the students’ practical execution should be mainly cultivated in the later practical teaching. 67.1% of students believe that the intelligent classroom has improved their performance over the traditional classroom according to the intelligent course model.

ОЦЕНКА НЕОДНОРОДНОСТИ НАУЧНО-ИННОВАЦИОННОГО РАЗВИТИЯ ТЕРРИТОРИЙ РОССИЙСКОЙ ФЕДЕРАЦИИ С ПРИМЕНЕНИЕМ ТЕОРИИ ЭНТРОПИИ

It is difficult to overestimate the role of the scientific and innovative sphere in the develop-ment of territories, especially in the conditions of current sanctions, which significantly limit the possi-bilities of further socio-economic growth ofthe country. It is science that can become a driver in over-coming crisis phenomena, since its formation is a necessary condition for achieving the technical and technological sovereignty of the state. The regions of Russia are characterized by heterogeneity in their development, and the scientific and innovative subsystem is no exception. The balanced growth of the country's territories involves the exchange of information between subjects under the conditions of regular influence of environmental factors on scientific and innovative processes. It is precisely this openness of regional systems in matters of scientific and innovative development that makes it possi-ble to use the entropy approach to assess the prospects for planning and forecasting. Within the frame-work of this study, it is proposed to calculate the integral characteristics of scientific and innovative development based on open statistical data, followed by an assessment of the measure of uncertainty in the development of districts according to this criterion. The found indicators are also compared with the minimum and maximum entropy values for the systems under consideration. It was revealed that the lowest value of entropy is typical for the North Caucasus Federal District, which indicates the wide possibilities of applying traditional approaches to planning scientific and innovative development of the regions of the district. Subjects of the Central Federal District in matters of scientific and innovative growth most need an individual approach when building strategic plans, since the value of the entropy function is the largest among all the districts under consideration. The versatility of the proposed ap-proach makes it possible to analyze processes taking into account the uncertainty of the systems. Con-sideration of entropy characteristics is the most important stage of planning. Its application can deter-mine the prospects for further goal-setting, taking into account the possibility of achieving the desired quantitative and qualitative characteristics of scientific and innovative development of regions in the future.

Tree Algorithm Model on Size Classification Data Mining

The goal of this research is to use a tree algorithm to categorize student clothing in order to acquire an accurate size. This research is qualitative through descriptive analysis, while the analysis used C.45 tree algorithm classification. Manual calculations utilizing the tree algorithm formula revealed that most students require XL-sized clothing. On the characteristic of X5 (length of the shoulder), the maximum entropy and information gain values were obtained at 0.212642462. According to the forecast, the shoulder length attribute is the first calculation in developing a decision tree scheme since it has the largest entropy and the value of information gain. Lastly, the findings of this study analysis can be used as a mapping prediction to make decisions on the size of the student group's clothing.

Tuning the magnetic and magnetocaloric properties of a compound via mixing (1–x).La0.67Ca0.33MnO3 +x.La0.67Sr0.33MnO3 (x = 0, 0.25, 0.50, 0.75, 1): Composite materials or composite compounds?

This study aims to optimize the magnetic and magnetocaloric properties of composite materials (or compounds) produced by mixing different ratios of two manganite compounds having different structural, magnetic, and magnetocaloric properties. The parent compounds were prepared using the sol–gel production method and the ultrasonic bath mixing technique was involved to prepare desired composite materials. SEM analyses revealed that the parents and composite materials have the same surface morphologies except for their grain sizes. EDS analyses were performed to identify the possible/candidate phases in the composite materials. These candidate phases are involved in refining XRD data. The fact that the Curie temperatures (TC) of the composite materials were found to be much higher than those of the parent compounds was another proof that composite compounds were obtained instead of composite materials by using the ultrasonic bath mixing technique. Although the TC of the composite compounds was higher than those of the parent compounds, the maximum magnetic entropy values were found to vary between the maximum magnetic entropy valuesof the parent compounds.

Sparse Compression-Based Image Encryption using Data Encryption Standards RC5

In this work, we have used the standard symmetric key block cipher data encryption algorithm RC5(32,16,8) for the encryption of digital greyscale images. For this, we have only considered the nonzero elements of the sparse matrix of the images which have been generated using the sparse representation technique. The security strength of the proposed technique is verified through different quality parameters, e.g. information entropy, correlation coefficients, NPCR, UACI, and NIST test. Our proposed algorithm achieved the maximum information entropy value of 7.9977 for the cameraman image and nearly zero correlation coefficient values establish the robustness of the cryptosystem. The highest NPCR and UACI values obtained in our work are 99.6916 and 33.9605, which are closer to the maximum theoretical values. The proposed technique is also compared with some of the contemporary works to validate the credibility of our proposed algorithm.

Lead-free medium-entropy (Na0.47(1-x)Bi0.47(1-x)Ba0.06(1-x)Sr0.7xNd0.2x)TiO3 relaxor ceramics with robust energy-storage performance

High-entropy engineering is becoming a new strategy in dielectric energy storage capacitors. However, high-entropy strategy alone is insufficient to produce good energy storage performance, as the polarization intensity is greatly reduced by the highly disordered state. We, herein, propose an “entropy engineering + polyphase” strategy and highlight that materials with medium entropy values, no necessity of high entropy values, can yield good energy storage performance under condition that polyphases are introduced in the materials. To illustrate the effectiveness of this strategy, the medium-entropy ceramics (Na0.47(1-x)Bi0.47(1-x)Ba0.06(1-x)Sr0.7xNd0.2x)TiO3 with x = 0.1, 0.2, 0.3, 0.4, and 0.5 were designed by doping ions with different ionic radii and valence states at the A-site. Investigations on the energy storage performance reveal that the sample of x = 0.4, with the maximum entropy value of 1.39R, has the largest recyclable energy storage density Wrec = 8.71 J/cm3 with a high efficiency η = 88.5%. The sample also shows excellent thermal stability of dielectric constant (Δε′/ε25oC′≤ ±15%) over a temperature range of −61–144 °C. The excellent performance is due to the introduction of multiphase in the medium entropy ceramics, which effectively refines the grain and domain sizes, leading to a high polarization intensity (44.23 μC/cm2) and excellent energy storage performance. This work shows that “entropy engineering + polyphase” is an effective strategy for excellent energy storage performance and paves a way of developing new energy storage materials by entropy engineering.

A High-Efficient Reinforcement Learning Approach for Dexterous Manipulation.

Robotic hands have the potential to perform complex tasks in unstructured environments owing to their bionic design, inspired by the most agile biological hand. However, the modeling, planning and control of dexterous hands remain unresolved, open challenges, resulting in the simple movements and relatively clumsy motions of current robotic end effectors. This paper proposed a dynamic model based on generative adversarial architecture to learn the state mode of the dexterous hand, reducing the model's prediction error in long spans. An adaptive trajectory planning kernel was also developed to generate High-Value Area Trajectory (HVAT) data according to the control task and dynamic model, with adaptive trajectory adjustment achieved by changing the Levenberg-Marquardt (LM) coefficient and the linear searching coefficient. Furthermore, an improved Soft Actor-Critic (SAC) algorithm is designed by combining maximum entropy value iteration and HVAT value iteration. An experimental platform and simulation program were built to verify the proposed method with two manipulating tasks. The experimental results indicate that the proposed dexterous hand reinforcement learning algorithm has better training efficiency and requires fewer training samples to achieve quite satisfactory learning and control performance.

Characterization of liquid permeation through fibrous structure by texture analysis

The interaction of liquids with materials is an important factor influencing many technological processes and describing the quality of the material itself. However, characterization of the wetting and penetration of liquids phenomena through the materials of heterogeneous structure is a very difficult task. Paper is an example of such material. Paper sizing is one of the most important operations in paper technology. Its purpose is to reduce the wettability of the paper. The aim of the present study was to evaluate the suitability of the texture analysis to assess the uniformity of liquid penetration through the paper structure in terms of the degree of the paper sizing. As a result of the research, a new method of measuring was proposed based on dynamic changes in their texture parameters. For this purpose, such texture parameters as entropy and contrast were used. Characteristic points were determined on the curves of the dynamic changes of both parameters. It was proved that there is a correlation between the dynamics of liquid penetration through the paper structure and the examined texture parameters. It was found that the maximum value of entropy and contrast, the time of reaching both values, the points of inflection of the curves during their decrease, and the times by which these points were reached can be useful parameters that provide information about the nature of the liquid flow through the porous material structure.

Study of the wave scattering in geological environments for the propagation velocity estimation

Diffraction is a naturally physical phenomenon which plays an extremely key role in forming some theoretical foundations of analyzing geophysical data such as seismic reflection and high frequency electromagnetic, Ground Penetrating Radar to study geological objects. In this phenomenon, when a wave field propagates from a source to an object with small size or a rough surface, its wave energy receivers act as the secondary sources and send their energy parts back to geophones on the ground surface. The relationship between the wave propagation time and the receiver coordinates is formulated as a diffraction hyperbola. This paper reported examples of the high frequency electromagnetic and seismic scattering phenomena with their applications in the study of the wave propagation velocity, location of civil underground objects and seabed depth. The research on scattering phenomenon for the electromagnetic waves has been known and widely applied; however, studying the wave velocity model by the diffraction analysis from the high resolution reflection seismic data for a fixed source receiver distance can be firstly considered in Vietnam and in the world. To determine the two wave velocity types, two graphs of their energy and entropy attributes were built and then calculated from their Kirchhoff migrated data in velocity ranges in order to find out their attributes’ extremes versus velocity variables. Their migrated sections with correct wave velocities could correctly locate diffractors as underground anomalies and produced the maximum energy and minimum entropy values in the peaks of diffraction hyperbolae and the surrounding zones of the diffractors, respectively. These geophysical data were measured at the urban and coastal area of Can Gio district, Ho Chi Minh city, Vietnam.

Entanglement Entropy Analysis in Dicke's Model Quantum System

Entanglement is a property of interacting particles in a quantum system. The measure of the interaction can be known by looking for the entanglement entropy value in the system. The quantum system used in this study is the Dicke model quantum system which consists of a single-mode electromagnetic radiation field and a two-level N-atom. This study aims to determine the influence of the coupling constant on entanglement entropy and system dynamics. Simulation of system dynamics is carried out with the Quantum Toolbox in Python (QuTiP) module. The simulation results show that the coupling constant has a significant effect on the entanglement entropy value. The greater the value of the coupling constant used, the entanglement entropy value increases. In addition, there is a maximum entanglement entropy value for N greater than one. The coupling constant also affects the dynamics of the system, that is, the greater the value of the coupling constant, the more quantum states can be accessed by atoms.

Use of maximum entropy to improve validation and prediction of active fires in a Brazilian savanna region

Monitoring fires using satellite images is a fundamental tool for managers of protected areas (PAs). However, false alerts hinder their ability and make their application unfeasible, since there are few fire brigades available for field checks. Thus, this research proposes the validation, identification, and prediction of active fires for the years 2001 to 2018 for a protected area of the Brazilian savanna. The validation was performed by counting the active fires that were effectively contained in a burning area by cross-referencing MODIS sensor images. Identification was performed by analyzing the spectral behavior of burning and non-burning in the active fire area. The maximum entropy was calculated from the spectral values and compared between an active focus with and without burning. In the prediction, the climatic conditions of the month before burning were analyzed, and the maximum entropy value was evaluated for model viability. The results indicated that only 30% of the active fires were actually in a burned area. The use of maximum entropy favors the improvement of the MODIS active fire product. The confirmed fires were in regions where the probability was above 75%, whereas the non-burning fires were approximately 60%. The variables evapotranspiration, wind speed, water deficit, and road proximity were the most relevant for the active fire prediction model. For the validation years 2019 and 2020, this method predicted the location of fires in 75% of the cases. This methodology, once employed by PA managers, can ensure accurate, efficient, and cost-effective monitoring of forest fire prevention and combat.

Water sorption isotherms of different sodium alginates: Thermodynamic evaluation and influence of mannuronate‐guluronate copolymers

AbstractWater desorption isotherms of three alginates with different structural features were determined at 25, 37, and 50°C. The Halsey model was selected to fit the equilibrium water sorption data. Differential and integral enthalpy and entropy were estimated for tested alginates. Optimal storage conditions of tested alginates (moisture content from 0.15 to 0.20 kg water/kg dry solid and relative humidity from 35% to 50%) were determined from the maximum and minimum integral enthalpy and entropy values, respectively. A model was proposed to estimate the water sorption isotherms of alginates based on the alginate monomers (mannuronate, M, and guluronate, G) at low water activity (<0.4). M fraction was mainly responsible for the hygroscopicity of alginates. Alginates with similar G fraction showed different hygroscopic features by the presence of more homopolymeric G blocks that could form helical structures at low moisture content, decreasing the water affinity.Practical applicationsDetermination of water sorption isotherms is fundamental to determine the optimal storage conditions at different temperatures. Their knowledge is essential for designing drying equipment, selecting adequately drying conditions (temperature and relative humidity of air) and drying time. Mathematical models are useful to estimate equilibrium moisture content in wide ranges of water activity and temperature. The thermodynamic study also provides valuable information about energy consumption and consequently operational costs. In this case, high content of mannuronate, M, increases the hygroscopic character of alginates, but the optimal moisture content of dried alginates to achieve maximum stability during storing varies in a narrow interval (0.15–0.20 kg water/kg dry solid).

Motion Video Image Based on Sensor and Multiprocessing Technology in Track and Field Sports

In order to use motion video image processing technology to better guide and evaluate athletes’ technical and tactical ability, this paper first constructed a motion video image acquisition system. Secondly, a fuzzy kernel estimation method for uniform linear motion based on cepstrum property is proposed. Then, the motion blur areas to be processed are selected, and only these areas are deblurred. Finally, the effective removal of local motion blur is realized, and a clear scene image is obtained. Then, the maximum value of the total entropy of the image is calculated by using the information entropy theory, and the particle swarm optimization algorithm is introduced to find the maximum threshold of image segmentation. Finally, small wave optical flow estimation algorithm and rectangular window scanning algorithm across scales of motion image target detection algorithm are proposed, to not only solve the traditional optical flow estimation for fast moving object detection accuracy but also improve the efficiency of the optical flow computation. Compared to many kinds of algorithms, this paper proposed an algorithm that can improve the accuracy of moving target detection and measurement accuracy. And, the detection accuracy of the proposed algorithm is up to 86.5%. The estimated accuracy was as high as 65%. The segmentation accuracy is up to 95%.

Effectiveness of Energy Transfer versus Mixing Entropy in Coupled Mechanical–Electrical Oscillators

Electrostatic energy harvesters convert kinetic energy into electrical energy via variable capacitors. Efforts to improve their power output are hampered by a lack of understanding of the fundamental limit for energy conversion efficiency. In heat engines, the theoretical limit of conversion efficiency is intrinsically related to entropy and the second law of thermodynamics. Laying the foundation for similar concepts for kinetic energy harvesters may be necessary for establishing a conversion efficiency limit. Thus, the mixing entropy concept is borrowed from statistical mechanics and is adapted here, for the first time, to characterize the energy transfer between coupled mechanical–electrical oscillators. The investigated system is composed of a spring-mass coupled to an inductance-capacitor circuit via a variable capacitor. Combining the two subsystems (electrical and mechanical) generates entropy, referred to as mixing entropy. A non-dimensional study of the governing equations of the systems and their energy terms is carried out. Trends in mixing entropy are compared with trends in the total energy of the system, assuming a conservative system, weak coupling between electrical and mechanical domains, and identical natural frequency of the two oscillators. It is found that mixing entropy can predict the peak in effectiveness of the energy transfer between the two domains. For the cases studied, the maximum mixing entropy and effectiveness values occur when the ratio of the mechanical domain energy to the total energy of the system is 67%. The maximum effectiveness is independent of the initial conditions and depends on the squared ratio of the natural frequency of the nominal coupling capacitor to the natural frequency of the mechanical system.

SUGGESTION ON THE CHOICE OF COMBINATIONS OF ENEMY’S GROUND OBJECTS BEING STRUCK AT PLANNING OF FIRE STRIKES TAKING INTO ACCOUNT CURRENT STATUS OF THESE OBJECTS

The article discusses suggestion to solving the problem of choosing a target combination when planning fire strikes against enemy targets. As a rule, such objects are important elements of C2 system for all services and branches of troops, as well as key infrastructure facilities of the state. It is reasonable to consider the objects selected for destruction as a system in which their functioning can be characterized by the level and completeness of interaction with each other. Representation of targets as a system allows you to highlight the existing connections and the nature of the relationship between these objects. In general, all connections can be reduced to control, functional and informational. It is proposed, depending on the purpose of each object in the system as a whole, on the basis of an expert assessment, to take into account the value of a particular relationship by the coefficient of importance. Note that the type of connection also determines the relationship of objects to each other. The state of links can change over time, thereby changing the position (significance) of an object in the system. Let us assume that some means of control establish the probability of the presence of connections of all objects in the system. Such connections (their presence or absence) determine the possible state of the objects under consideration. Then, making the assumption that the process of transition of objects from state to state is stationary, on the basis of the Kolmogorov equations, the probabilities of finding objects in the states under consideration are calculated. The absence (restoration) of any given connection is a random event and introduces some uncertainty in the knowledge of the true state of the object under consideration. Let us estimate this uncertainty in terms of the object's entropy. The maximum value of entropy is achieved when the probability of finding an object in a working (initial) state is equal to 0.5. Any other value of entropy corresponds to two probabilities characterizing, respectively, two states of the object. In order to distinguish them, we introduce a characteristic variable. The value of the introduced variable increases with an increase in the probability of finding an object in good condition and, accordingly, decreases with a decrease in this probability. The potential of an object to perform its functions in the system is also significantly influenced by the number of connections connecting it with other objects in the system. It is proposed to introduce the indicator "potential of the object". This indicator combines both the uncertainty of the state of an object through the introduced characteristic variable and the number of connections with other objects in the system. In other words, it determines the ability of the object to fulfill its purpose at this stage of the system's functioning. The ranking of objects in the system according to this indicator makes it possible to single out the affected combination, which leads to a maximum decrease in the quality of the functioning of the system as a whole. Determining the combination to be hit can also be based on a ranged number of objects by the time to restore their readiness, while setting the requirement to maximize the required time to restore the readiness of the functioning of the system as a whole. If the number of objects included in the system is significant, and the number of combat units allocated for their destruction is limited, then the solution to the problem of choosing the combination to be hit becomes not trivial. In this case, it is proposed to reduce the problem of determining the target combination to the problem of resource allocation, which is solved by the method of dynamic programming. The number of stages considered is reduced to the number of objects. Combat units act as a resource. The damage function is expressed through the entered indicator - “object potential”. In this case, we are talking about the choice of the affected combination, which leads to the maximum damage to the system of objects in terms of its functioning as a whole. If we imagine the function of damage after the recovery time after the strike, then the selected combination to be hit corresponds to the target of the fire strike, leading to the incapacitation of the system for the maximum time. The presented approaches to the determination of the target combination can be used in the development of automation tools for the decision support system when planning fire strikes against enemy target.

Information Fusion Method for Building Grassroots Teaching Organization Based on Intelligent Optimization

At present, the existing teaching construction information fusion methods are based on the classification results of teaching resources, but ignoring the global intelligent optimization of the fusion results, which leads to the deviation of the grassroots teaching organization construction information fusion results, and the fusion index value is low. Therefore, the information fusion method of the grassroots teaching organization construction based on intelligent optimization is proposed. The basic framework of information fusion is designed, and the information fusion is divided into the data layer, characteristic layer, and decision layer. The information characteristics of the construction of grassroots teaching organizations were extracted. The particle swarm optimization algorithm is used to search the maximum value of the work entropy of teaching grassroots unit, and the threshold value of teacher construction and grassroots unit work is used to realize the information fusion of teaching grassroots unit construction. Experimental results show that the proposed method has higher error rate, stability, efficiency index, and higher information fusion value and accuracy than the traditional method.

Novel compressive sensing image encryption using the dynamics of an adjustable gradient Hopfield neural network

In this contribution, the nonlinear dynamics of a non-autonomous model of two neurons based on the Hopfield neural network is considered. Using activation gradients as bifurcation control parameters, the properties of the model include dissipation with the existence of attractors and equilibrium points with their stability. Using traditional nonlinear analysis tools such as bifurcation diagrams, the graph of the maximum Lyapunov exponent, phase portraits, two-parameter diagrams, and attraction basins, the complex behaviour of the two-dimensional Hopfield neural network has been investigated and several windows of multistability involving the coexistence of up to four coexisting attractors have been found. Besides, the results of our numerical simulation of the multistability have been further supported using some Pspice simulation. The effect of the fractional-order derivative is also explored, and it is found that the route toward chaos is completely different when the order q of the HNN is varied between 0<q<1. Finally, a compressive sensing approach is used to compress and encrypt color images based on the sequences of the above-mentioned system. The plain color image is decomposed into Red, Green, and Blue components. The Discrete Wavelet Transform (DWT) is applied to each component to obtain the corresponding sparse components. Confusion keys are obtained from the proposed chaotic system to scramble each sparse component. The measurement matrices obtained from the chaotic sequence are used to compress the confused sparse matrices corresponding to the Red, Green, and Blue components. Each component is quantified and a diffusion step is then applied to improve the randomness and, consequently, the information entropy. Experimental analysis of the proposed method yields a running time (t) of 6.85 ms, a maximum entropy value of 7.9996 for global and 7.9153 for local, an encryption throughput (ET) value of 114.80, and a number of cycles (NC) of 20.90. Analysis of these metrics indicates that the proposed scheme is competitive with some recent literature.

Entropy on Intuitionistic Fuzzy Sets and Hesitant Fuzzy Sets

Since the sufficient conditions for the maximum value of the intuitionistic fuzzy entropy are not unified and the hesitant fuzzy entropy cannot be compared when the lengths of the hesitation fuzzy elements are not equal, improved axiomatic definitions of intuitionistic fuzzy entropy and hesitant fuzzy entropy are proposed, and new intuitionistic fuzzy entropy and hesitant fuzzy entropy based on the improved axiomatic definitions are established. This paper defines the fuzzy entropy that satisfies the properties based on the axiomatized definition of fuzzy entropy and, based on the fuzzy entropy, defines new intuitionistic fuzzy entropy and hesitant fuzzy entropy, so that the three are unified in form. The validity and rationality of the proposed intuitionistic fuzzy entropy and hesitant fuzzy entropy are verified by analysis.