Entropy Measures Research Articles

Continuous Vector-Based Entropy Measurement on the Organizational Culture Evaluation

It is believed that organizational culture is one of the primary strategies that drive employee productivity and competitiveness. The abstract of organizational culture is a complex and dynamic phenomenon and challenge in the field of research till the present. The efficacy of human interaction with an organization is closely related to the propagation of organizational culture. In the meantime, cultural entropy is a metric for assessing the process of cultural dissemination in organizations, where a reduced entropy value is preferable. This study aims to modify the entropy culture algorithms that accommodate discrete and continuous vectors. We applied Shanon’s entropy as the fundamental formulation and the Axelrod model as the peer interaction analysis. The proposed measurement of cultural entropy considers not only the desired values but also evaluates the gap with the espoused value of the organization. The modified cultural entropy algorithm can measure the entropy value for discrete and continuous vectors. Measuring cultural entropy using continuous data results in an approach that can better display value heterogeneity within organizations.

Every complex Hénon map is exponentially mixing of all orders and satisfies the CLT

Abstract We show that the measure of maximal entropy of every complex Hénon map is exponentially mixing of all orders for Hölder observables. As a consequence, the Central Limit Theorem holds for all Hölder observables.

Direct measurement of the hydrogen adsorption entropy on shape-controlled Pt nanoparticles using electrochemical microcalorimetry

We measured the entropy of hydrogen adsorbed on Pt NPs with 3 different shapes. The entropy depends on the local geometry of the particles and matches the entropy of hydrogen adsorbed on single crystals with the corresponding orientation.

Properties of the entropic risk measure EVaR in relation to selected distributions

Entropic Value-at-Risk (EVaR) measure is a convenient coherent risk measure. Due to certain difficulties in finding its analytical representation, it was previously calculated explicitly only for the normal distribution. We succeeded to overcome these difficulties and to calculate Entropic Value-at-Risk (EVaR) measure for Poisson, compound Poisson, Gamma, Laplace, exponential, chi-squared, inverse Gaussian distribution and normal inverse Gaussian distribution with the help of Lambert function that is a special function, generally speaking, with two branches.

Validation of Linear and Nonlinear Gait Variability Measures Derived From a Smartphone System Compared to a Gold-Standard Footswitch System During Overground Walking.

Smartphones, with embedded accelerometers, may be a viable method to monitor gait variability in the free-living environment. However, measurements estimated using smartphones must first be compared to known quantities to ensure validity. This study assessed the validity and reliability of smartphone-derived gait measures compared to a gold-standard footswitch system during overground walking. Seventeen adults completed three 8-minute overground walking trials during 3 separate visits. The stride time series was calculated as the time difference between consecutive right heel contact events within the footswitch and smartphone-accelerometry signals. Linear (average stride time, stride time standard deviation, and stride time coefficient of variation) and nonlinear (fractal scaling index, approximate entropy, and sample entropy) measures were calculated for each stride time series. Bland-Altman plots with 95% limits of agreement assessed agreement between systems. Intraclass correlation coefficients assessed reliability across visits. Bland-Altman plots revealed acceptable limits of agreement for all measures. Intraclass correlation coefficients revealed good-to-excellent reliability for both systems, except for fractal scaling index, which was moderate. The smartphone system is a valid method and performs similarly to gold-standard research equipment. These findings suggest the development and implementation of an inexpensive, easy-to-use, and ubiquitous telehealth instrument that may replace traditional laboratory equipment for use in the free-living environment.

THE FRACTIONAL DISEN–FISHER PLANE: AN EFFECTIVE APPROACH TO DISTINGUISH COMPLEX TIME SERIES

With the explosive growth of data quantity and rapid development of nonlinear dynamics as well as the growing demand for complex data classification in the field of artificial intelligence and machine learning, the research of complex time series, generated by complex systems, has attracted enormous interests. However, how to simultaneously distinguish different types of time series data and extract more accurate and detailed information from them in the light of localized and global scale perspectives remains significant and needs to be tackled. Thus, in this paper, we propose the fractional DisEn–Fisher plane, which is innovatively constructed by the fractional form of dispersion entropy and Fisher information measure. These are both effective tools to diagnose the essential properties of complex time series, to analyze the complexity of systems and to depict the contained statistical information with higher accuracy and effectiveness. Several classical entropy plane methods are selected as a comparison to design simulation experiments by simulated data and three real-world datasets. Comparative experimental results show that this method is a feasible and reliable improvement method, which will help to provide more additional information in time series recognition and dynamic characterization. It may not only provide new insights for further improvement of complex time series analysis, but also have important implications for developing complex data clustering methods.

Fractional Cumulative Residual Inaccuracy Information Measure and Its Extensions with Application to Chaotic Maps

The purpose of this work is to introduce fractional cumulative residual inaccuracy (FCRI) information, Jensen-cumulative residual inaccuracy (JCRI), and Jensen-fractional cumulative residual inaccuracy (JFCRI) information measure. Further, we study the FCRI information for some well-known models used in reliability, economics and survival analysis. The associated results reveal some interesting connections between the FCRI information measure and cumulative residual entropy and Gini mean difference measures. Applications to two chaotic discrete-time dynamical systems (Chebyshev and Logistic) are presented to illustrate the behavior of the proposed information measures. FCRI and JFCRI measures allow to determine regions of discrepancy between systems, depending on their respective fractional and chaotic map parameters.

Software Reliability Growth Model Selection by using VIKOR Method Based on q-Rung Orthopair Fuzzy Entropy and Divergence Measures

Software Reliability Growth Model Selection by using VIKOR Method Based on q-Rung Orthopair Fuzzy Entropy and Divergence Measures

Энтропийная космология на основе модифицированной энтропии Шарма-Миттала на космологическом горизонте Вселенной

In the framework of entropic cosmology, several scenarios of the evolution of the Friedman-Robertson-Walker (FRW) Universe are considered, based on a new modification of the non-additive Sharma-Mittal and Renyi entropy measures on the cosmological horizon. This is done by replacing in the original logarithmic formulas for these entropies, the Tsallis entropy by the Barrow entropy associated with the modification of the horizon surface due to quantum gravitational effects. Several versions of the generalised multi-parametric FRW equations have been constructed, which can serve as an effective theoretical basis for describing the accelerating phase of the expansion of the late Universe. In the considered model there is no mutual interaction between the black components of the cosmos. The proposed approach, based on the use of non-additive extensive entropic measures on the cosmological horizon, meets the well-known requirements for thermodynamic modelling of the dynamical evolution of the Universe without involving the concept of hypothetical dark energy, but using the antigravity effect of entropic forces. The obtained results show that the generalised entropic formalism can open new possibilities for a deeper insight into the nature of spacetime and its fractal properties.

Some Tsallis entropy measures in concomitants of generalized order statistics under iterated FGM bivariate distribution

<p>Shannon differential entropy is extensively applied in the literature as a measure of dispersion or uncertainty. Nonetheless, there are other measurements, such as the cumulative residual Tsallis entropy (CRTE), that reveal interesting effects in several fields. Motivated by this, we study and compute Tsallis measures for the concomitants of the generalized order statistics (CGOS) from the iterated Farlie-Gumbel-Morgenstern (IFGM) bivariate family. Some newly introduced information measures are also being considered for CGOS within the framework of the IFGM family, including Tsallis entropy, CRTE, and an alternative measure of CRTE of order $ \eta $. Applications of these results are given for order statistics and record values with uniform, exponential, and power marginals distributions. In addition, the empirical cumulative Tsallis entropy is suggested as a method to calculate the new information measure. Finally, a real-world data set has been analyzed for illustrative purposes, and the performance is quite satisfactory.</p>

Some Information Measures for Interval‐Valued Hesitant Fuzzy Sets in Multiple Criteria Decision‐Making

In the fields of information science and artificial intelligence, dealing with uncertainty, fuzziness, and complexity has always been a hot and difficult research topic. Especially in modern society, with the continuous development of science and technology, people are facing more and more complex problems. Interval‐valued hesitant fuzzy set (IVHFS) is an extended form of a fuzzy set. It can more flexibly express and handle uncertainty and fuzziness in decision‐making processes. However, in the practical application of the IVHFS, its information measurement is crucial, which is directly related to the application value of the IVHFS in various fields. Therefore, studying the information measurement of the IVHFS has important theoretical significance and practical value for the fields of information science and artificial intelligence. In spite of significant advances, entropy and similarity as the well‐known information measures for interval‐valued hesitant fuzzy information have not yet been thoroughly researched. In this contribution, we investigate information measures in the IVHFS, including nonprobabilistic entropy, similarity, and cross‐entropy. We first analyze the change law of hesitating uncertainty and fuzzy uncertainty in geometric space, and a nonprobabilistic entropy measurement method and its axiomatic definition for IVHFS are further developed. Then, a novel similarity measurement formula for IVHFS and its axiomatic requirements are proposed on the basis of the two nonfuzzy elements ( and ). Furthermore, the novel similarity measure is used to construct the cross‐entropy measure for IVHFS and its axiomatic requirements based on the association between the similarity and the cross‐entropy. Lastly, a MAGDM method is proposed by using the developed three information measures, and the efficacy of the proposed method is demonstrated by a numerical example of emergency communication support capacity evaluation. Comparative analysis and computational cost analysis are implemented to demonstrate the superiority and validity of the proposed information measures.

Impacto da COVID-19 nas PMEs no Brasil e drivers de percepção gerencial: um novo modelo neural baseado em funções de utilidade ponderadas pela entropia

Abstract Departing from the inconclusive results of the scant literature on the COVID-19 impact on Small and Medium Enterprises (SMEs), this paper proposes a novel evaluation model for addressing this issue through managerial perceptions. Over 6000 SMEs responded to twelve rounds of surveys from 2020 to 2021 during the pandemic, allowing to track the evolution over time of the perceived impact of the pandemic on small businesses. A novel entropy-weighted utility function approach is proposed here, followed by artificial neural network regression to map the variables related to the SME’s businesses that most foster the perceived utility of each business criterion during the pandemic. First, weights of business-related criteria were computed using Stepwise Weight Assessment Ratio Analysis (SWARA), sorting their relative importance - or perceptions - based on information entropy ranks derived from questionnaires collected. Transfer entropy measurements also helped in unveiling the hidden cause-effect relationships among criteria. Second, business utility functions for each criterion were computed using Complex Proportional Assessment based on SWARA weights. Third, neural network regressions were used to explain the managerial perceptions on each business criterion during the pandemic, considering each business variable. Our expected and unexpected results suggest that more resilient SMEs in Brazil are 5-10 years old and operating in the services and construction sectors. Moreover, loan success is the second most impactful criterion, deeply impacting the continuity of economic activity levels, and it is not impacted by any other business criteria. Implications for policymakers and governmental actions are highlighted.

A Novel Group Decision-Making Approach With Entropy Measure for Energy Aware in Wireless Sensor Network Architecture

A Novel Group Decision-Making Approach With Entropy Measure for Energy Aware in Wireless Sensor Network Architecture

Interval-valued Pythagorean fuzzy entropy and its application to multi-criterion group decision-making

<abstract><p>Entropy is an important tool of information measurement in the fuzzy set and its inference. The research on information measurement based on interval-valued Pythagorean fuzzy sets mostly involves the distance formula for interval-valued Pythagorean fuzzy numbers, but seldom involves the measurement of fuzziness. In view of this situation, we have aimed to propose new interval-valued Pythagorean fuzzy entropy and weighted exponential entropy schemes. Based on the interval-valued Pythagorean fuzzy weighted averaging operator, a strategy based on weighted exponential entropy is proposed to solve the multi-criteria group decision-making (MCGDM) problem in the interval-valued Pythagorean environment. Two examples illustrate that this paper provides a feasible new method to solve the MCGDM problem in an interval-valued Pythagorean fuzzy (IVPF) environment. Finally, by comparing with the existing methods, it is concluded that the entropy measure of IVPF schemes and the corresponding MCGDM method can select the optimal solution of the practical problem more precisely and accurately. Therefore, the comparative analysis shows that the proposed measurement method has the characteristics of flexibility and universality.</p></abstract>

Classification of Renewable Energy Trends by Utilizing the Novel Entropy Measures under the Environment of q-rung Orthopair Fuzzy Soft Sets

Energy generated from naturally replenishing sources such as the sun and wind, is said to be renewable energy (RE). The production of electricity water heating and cooling can all be done with renewable energy. Some recent trends in renewable energy are (1) Advanced photovoltaic (2) Distributed energy storage systems (3) Hydro Power (4) Bioenergy. The utilization of fuzzy set theory is very important for the classification of renewable energy trends. q-rung orthopair fuzzy soft set (q-ROFSS) is a parameterization tool and a more efficient apparatus to resolve unclear and vague data in general. As entropy is a quantitated measure of disordered or randomness in a system it can handle the uncertainty of data in fuzzy set theory for a disordered system. So, in this article, based on q-ROFSS, we have initiated some novel entropy measures under the environment of q-ROFSS to relate more complex data and to give more room to decision-makers for handling many decision-making problems. So, the entropy of q-ROFSS is the measure of ambiguity related to q-ROFSS. To show the authenticity of the established work further, we have established an algorithm for the introduced work along with a descriptive example to substantiate the reliability of the initiated work. We have also initiated a comparative study of the introduced notion with some existing theories to demonstrate the usefulness and consistency of the given idea.

Similarity and entropy measures for circular intuitionistic fuzzy sets

A recent extension of intuitionistic fuzzy sets (IFSs) is the circular intuitionistic fuzzy set (C-IFS), where the performance of each alternative is described by a circle with a fixed radius rather than a specific orthopair. This article presents the similarity and dissimilarity measures for C-IFSs. Their basic axioms are proven, and some of their characteristics are brought to light. The axiomatic definition of entropy measures for C-IFSs is given. Several mathematical expressions are provided to measure the entropy of C-IFSs. The conversions of entropy into similarity measures and from similarity into entropy are given. The inferior ratio method, which relies on similarity measures, is extended for the C-IFS framework. The method is illustrated through a case study of site selection for an epidemic hospital. The solutions of the given approach are compared with the existing decision-making techniques.

Use of Intrinsic Entropy to Assess the Instantaneous Complexity of Thoracoabdominal Movement Patterns to Indicate the Effect of the Iso-Volume Maneuver Trial on the Performance of the Step Test.

The recent surge in interest surrounds the analysis of physiological signals with a non-linear dynamic approach. The measurement of entropy serves as a renowned method for indicating the complexity of a signal. However, there is a dearth of research concerning the non-linear dynamic analysis of respiratory signals. Therefore, this study employs a novel method known as intrinsic entropy (IE) to assess the short-term dynamic changes in thoracoabdominal movement patterns, as measured by respiratory inductance plethysmography (RIP), during various states such as resting, step test, recovery, and iso-volume maneuver (IVM) trials. The findings reveal a decrease in IE of thoracic wall movement (TWM) and an increase in IE of abdominal wall movement (AWM) following the IVM trial. This suggests that AWM may dominate the breathing exercise after the IVM trial. Moreover, due to the high temporal resolution of IE, it proves to be a suitable measure for assessing the complexity of thoracoabdominal movement patterns under non-stationary states such as the step test and recovery. The results also demonstrate that the instantaneous complexity of TWM and AWM can effectively capture instantaneous changes during non-stationary states, which may prove valuable in understanding the respiratory mechanism for healthcare purposes in daily life.

Thermodynamic Analysis of Financial Markets: Measuring Order Book Dynamics with Temperature and Entropy.

This study bridges finance and physics by applying thermodynamic concepts to model the limit order book (LOB) with high-frequency trading data on the Bitcoin spot. We derive the measures of Market Temperature and Market Entropy from the kinetic and potential energies in the LOB to provide a deeper understanding of order activities and market participant behavior. Market Temperature emerges as a robust indicator of market liquidity, correlating with liquidity measures such as Active Quote Volume, bid-ask spread and match volume. Market Entropy, on the other hand, quantifies the degree of disorder or randomness in the LOB, providing insights into the instantaneous volatility of price in the high-frequency trading market. Our empirical findings not only broaden the theoretical framework of econophysics but also enhance comprehensive understanding of the market microstructure and order book dynamics.

Density of periodic measures and large deviation principle for generalised mod one transformations

We introduce a new class of piecewise monotonic maps, called generalised mod one transformations, which include all (α,β) and generalised β -transformations, and prove that all transitive generalised mod one transformations with positive topological entropy satisfy the level-2 large deviation principle with a unique measure of maximal entropy. This is obtained by our result on the density of periodic measures for more general class of piecewise mototonic maps, which is a partial answer to the open problem posed by Hofbauer and Raith (1998 Fund. Math. 157 221–34); Raith (www.math.iupui.edu/~mmisiure/open/PR1.pdf).

Fast Estimation of Entropy Profiles for Lithium-Ion Batteries

The operating temperature of a lithium-ion battery (LIB) has strong effects on its electrochemical performance, safety, and lifetime. Reliable predictions of cell temperature and heat generation are required for the design and thermal management of battery systems. During the normal operation of LIBs, heat sources can be classified into irreversible heat from resistive losses such as ohmic resistance, charge-transfer overpotentials, and mass-transfer limitations; and reversible heat from entropy change . The irreversible heat generation is related to the cell's internal resistance and the applied current. The reversible heat depends on the entropy variation of electrode materials, the state of charge (SoC), and the temperature. An accurate measurement of entropy-variation will not only help to improve the battery operation under optimal thermal conditions but can also be used to diagnose the battery aging since it can reveal crystal structure changes in the electrodes [1, 2].Techniques for measuring the entropy of a battery can mainly be classified into potentiometric [3] and calorimetric methods. The potentiometric method measures the open circuit voltage (OCV) changes while the cell temperature is varied at different SoCs. This method requires a long relaxation time to obtain the OCV equilibrium state following each SoC point and temperature step. The calorimetric method [4-6] is based on measuring the heat generation during charge and discharge, and various models are applied to differentiate between and quantify the reversible and irreversible heat sources. The entropy variation with SOC is obtained via the reversible heat rate.Recent improved methods include e.g., Schmidt et al. [4] who proposed a reversible heat extraction method based on electrothermal impedance spectroscopy (ETIS) and Damay et al. [5] proposing a fast calorimetric method to obtain a continuous entropy profile. The cell surface temperature is monitored while the battery is charged and discharged continuously. A thermal balance is used to estimate the heat generation from the monitored cell temperature changes during charge and discharge. The benefit of this method can be low cost, fast and high resolution. Bedürftig et al. [6] proposed a calorimetric method named ‘Double Pulse Method’ to measure reversible heat in lithium-ion battery cells by exciting the cell with charge and discharge current pulses.Here we present a new entropy characterization method via charge and discharge cycles of a LIB at low constant C-rates using simple insulating condition. Through monitoring the variations of cell surface temperature and voltage with the state of charge, the continuous variation of entropy with the state of charge can be extracted. These results were compared to classical entropy measurements obtained through the potentiometric method as shown in Figure 1. In addition, the extracted entropy variation data is input into a LIB modelling approach, combining a P2D-electrochemical sub-model for battery operation and a 3D-finite-element sub-model for thermal behavior while battery charge and discharge. The model predictions on the cell outer surface temperature variation while charge and discharge under different C-rates are compared with the data obtained in the battery characterization tests as shown in Figure 2. Good agreements between the model predictions and tests are achieved.