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The q-rung orthopair fuzzy soft set theory provides effective tools for dealing with the imprecision and uncertainty in the data. Its potential to incorporate adequate parameters helps the business experts in processing the data effectively which is an important ingredient of decision-making processes. The objective of this paper is first to define the notion of entropy measures for the q-rung orthopair fuzzy soft sets (q-ROFSSs) and then to study its characterizations. Based on the concepts defined herein, an effective decision-making approach is proposed in the selection of project contractors for the construction of a mega project. A numerical example is presented to demonstrate the technique given in this paper and a comparative study with other existing approaches is executed as well. It is concluded that the proposed technique proves to be an innovative in handling the data where the comparable techniques were unable to deal and handle the data effectively. [ABSTRACT FROM AUTHOR]

The Fermatean fuzzy soft set (FFSS) is a natural extension of the intuitionistic fuzzy soft set (IFSS) and the Pythagorean fuzzy soft set (PyFSS). It retains the corresponding benefits of IFSS, PyFSS, and their extensions, including the ability to represent an entity from both favorable and adverse perspectives. It renders it feasible to mimic real-world situations where uncertainty is prevalent more precisely. It is possible to portray uncertain circumstances more effectively with the incorporated dimension of hesitation degree. The current study presents an innovative form of FFSS, known as complex Fermatean fuzzy soft set (cFRFSS), aiming at addressing the complexities related to data uncertainty and periodicity. The basic idea of cFRFSS, including set-theoretic operations and properties, is demonstrated numerically, and associated results are provided. To mitigate inconsistent information, modified entropy metrics for cFRFSS are put forward in the following section. Then, to assist university managers in assessing the research output of their faculty members within the institution, a robust method employing suggested cFRFSS-based entropy measures is offered. The suggested strategy’s adaptability is assessed by contrasting it with other strategies that have been previously put forth.

Abstract The cut method is a computational approach utilized to predict the fundamental activities of physicochemical properties of chemical networks, also called topological indices. The connection number is a new idea, that gives interesting and good results of the topological indices (TIs) and entropy measures (EMs) for structural representation of chemical compounds and networks. The physical density of chemical networks is characterized by these indices. In this paper, we determined the computational results for indices based on connection numbers for a two-dimensional lattice sheet of hydrogen-bonded boric acid. Boric acid, an inorganic compound, is not very harmful when applied to the skin or consumed. Finally, graphical and numerical comparisons of topological numbers including the number of borate hydrogen-bonded double lattice forms are also included in this study.

The cut method is a computational approach utilized to predict the fundamental activities of physicochemical properties of chemical networks, also called topological indices. The connection number is a new idea, that gives interesting and good results of the topological indices (TIs) and entropy measures (EMs) for structural representation of chemical compounds and networks. The physical density of chemical networks is characterized by these indices. In this paper, we determined the computational results for indices based on connection numbers for a two-dimensional lattice sheet of hydrogen-bonded boric acid. Boric acid, an inorganic compound, is not very harmful when applied to the skin or consumed. Finally, graphical and numerical comparisons of topological numbers including the number of borate hydrogen-bonded double lattice forms are also included in this study. [ABSTRACT FROM AUTHOR]

The unit new X-Lindley distribution, which is a novel one-parameter distribution on the unit interval, is presented in this study. It was developed by altering the new X-Lindley distribution using the exponential transformation. This new one-parameter distribution’s fundamental features, including moments, incomplete moments, Lorenz and Bonferroni curves, Gini index, mode, extropy, Havrda and Charvat entropy, Renyi entropy, and Tsallis entropy, are explored. Additionally, it has ´ bathtub-shaped hazard rate functions and monotonically increasing hazard rate functions with a single parameter. The new distribution is therefore sufficiently rich to model real data. Also, different estimation methods, such as maximum likelihood, least-squares, and weighted least-squares, are used to estimate the parameters of this model, and using a simulation research, their respective performances are evaluated. Finally, two real-life datasets are used to demonstrate the suggested model’s competency. [ABSTRACT FROM AUTHOR]

The unit new X-Lindley distribution, which is a novel one-parameter distribution on the unit interval, is presented in this study. It was developed by altering the new X-Lindley distribution using the exponential transformation. This new one-parameter distribution's fundamental features, including moments, incomplete moments, Lorenz and Bonferroni curves, Gini index, mode, extropy, Havrda and Charvat entropy, Rényi entropy, and Tsallis entropy, are explored. Additionally, it has bathtub-shaped hazard rate functions and monotonically increasing hazard rate functions with a single parameter. The new distribution is therefore sufficiently rich to model real data. Also, different estimation methods, such as maximum likelihood, least-squares, and weighted least-squares, are used to estimate the parameters of this model, and using a simulation research, their respective performances are evaluated. Finally, two real-life datasets are used to demonstrate the suggested model's competency.

We provide an analytic examination for a new proposed relative weights to find the inherent property of this new relative weight. Our findings will help researchers in the future to apply this new relative weight and develop their own new relative weights to face the complex and changing real world. [ABSTRACT FROM AUTHOR]

This paper aims to give statistical significance to the measurement of spatial concentration in the context of entropy-based approaches. We simulate confidence intervals based on a null hypothesis able to capture systematic spatial concentration of firms from random patterns, and dissimilarities between the distributions of firms and employees. We implement this two-step methodology to the European manufacturing economy, and we find a substantive spatial clustering of establishments whereby the spatial divergence between employees and firms is significant both for small-scale industries typically considered as localized because of industry-specific Marshallian external economies and for those industries characterized by considerable internal scale economies. We suggest that a high heterogeneity in firm size may have positive implications for aggregate competitiveness at the sectoral level. [ABSTRACT FROM AUTHOR]

In this work, a novel bounded three-parameter power Lomax distribution termed the unit power Lomax(UPLoD) is presented. The UPLoD is capable of handling data with left and right skewed shapes according to its probability density function. Additionally, according to the hazard rate function, the distribution may be used to analyse data containing J-shaped hazard rates. It is possible to determine some of the distribution's mathematical characteristics like moments, probability-weighted moments, incomplete moments, residual and reversed residual life, quantile function, stress strength model, and entropy (Rényi, Havrda and Charvát, Tsallis, and Arimoto) measures. The Cramér-von Mises, weighted least squares, maximum likelihood, Anderson-Darling, maximum product of spacing, and least squares approaches are among the conventional estimating techniques that are taken into account. The performance of the resulting estimates is compared using a Monte Carlo simulation based on some precision metrics. An actual data application is presented using water capacity data, and data about the Susquehanna River's maximum flood levels to show the importance of the new distribution compared to several other known distributions. [ABSTRACT FROM AUTHOR]

Fuzzy entropy measures are valuable tools in decision-making when dealing with uncertain or imprecise information. There exist many entropy measures for Pythagorean Fuzzy Sets (PFS) in the literature that fail to deal with the problem of providing reasonable or consistent results to the decision-makers. To deal with the shortcomings of the existing measures, this paper proposes a robust fuzzy entropy measure for PFS to facilitate decision-making under uncertainty. The usefulness of the measure is illustrated through an illustration of decision-making in a supplier selection problem and compared with existing fuzzy entropy measures. The Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) approach is also explored to solve the decision-making problem. The results demonstrate that the proposed measure can effectively capture the degree of uncertainty in the decision-making process, leading to more accurate decision outcomes by providing a reliable and robust ranking of alternatives. [ABSTRACT FROM AUTHOR]

The extension of intuitionistic fuzzy sets (IFS) to Pythagorean fuzzy sets (PFS) is a significant advancement, addressing the inherent limitations of IFS. This study introduces a novel entropy measure specifically designed for Pythagorean fuzzy sets, establishing its axiomatic definition and presenting key properties. Decision making guided by entropy is advantageous, as it effectively mitigates ambiguity with increasing entropy values. Furthermore, a numerical example is provided to facilitate a comparative assessment of our newly introduced entropy measure in contrast to existing PFS entropy measures. The validation of our findings is achieved through the application of the COPRAS method, which determines decision outcomes based on a multitude of influencing factors. Notably, the determination of weights in this method is underpinned by the utilization of our innovative entropy measure. [ABSTRACT FROM AUTHOR]

The diverse applications of various carbon nanostructures have sparked significant research interest. The potential significance of carbon nanosheets lies in their exceptional mechanical, electrical, and thermal properties, enabling advancements in various technological applications such as energy storage, electronics, and engineering, playing important roles in material science and nanotechnology. In the field of mathematical chemistry, topological indices play a crucial role by providing numerical insights into molecular structures. These insights facilitate predictive correlations with chemical properties and reactivity, ultimately finding utility in areas like drug design and material sciences. Expanding on this, the study delves into the application of entropy‐based methodologies that originates from the arrangement of chemical structures. By assessing the complexity and other features of these structures, graph entropies are translated into information‐theoretic metrics. This article examines modified reverse degree‐based topological indices with its universal applicability to all degree‐based indices. The standout feature is the adaptable parameter "k$$ k $$" effectively shaping the molecular graphs degree sequence to best fit each dataset with their unique physicochemical properties, distinguishing it from conventional fixed degree methodologies. Additionally, we investigate graph entropies and examine the impact of varying the parameter "k$$ k $$" on entropy measures across a range of nanosheet structures. The research focuses on characterizing carbon nanosheets, employing effective (MCDM) multiple criteria decision‐making methods like VIKOR, TOPSIS, and SAW. Through these techniques, a comprehensive comparative analysis of the nanosheets is conducted with the aim of establishing optimized rankings for each type based on their unique attributes and characteristics. [ABSTRACT FROM AUTHOR]

In this study, we introduce a new flexible distribution constructed by a modification to the Rayleigh distribution and we referred it as unit generalized Rayleigh distribution (UGRD). Varied statistical properties were established, such as reliability, hazard rate, survival rate, moments, quantiles, ordered statistics, etc. The maximum likelihood estimation method is applied to estimate the parameters of the proposed model and different entropy measures including: Rényi entropy, Shannon entropy, Havrda and Charvat entropy, Tsallis entropy, Arimoto entropy, and Mathai–Haubold entropy are provided. The effectiveness of the proposed entropy estimators have been conducted through Monte Carlo (MC) simulation experiments regarding average estimate, average bias, mean square error, and mean relative errors compared to the simple random sample. Finally, we illustrated two real engineering data sets to assess the potential of the proposed UGRD among some existing models.

One of the most recent advancements in graph theory is the use of a multidisciplinary approach to the investigation of specific structural dependent features, such as physico-chemical properties, biological activity and the entropy measure of a graph representing objects like a network or a chemical compound. The ability of entropy measures to determine both the certainty and uncertainty about objects makes them one of the most investigated topics in science along with its multidisciplinary nature. As a result, many formulae, based on vertices, edges and symmetry, for determining the entropy of graphs have been developed and investigated in the field of graph theory. These measures assist in understanding the characteristics of graphs, such as the complexity of the networks or graphs, which may be determined using entropy measures. In this paper, we derive formulae of entropy measures of an extensively studied family of the interconnection networks and classify them in terms of complexity. This is accomplished by utilizing all three tools, including analytical formulae, graphical methods and numerical tables. [ABSTRACT FROM AUTHOR]

A topological index, also known as a connectedness index, is a numerical characteristic of chemical structure that is computed by using its molecular graph in theoretical chemistry. In quantitative structure‐activity relationships (QSARs), which relate a molecule's chemical structure to its physical and chemical properties, topological indices are employed. The graph entropies with topological indices were inspired by Shannon's entropy concept and became the information‐theoretic quantities for measuring the structural information of chemical graphs. The theory of graphs is useful in determining the relationship between specific properties of chemical structures using different graph entropy measures. Through these entropies, many physical and chemical characteristics, such as melting point, energy generation, Henry's Law, and molar mass of chemical compounds, can be calculated. For this, the quantitative structure‐property relationship (QSPR) models are designed using ve‐degree‐based entropies to examine some physical properties of benzene derivatives. For the computation of entropies, a Maple‐based program is developed. The QSPR study is performed using SPSS and linear regression techniques. In this work, we have observed that the redefined third Zagreb entropy, the Balaban entropy, and the Randic entropy are the best predictors. The physiochemical characteristics, namely Henry's Law and critical pressure, can be predicted by Randic entropy and Balaban entropy, respectively. The redefined third Zagreb entropy can predict four other properties: enthalpy, molar mass, π‐electronic energy, and molecular weight. [ABSTRACT FROM AUTHOR]

The donut benzenoid system is a subclass of polycyclic aromatic hydrocarbons (PAHs) that is produced when a few hexagons are selectively removed from planar benzenoid networks. The nature and behavior of the donut benzenoid system are determined by the cavity that is generated as a result. The donut benzenoid system that has been synthesized up to this point has several geometric and electrical features that are entirely unique. By adjusting the dimensions and contours of the cavity, it is possible to modify these properties so that they are better suited to a given application. Therefore, doing theoretical research on this system from a structural point of view can be of great assistance in the process of designing and synthesizing a new form of donut benzenoid system. This article is primarily concerned with the process of obtaining the analytical formulations for four different types of Vertex Degree Based (VDB) indices, including Multiplicative Topological Indices (TIs), M-Polynomial, Entropy Measures, and Irregularity based TIs for the donut benzenoid system. [ABSTRACT FROM AUTHOR]

The probabilistic hesitant fuzzy sets (P-HFSs) allow experts to express their preferences regarding different membership degrees with probabilistic information. Fuzzy entropy is an important concept to measure the uncertainty of probabilistic hesitant fuzzy information. In this paper, we propose a novel fuzzy entropy named as the exponential probabilistic hesitant fuzzy entropy for the P-HFEs. This novel fuzzy entropy not only observes the basic property of fuzzy entropy, but also has the same characteristics and change tends with the existing fuzzy entropy proposed and studied by other scholars. Then, based on the cardinal reconciliation method and TODIM(Tomada de decisao interativa multicriterio) method, we propose a multi-criteria decision-making (MCDM) problem, where the attribute weight is determined by the exponential probabilistic hesitant fuzzy entropy of the integration results. Finally, a application case in green building is given for the sake of illustrating the efficiency of the MCDM problem. Numerical and theoretical results show that a MCDM problem based on the proposed novel fuzzy entropy and the TODIM method have a wide range of application.

The compounded Bell generalized class of distributions is proposed in this article as an alternative to the compounded Poisson generalized family of distributions. Some properties and actuarial measures are presented. The properties of a special model named Bell Weibull (BellW) are obtained such as the linear representation of density, rth moment, incomplete moment, moment generating function using Wright generalized hypergeometric function and Meijer’s G function, the pth moment of order statistics, reliability, stochastic ordering, and residual and reversed residual life. Moreover, some commonly used entropy measures, namely, Rényi, Havrda and Charvat, and Arimoto and Tsallis entropy are obtained for the special model. From the inferential side, parameters are estimated using maximum likelihood estimation. The simulation study is performed to highlight the behavior of estimates. Some actuarial measures including expected shortfall, value at risk, tail value at risk, tail variance, and tail variance premium for the BellW model are presented with the numerical illustration. The usefulness of the proposed family is evaluated using insurance claims and COVID-19 datasets. Convincing results are obtained.

In this article, we make mathematical and practical contributions to the Bell-X family of absolutely continuous distributions. As a main member of this family, a special distribution extending the modeling perspectives of the famous Burr XII (BXII) distribution is discussed in detail. It is called the Bell-Burr XII (BBXII) distribution. It stands apart from the other extended BXII distributions because of its flexibility in terms of functional shapes. On the theoretical side, a linear representation of the probability density function and the ordinary and incomplete moments are among the key properties studied in depth. Some commonly used entropy measures, namely Rényi, Havrda and Charvat, Arimoto, and Tsallis entropy, are derived. On the practical (inferential) side, the associated parameters are estimated using seven different frequentist estimation methods, namely the methods of maximum likelihood estimation, percentile estimation, least squares estimation, weighted least squares estimation, Cramér von-Mises estimation, Anderson-Darling estimation, and right-tail Anderson-Darling estimation. A simulation study utilizing all these methods is offered to highlight their effectiveness. Subsequently, the BBXII model is successfully used in comparisons with other comparable models to analyze data on patients with acute bone cancer and arthritis pain. A group acceptance sampling plan for truncated life tests is also proposed when an item's lifetime follows a BBXII distribution. Convincing results are obtained.

In this study, we introduce a new flexible distribution constructed by a modification to the Rayleigh distribution and we referred it as unit generalized Rayleigh distribution (UGRD). Varied statistical properties were established, such as reliability, hazard rate, survival rate, moments, quantiles, ordered statistics, etc. The maximum likelihood estimation method is applied to estimate the parameters of the proposed model and different entropy measures including: Rényi entropy, Shannon entropy, Havrda and Charvat entropy, Tsallis entropy, Arimoto entropy, and Mathai–Haubold entropy are provided. The effectiveness of the proposed entropy estimators have been conducted through Monte Carlo (MC) simulation experiments regarding average estimate, average bias, mean square error, and mean relative errors compared to the simple random sample. Finally, we illustrated two real engineering data sets to assess the potential of the proposed UGRD among some existing models. [ABSTRACT FROM AUTHOR]

The paper presents a novel class (family) of statistical distributions termed Odd Transmuted Rayleigh-X (OTRX) that was created through a transform-transformer (T-X) approach. The CDF and PDF of the OTR-X family were derived. The available statistical literature studied earlier highlighted that almost all generalized distributions (in which one or more parameters were added) performed well and have better presentation of data than their counterparts with less number of parameters. This has motivated us to developed new family that is capable of producing new distributions. The research paper also presented a clear mathematical formula for several characteristics of the OTR-X family, such as the ordinary moments, moment generating, quantile, and reliability function. In order to find the estimate of the corresponding parameters of the OTR-X family, the technique of maximum likelihood is used in the study. A new sub-model Odd Transmuted Rayleigh Inversed Exponential Distribution (OTRIED) was generated from the OTR-X class and compared its performance to Transmuted Inversed Exponential Distribution (TIED), Exponential Inversed Exponential Distribution (EIED), and Inversed Exponential Distribution using two different datasets. The results have shown that the proposed distribution out performed its competitors when using two different real-world datasets. Furthermore, the proposed distribution can be practicalized to any skewed dataset. [ABSTRACT FROM AUTHOR]

Owing to the lack of information, it is more realistic that the sum of probabilities is less than or equal to one in the probabilistic hesitant fuzzy elements (P-HFEs). Probabilistic-normalization method and cardinal-normalization method are common processing methods for the P-HFEs with incomplete information. However, the existed probabilistic-normalization method of sharing the remaining probabilities will lose information and change the information integrity of the P-HFEs. The first existed cardinal-normalization method of adding maximum or minimum membership degree with probability zero are influenced by the subjectivity of the decision makers. And the second existed cardinal-normalization method named as reconciliation method only applicable to the P-HFEs with complete information. Aiming at solving those shortcomings, we propose a possibility degree method based on a novel cardinal-normalization method for the sake of comparing the P-HFEs in pairs. In the process of comparison, the information integrity remains unchanged. Then, we propose a multi-criteria decision making (MCDM) problem, where the attribute weight is determined by entropy measures of the integration results. Finally, an application case in green logistics area is given for the sake of illustrating the efficiency of the proposed method, where the evaluation values are given in the P-HFEs form with incomplete information. Numerical and theoretical results show that a MCDM problem based on the proposed cardinal-normalization method and possibility degree method have a wide range of application. [ABSTRACT FROM AUTHOR]

The recent link discovered between generalized Legendre transforms and non-dually flat statistical manifolds suggests a fundamental reason behind the ubiquity of Rényi's divergence and entropy in a wide range of physical phenomena. However, these early findings still provide little intuition on the nature of this relationship and its implications for physical systems. Here we shed new light on the Legendre transform by revealing the consequences of its deformation via symplectic geometry and complexification. These findings reveal a novel common framework that leads to a principled and unified understanding of physical systems that are not well-described by classic information-theoretic quantities. [ABSTRACT FROM AUTHOR]

Epilepsy is the most common neurological disorder by which over 65 million people are affected across the world. Recent research has shown a very large interest to predict and diagnose epilepsy well before time. The continuous monitoring of EEG signals for seizure detection in electroencephalogram (EEG) is a very tedious and time taking process and therefore requires a qualified and trained clinical specialist. This paper presents a novel approach to detect and predict the epileptic signal in the recorded electroencephalogram (EEG). There is always a requirement for a nonlinear technique to examine the EEG signals due to the random nature of EEG signals. Therefore, we are providing an alternate method that extracts various entropy measures such Sample Entropy, Spectral Entropy, Permutation Entropy, and Shannon Entropy as statistical features from EEG signal. Based on these extracted features LSTM Fully connected Neural Network is used to classify the EEG signals as Focal and Non-focal. The proposed method gives a new insight into EEG signals by providing sensitivity as an added measure using deep learning along with accuracy and precision. [ABSTRACT FROM AUTHOR]

The probabilistic hesitant fuzzy sets (P-HFSs) allow experts to express their preferences regarding different membership degrees with probabilistic information. Fuzzy entropy is an important concept to measure the uncertainty of probabilistic hesitant fuzzy information. In this paper, we propose a novel fuzzy entropy named as the exponential probabilistic hesitant fuzzy entropy for the P-HFEs. This novel fuzzy entropy not only observes the basic property of fuzzy entropy, but also has the same characteristics and change tends with the existing fuzzy entropy proposed and studied by other scholars. Then, based on the cardinal reconciliation method and TODIM(Tomada de decisao interativa multicriterio) method, we propose a multi-criteria decision-making (MCDM) problem, where the attribute weight is determined by the exponential probabilistic hesitant fuzzy entropy of the integration results. Finally, a application case in green building is given for the sake of illustrating the efficiency of the MCDM problem. Numerical and theoretical results show that a MCDM problem based on the proposed novel fuzzy entropy and the TODIM method have a wide range of application. [ABSTRACT FROM AUTHOR]

The unit exponentiated half logistic power series (UEHLPS), a family of compound distributions with bounded support, is introduced in this study. This family is produced by compounding the unit exponentiated half logistic and power series distributions. In the UEHLPS class, some interesting compound distributions can be found. We find formulas for the moments, density and distribution functions, limiting behavior, and other UEHLPS properties. Five well-known estimating approaches are used to estimate the parameters of one sub-model, and a simulation study is created. The simulated results show that the maximum product of spacing estimates had lower accuracy measure values than the other estimates. Ultimately, three real data sets from various scientific areas are used to analyze the performance of the new class. [ABSTRACT FROM AUTHOR]

Triazine-based covalent organic frameworks (TriCFs) were synthesized using melamine, and cyanuric acid is a brand-new synthetic lubricant, which is thermo-stable and possesses a lamellar structure. This article demonstrates how topological descriptors for the TriCF structure are precisely evaluated using the degree sum of the end vertex neighbors and also some molecular descriptors with multiplicative neighborhood degree sums are evaluated. Furthermore, the neighborhood entropy measures for the outcomes are provided. The results are compared using the graph theoretical method. [ABSTRACT FROM AUTHOR]

The half-logistic modified Kies exponential (HLMKEx) distribution is a novel three-parameter model that is introduced in the current work to expand the modified Kies exponential distribution and improve its flexibility in modeling real-world data. Due to its versatility, the density function of the HLMKEx distribution offers symmetrical, asymmetrical, unimodal, and reversed-J-shaped, as well as increasing, reversed-J shaped, and upside-down hazard rate forms. An infinite linear representation can be used to represent the HLMKEx density. The HLMKEx model's fundamental mathematical features are obtained, such as the quantile function, moments, incomplete moments, and moments of residuals. Additionally, some measures of uncertainty as well as stochastic ordering are derived. To estimate its parameters, eight estimation methods are used. With the use of detailed simulation data, we compare the performance of each estimating technique and obtain partial and total ranks for the accuracy measures of absolute bias, mean squared error, and mean absolute relative error. The simulation results demonstrate that, in contrast to other competing distributions, the proposed distribution can actually fit the data more accurately. Two actual data sets are investigated in the field of engineering to demonstrate the adaptability and application of the suggested distribution. The findings demonstrate that, in contrast to other competing distributions, the provided distribution can actually fit the data more accurately. [ABSTRACT FROM AUTHOR]

In this article, we make mathematical and practical contributions to the Bell-X family of absolutely continuous distributions. As a main member of this family, a special distribution extending the modeling perspectives of the famous Burr XII (BXII) distribution is discussed in detail. It is called the Bell-Burr XII (BBXII) distribution. It stands apart from the other extended BXII distributions because of its flexibility in terms of functional shapes. On the theoretical side, a linear representation of the probability density function and the ordinary and incomplete moments are among the key properties studied in depth. Some commonly used entropy measures, namely R'enyi, Havrda and Charvat, Arimoto, and Tsallis entropy, are derived. On the practical (inferential) side, the associated parameters are estimated using seven different frequentist estimation methods, namely the methods of maximum likelihood estimation, percentile estimation, least squares estimation, weighted least squares estimation, Cram'er von-Mises estimation, Anderson-Darling estimation, and right-tail Anderson-Darling estimation. A simulation study utilizing all these methods is offered to highlight their effectiveness. Subsequently, the BBXII model is successfully used in comparisons with other comparable models to analyze data on patients with acute bone cancer and arthritis pain. A group acceptance sampling plan for truncated life tests is also proposed when an item's lifetime follows a BBXII distribution. Convincing results are obtained. [ABSTRACT FROM AUTHOR]

This study presents a comprehensive structural analysis of Iridium-cored dendrimers, denoted by I n mlr ; n ≥ 1 , with an emphasis on degree and distance based metrics to elucidate their structure-property relationships. Dendrimers, known for their highly branched architectures, are versatile macromolecules with applications across various scientific fields. In this work, molecular descriptors serve as essential numerical indicators, capturing bonding characteristics and aiding in the prediction of material properties. Leveraging a novel quotient graph approach, we compute a range of distance based indices, including the Wiener (W), Szeged (Sz and S z e), Mostar (Mo and M o e), and Padmakar-Ivan (PI) indices. We further derive generalized expressions for entropy measures associated with degree based indices, such as Shannon's entropy, providing a robust framework for assessing the structural complexity of these compounds. Additionally, we examine various degree based descriptors with entropy measures—including the Zagreb (M 1 , M 2 , and HM), Harmonic (H), Forgotten (F), Randic (R and RR), ABC, GA, SC, σ , and Irregularity indices (irr). A linear regression analysis is conducted to model dendrimer properties and forecast attributes for subsequent generations, potentially minimizing the need for extensive laboratory experimentation. Our findings provide valuable insights into the molecular intricacies of Iridium-cored dendrimers, bridging theoretical chemistry with practical applications and contributing to future advancements in materials science and engineering.   • Topological analysis of Iridium-cored dendrimers using degree- and distance-based topological indices. • Quotient graph approach simplifies derivation of distance-based indices, preserving key structural properties. • Edge partition technique refines calculation of degree-based indices, revealing dendrimer topology insights. • Entropy from degree indices enhances understanding of molecular complexity and structure-property links. • Graphical comparisons highlight indices capturing structural variations, aiding dendrimer property prediction. [ABSTRACT FROM AUTHOR]

A topological index (TI) is a real number that defines the relationship between a chemical structure and its properties and remains invariant under graph isomorphism. TIs defined for chemical structures are capable of predicting physical properties, chemical reactivity and biological activity. Several kinds of TIs have been defined and studied for different molecular structures. Graphene is the thinnest material known to man and is also extremely strong while being a good conductor of heat and electricity. With such unique features, graphene and its derivatives have found commercial uses and have also fascinated theoretical chemists. In this article, the neighbourhood sum degree-based M-polynomial and entropy measures have been computed for graphene, graphyne and graphdiyne structures. The proper analytical expressions for these indices are derived. The obtained results will enable theoretical chemists to study these exciting structures further from a structural perspective. [ABSTRACT FROM AUTHOR]

Articulation imagery, a form of mental imagery, refers to the activity of imagining or speaking to oneself mentally without an articulation movement. It is an effective domain of research in speech impaired neural disorders, as speech imagination has high similarity to real voice communication. This work employs electroencephalography (EEG) signals acquired from articulation and articulation imagery in identifying the vowel being imagined during different tasks. EEG signals from chosen electrodes are decomposed using the empirical mode decomposition (EMD) method into a series of intrinsic mode functions. Brain connectivity estimators and entropy measures have been computed to analyze the functional cooperation and causal dependence between different cortical regions as well as the regularity in the signals. Using machine learning techniques such as multiclass support vector machine (MSVM) and random forest (RF), the vowels have been classified. Three different training and testing protocols (Articulation-AR, Articulation imagery-AI and Articulation vs Articulation imagery-AR vs AI) were employed for identifying the vowel being imagined of articulating. An overall classification accuracy of 80% was obtained for articulation imagery protocol which was found to be higher than the other two protocols. Also, MSVM techniques outperformed the RF technique in terms of the classification accuracy. The effect of brain connectivity estimators and machine learning techniques seems to be reliable in identifying the vowel from the subjects' thought and thereby assisting the people with speech impairment. [ABSTRACT FROM AUTHOR]

Unit distributions are typically used in probability theory and statistics to illustrate useful quantities with values between zero and one. In this paper, we investigated an appropriate transformation to propose the unit-exponentiated half-logistic distribution (UEHLD), which is also beneficial for modelling data on the unit interval. This distribution's mathematical features are supplied, including moments, probability-weighted moments, incomplete moments, various entropy measures, and stress–strength reliability. Using well-known estimation techniques such as the maximum likelihood, maximum product of spacing, and Bayesian inference, the estimators of the parameters relevant to the proposed distribution were determined. A comprehensive simulation analysis is provided to examine the performance of parameter estimation approaches on finite samples. The proposed distribution was realistically applied to data on economic growth and data on the tensile strength of polyester fibers to provide an explanation. Furthermore, the analysis of COVID-19 data from Britain as a medical statistical dataset is provided. The experimental results demonstrate that the suggested UEHLD yields a better comparison with some new unit distributions, as well as other unbounded distributions. [ABSTRACT FROM AUTHOR]

Most of the research has evidenced that there is a strong natural correlation among the chemical properties of molecular structures. This study analyses supramolecular chemistry and investigates topological indices of supramolecular structures called triazine-based covalent-organic frameworks. The use of degree-based topological indices on these chemical molecular structures can aid material scientists in better understanding their chemical and biological properties, thus compensating for the lack of chemical tests. This study aims to theoretically examine the triazine-based covalent-organic frameworks (TriCF) utilizing degree-based topological indices, specifically multiplicative topological indices and entropy measures. A detailed comparison of the computed topological indices of the aforementioned chemical structures is described using graphical depiction. [ABSTRACT FROM AUTHOR]

In this contribution, we specify the conditions for assuring the validity of the synergy of the distribution of probabilities of occurrence. We also study the subsequent restriction on the maximal extension of the strict concavity region on the parameter space of Sharma–Mittal entropy measures, which has been derived in a previous paper in this journal. The present paper is then a necessary complement to that publication. Some applications of the techniques introduced here are applied to protein domain families (Pfam databases, versions 27.0 and 35.0). The results will show evidence of their usefulness for testing the classification work performed with methods of alignment that are used by expert biologists. [ABSTRACT FROM AUTHOR]

Despite the importance of divergence measures, the literature has not provided a satisfactory formulation for the case of intuitionistic fuzzy sets (IFS). This paper criticizes the existing attempts in terms of respect of the basic axioms of a divergence measure. Then, new improved, axiomatically supported divergence measures for IFSs are proposed. Additional properties of the new divergence measures are discussed to guarantee their good performance. Transformation relationships with entropy and dissimilarity measures are debated. As an application, a new intuitionistic fuzzy set theory-based ranking method for figure skaters is designed. A numerical example illustrates its applicability. It uses real data produced during the Men Single Skating Short Program performed in the Team Event in Figure Skating during the Olympic Winter Games 2018 PyeungChang held in Korea from 09.02.2018 to 25.02.2018. [ABSTRACT FROM AUTHOR]

Approaches to measuring health inequalities are often problematic because they use methods that are inappropriate for categorical data. In this paper we focus on "pure" or univariate health inequality (rather than income-related or bivariate health inequality) and use a concept of individual status that allows a consistent treatment of such data. We take alternative versions of the status concept and apply methods for treating categorical data to examine self-assessed health inequality for the countries included in the World Health Survey. We also use regression analysis on the apparent determinants of these health inequality estimates. We show that the status concept that is used will affect health-inequality rankings across countries and the way health inequality is related to countries' median health, income, demographics and governance. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy soft set (PFSS) is one of the useful extension of the Pythagorean fuzzy set (PFS) to deal with the vagueness and uncertainties in the data. The major advantages of PFSS over the other existing sets are to consider the parameterized tool of the family of PFS. Keeping this advantage, in this paper we define some new entropy measures for PFSS to compute the degree of fuzziness of the set. The axiomatic definition and their validity are stated. The larger the entropy, the lesser the vagueness and so, the decision making based on entropy is a useful one. Further, a decisionmaking algorithm is explored to solve the decision-making problem under the PFSS environment. A numerical example is given to validate the method and compare their performance with the existing intuitionistic fuzzy soft set entropy measures.

Unit distributions are typically used in probability theory and statistics to illustrate useful quantities with values between zero and one. In this paper, we investigated an appropriate transformation to propose the unit-exponentiated half-logistic distribution (UEHLD), which is also beneficial for modelling data on the unit interval. This distribution’s mathematical features are supplied, including moments, probability-weighted moments, incomplete moments, various entropy measures, and stress–strength reliability. Using well-known estimation techniques such as the maximum likelihood, maximum product of spacing, and Bayesian inference, the estimators of the parameters relevant to the proposed distribution were determined. A comprehensive simulation analysis is provided to examine the performance of parameter estimation approaches on finite samples. The proposed distribution was realistically applied to data on economic growth and data on the tensile strength of polyester fibers to provide an explanation. Furthermore, the analysis of COVID-19 data from Britain as a medical statistical dataset is provided. The experimental results demonstrate that the suggested UEHLD yields a better comparison with some new unit distributions, as well as other unbounded distributions.

Emotion recognition system from speech signal is a widely researched topic in the design of the Human–Computer Interface (HCI) models, since it provides insights into the mental states of human beings. Often, it is required to identify the emotional condition of the humans as cognitive feedback in the HCI. In this paper, an attempt to recognize seven emotional states from speech signals, known as sad, angry, disgust, happy, surprise, pleasant, and neutral sentiment, is investigated. The proposed method employs a non-linear signal quantifying method based on randomness measure, known as the entropy feature, for the detection of emotions. Initially, the speech signals are decomposed into Intrinsic Mode Function (IMF), where the IMF signals are divided into dominant frequency bands such as the high frequency, mid-frequency , and base frequency. The entropy measures are computed directly from the high-frequency band in the IMF domain. However, for the mid- and base-band frequencies, the IMFs are averaged and their entropy measures are computed. A feature vector is formed from the computed entropy measures incorporating the randomness feature for all the emotional signals. Then, the feature vector is used to train a few state-of-the-art classifiers, such as Linear Discriminant Analysis (LDA), Naïve Bayes, K-Nearest Neighbor, Support Vector Machine, Random Forest, and Gradient Boosting Machine. A tenfold cross-validation, performed on a publicly available Toronto Emotional Speech dataset, illustrates that the LDA classifier presents a peak balanced accuracy of 93.3%, F1 score of 87.9%, and an area under the curve value of 0.995 in the recognition of emotions from speech signals of native English speakers. [ABSTRACT FROM AUTHOR]

Auckland, the largest city of New Zealand, is one of the most diverse cities in the world, with more than 40% of its population born abroad, more than 200 ethnicities represented and 160 languages spoken. In this paper, we measure residential sorting of individuals in Auckland by their cultural (ethnicity) and economic (income, education and occupation) characteristics for the years 1991–2013. Using entropy-based measures of residential sorting and of neighbourhood diversity, we find that individuals exhibit greater residential sorting by ethnicity than by economic characteristics. Geographically, the semi-rural fringes of the city exhibit less diversity than the central urban area. Multi-group indexes of cultural and economic sorting showed a small decline over the 1991–2013 period. We also observe that ethnic sorting declined over that period for broad ethnic groups, but that sorting within the broad ethnic groups increased since 2001. A similar pattern of decreasing sorting at the aggregate level, with increasing sorting within groups in the more recent sub-period, is observed for occupations. [ABSTRACT FROM AUTHOR]

Zeolites serve as multifunctional microporous materials and have potential applications as catalysts, ion exchangers, and adsorbents. Researchers are interested in the topological characterization of zeolite frameworks due to their complex 3D arrangement of atoms. ATN is one of the variants of zeolite whose building block is arranged in a non-isometric cyclic permutation. The long-range and short-range molecular interactions of the ATN framework are influenced by the geometric arrangement of molecules. In this paper, we have investigated Shannon's information entropy measures of the ATN framework using bond degree and neighborhood degree sum based indices as weights. Further, a predictive analysis with the aid of entropy measures to determine the long-range and short-range potential energies has been implemented. The model proposed in this study can be incorporated into the fields of molecular physics and theoretical chemistry to determine the energy levels of microporous materials. Therefore, the predictive model will make a substantial contribution to QSAR/QSPR modeling. • Analytical formulations of bond additive indices are obtained for the zeolite ATN framework using the edge partition technique. • Graph entropy measures incorporating multiplicative degree-based indices are tabulated to investigate their predicting ability. • Developed regression models to predict the long-range and short-range potential energies of the ATN framework. • Graphical representation of linear and cubic regression models is provided for comparing the best model suited for predictions. [ABSTRACT FROM AUTHOR]

The Khinchin–Shannon generalized inequalities for entropy measures in Information Theory, are a paradigm which can be used to test the Synergy of the distributions of probabilities of occurrence in physical systems. The rich algebraic structure associated with the introduction of escort probabilities seems to be essential for deriving these inequalities for the two-parameter Sharma–Mittal set of entropy measures. We also emphasize the derivation of these inequalities for the special cases of one-parameter Havrda–Charvat’s, Rényi’s and Landsberg–Vedral’s entropy measures.

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.

In this research, we develop an affective computing method based on machine learning for emotion recognition using a wireless protocol and a wearable electroencephalography (EEG) custom-designed device. The system collects EEG signals using an eight-electrode placement on the scalp; two of these electrodes were placed in the frontal lobe, and the other six electrodes were placed in the temporal lobe. We performed experiments on eight subjects while they watched emotive videos. Six entropy measures were employed for extracting suitable features from the EEG signals. Next, we evaluated our proposed models using three popular classifiers: a support vector machine (SVM), multi-layer perceptron (MLP), and one-dimensional convolutional neural network (1D-CNN) for emotion classification; both subject-dependent and subject-independent strategies were used. Our experiment results showed that the highest average accuracies achieved in the subject-dependent and subject-independent cases were 85.81% and 78.52%, respectively; these accuracies were achieved using a combination of the sample entropy measure and 1D-CNN. Moreover, our study investigates the T8 position (above the right ear) in the temporal lobe as the most critical channel among the proposed measurement positions for emotion classification through electrode selection. Our results prove the feasibility and efficiency of our proposed EEG-based affective computing method for emotion recognition in real-world applications.

Differential entropy can be negative, while discrete entropy is always non-negative. This article shows that negative entropy is a significant flaw when entropy is used as a sensitivity measure in global sensitivity analysis. Global sensitivity analysis based on differential entropy cannot have negative entropy, just as Sobol sensitivity analysis does not have negative variance. Entropy is similar to variance but does not have the same properties. An alternative sensitivity measure based on the approximation of the differential entropy using dome-shaped functionals with non-negative values is proposed in the article. Case studies have shown that new sensitivity measures lead to a rational structure of sensitivity indices with a significantly lower proportion of higher-order sensitivity indices compared to other types of distributional sensitivity analysis. In terms of the concept of sensitivity analysis, a decrease in variance to zero means a transition from the differential to discrete entropy. The form of this transition is an open question, which can be studied using other scientific disciplines. The search for new functionals for distributional sensitivity analysis is not closed, and other suitable sensitivity measures may be found.