Proposed Information Measure Research Articles

Belief Inaccuracy Information Measures and Their Extensions

This work introduces belief inaccuracy information (BII) and Jensen–belief inaccuracy information (JBII), grounded in the foundational concept of basic probability assignment. The significance of these novel methodologies lies in their potential to advance the field by providing valuable insights into belief accuracy assessment. The research not only establishes these measures but also highlights their relevance in addressing critical challenges within the realm of probability assignment. Further, some results associated with these proposed information measures were established. In addition, the BII and JBII measures were examined for escort and generalized escort of basic probability assignment functions, where an escort basic probability assignment with order [Formula: see text] is constructed based on the power [Formula: see text] of a baseline basic probability assignment with a normalizing constant. Finally, this paper presents compelling results derived from the application of BII and JBII measures. A detailed simulation of Conway’s game of life cellular automaton is described, showcasing the utility of these measures in analyzing belief inaccuracies within complex dynamic systems. Furthermore, an application to ozone time series is explored, employing belief Kullback–Leibler and belief chi-square divergences. This application specifically focuses on the study of station discrepancies, revealing the versatility of the proposed measures in addressing diverse scenarios.

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.

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.

Deng–Fisher information measure and its extensions: Application to Conway’s Game of Life

The purpose of this work is to introduce Deng–Fisher information (DFI), Deng–Fisher information distance (DFID) and Jensen–Deng–Fisher (JDF) information distance measures based on the basic probability assignment concept. We also present results associated with these proposed information measures and examine DFI and DFID measures for escort of basic probability assignment functions. For illustrative purpose, we examined Conway’s Game of Life cellular automaton and present numerical results in terms of the proposed information measures. Results indicate that JDF information distance measures living cell population dynamics along time.

Jensen–Fisher information and Jensen–Shannon entropy measures based on complementary discrete distributions with an application to Conway’s game of life

Several information and divergence measures existing in the literature assist in measuring the knowledge contained in sources of information. Studying an information source from both positive and negative aspects will result in more accurate and comprehensive information. In many cases, extracting information through the positive approach could be not an easy task while it may be feasible when dealing with the negative aspect. Negation is a new perspective and direction to quantify the information or knowledge in a given system from the negative approach. In this work, we study some new information measures, such as Fisher information, Fisher information distance, Jensen–Fisher information and Jensen–Shannon entropy measures, based on complementary distributions. We then show that the proposed Jensen–Fisher information measure can be expressed based on Fisher information distance measure. We have further shown that the Jensen–Shannon entropy measure has two representations in terms of Kullback–Leibler divergence and Jensen–extropy measures. Some illustrations related to complementary distribution of Bernoulli and Poisson random variables are then presented. Finally, for illustrative purpose, we have examined a real example on Conway’s game of life and have presented some numerical results in terms of the proposed information measures.

Fisher information and its extensions based on infinite mixture density functions

In this work, we consider the Fisher information and some of its well-known extended versions and then establish some results based on infinite mixture density functions for the proposed information measures. Specifically we introduce the Jensen-type of Fisher information (parametric-type and density-based) and generalized Fisher information measures based on infinite mixture density functions. We then show that the proposed Jensen–Fisher information measure have two representations in terms of Fisher information distance in the both parametric-type and density-based cases. We have further shown that the generalized Fisher information of an infinite mixture density can be stated based on Pearson–Vajda χk divergence. Finally, we examine the convexity property of q−Fisher information measure based on finite mixture density functions under a mild condition. Some examples related to scale mixture of skew-normal family of distributions, with emphasis on skew-normal density, are illustrated within the paper.

Developing a semi-supervised learning and ordinal classification framework for quality level prediction in manufacturing

The authors of this work propose a novel semi-supervised learning framework for quality prediction in manufacturing. Semi-supervised learning is a promising method in neural network applications, where label generation incurs significant time and cost. However, a semi-supervised learning mechanism in the manufacturing industry has not been as popular as a supervised learning method, especially in quality prediction tasks. The proposed framework trains a deep neural network-based model in a self-training scheme that uses filtered unlabeled data based on prediction confidence. In particular, the framework successfully handles ordinal classification tasks by using ordinal label rendering based on a state-of-the-art technique called the soft ordinal vector (SORD) that reflects ordinality in multiple labels. Furthermore, a newly proposed information measure named ordinal entropy, which takes ordinality into account, is used to selectively utilize confident labels among generated pseudo-labels. The proposed framework’s efficacy is validated through a case study using real-world data from the ultraviolet (UV) lamp manufacturing process. The proposed framework has shown better performance in quality prediction than the learned model with only supervision. In addition, various configurations of the proposed framework have been validated with extensive experiments.

Information measures for MADM under m-polar neutrosophic environment

Multiploar information plays a vital role in making reliable decisions in one’s daily life encompassing micro- to large-scale decisions. These decision-making problems often include imprecise and inconsistent data. This article presents information measures for m-polar neutrosophic sets. These include similarity, distance, correlation, divergence and Dice measures for m-polar neutrosophic sets. Furthermore, the paper presents the desirable characteristics of these measures along with the notions of angle of similarity between two m-polar neutrosophic sets, \(\lambda\)-similarity, entropy and less and more fuzzy aspects. The paper also presents an application of m-polar neutrosophic sets using the suggested measures in health sciences accompanied by five algorithms. Moreover, the paper presents the comparative analysis of the proposed information measures with some existing measures.

Probabilistic damage localization by empirical data analysis and symmetric information measure

This article aims to address some challenges in data-based damage localization by proposing innovative methods including a hybrid algorithm for feature extraction, a symmetric information measure for feature classification, and a probabilistic approach to threshold estimation. The hybrid feature extraction combines an autoregressive (AR) model with a novel non-parametric estimator of probability density function (PDF) under empirical data analysis. The great novelty of this method is to propose a new probabilistic feature as an empirical PDF of the AR coefficients. The proposed information measure is a symmetric divergence aiming at addressing the main limitation of the classical Kullback-Leibler divergence regarding its non-symmetric characteristic. Finally, the proposed probabilistic approach exploits the concept of Markov Chain Monte Carlo to estimate a trustworthy threshold for locating damage. Vibration responses of two civil structures are used to verify the proposed methods with several comparisons. Results confirm that the methods are successful in identifying damage.

Fuzzy Rough Information Measures and their Applications

The degree of roughness characterizes the uncertainty contained in a rough set. The rough entropy was defined to measure the roughness of a rough set. Though, it was effective and useful, but not accurate enough. Some authors use information measure in place of entropy for better understanding which measures the amount of uncertainty contained in fuzzy rough set .In this paper three new fuzzy rough information measures are proposed and their validity is verified. The application of these proposed information measures in decision making problems is studied and also compared with other existing information measures.

The context-based distance measure for intuitionistic fuzzy set with application in marine energy transportation route decision making

Background and motivation:The distance measure is a classical topic in the intuitionistic fuzzy set theory. Although plenty of distance measures have been proposed and successfully applied to the decision-making problems, it is found that there still exists the counter-intuitive phenomenon where the context information in the alternatives is seldom considered in the existing distance measures. Methods:A context-based distance measure for the intuitionistic fuzzy set is proposed to solve this problem in this paper. The domination and competition relationships of the alternatives are integrated into the new distance measure. To fully take advantage of the proposed distance measure, a new similarity measure that utilizes the nonlinear function of the distance and additional parameters to control its discrimination capability is also defined. To demonstrate the effectiveness of the proposed information measures and their practical applications, an extended decision making method based on the order preference by similarity to ideal solutions is proposed. Results:A practical case study of the marine energy transportation route decision making problem is provided as the validation. The comparative results comparing with other methods demonstrate the fine discrimination ability and effectiveness of the proposed methods.

Non-Empirical Metrics for Ontology Visualizations Evaluation and Comparing

There are numerous ontology visualization systems, however, the choice of a visualization system is non-trivial, as there is no method for evaluation and comparing them, except for empirical experiments, that are subjective and costly. In this research, we aim to develop non- empirical metrics for ontology visualizations evaluation and comparing. First, we propose several half-formal metrics that require expert evaluation. These metrics are completeness, semanticity, and conservativeness. We apply the proposed metrics to evaluate and compare VOWL and Logic Graphs visualization systems. And second, we develop a com- pletely computable measure for the complexity of ontology visualizations, based on graph theory and information theory. In particular, ontology visualizations are considered as hypergraphs and the information mea- sure is derived from the Hartley function. The usage of the proposed information measure is exemplified by the evaluation of visualizations of the sample of axioms from the DoCO ontology in Logic Graphs and Graphol. These results can be practically applied for choosing ontology visualization systems in general and regarding a particular ontology.

Study of Quantile-Based Cumulative Renyi Information Measure

In this paper, we proposed a quantile version of cumulative Renyi entropy for residual and past lifetimes and study their properties. We also study quantile-based cumulative Renyi entropy for extreme order statistic when random variable untruncated or truncated in nature. Some characterization results are studied using the relationship between proposed information measure and reliability measure. We also examine it in relation to some applied problems such as weighted and equillibrium models.

An (R, S)-norm information measure for hesitant fuzzy sets and its application in decision-making

To characterize the uncertainty of a hesitant fuzzy set, a new entropy, which is called (R, S)-norm information measure, is proposed in this paper. It is proved that the proposed measure satisfies the axiomatic definition of entropy measures for hesitant fuzzy sets, and then, some properties of the proposed measure are also explored. Furthermore, several examples are presented to show the advantages of the (R, S)-norm information measure compared with some existing entropy measures. Then, based on the new information measure, we utilize decision-making method by combining prospect theory with technique for order preference by similarity to an ideal solution to address multi-attribute decision-making problems. Finally, a concrete example of business investment is provided to illustrate the effectiveness of our proposed information measure, and comparative analysis is also completed to verify the validity of the (R, S)-norm information measure.

RenyiBS: Renyi entropy basis selection from wavelet packet decomposition tree for phonocardiogram classification

Wavelet packet transform (WPT) is a powerful mathematical tool for analyzing nonlinear biomedical signals, such as phonocardiogram (PCG). WPT decomposes a PCG signal into a full binary tree of details and approximation coefficients. Appropriate nodes of the tree could be selected as a basis for generating features. Motivated by this, we propose the Renyi entropy basis selection (RenyiBS) method. In RenyiBS method, we use the Renyi entropy as an information measure to choose the best basis of the wavelet packet tree of PCG signals for feature selection and classification. The Renyi entropy estimates the spectral complexity of a signal, which is vital for characterizing nonlinear signals such as PCGs. After selecting the best basis, we define features on the coefficients of the selected nodes. Then, we classify PCGs using the support vector machine (SVM) classifier. In the simulation, we examine a set of 820 heart sound cycles, including normal heart sounds and three types of heart murmurs. The three murmurs examined include aortic regurgitation, mitral regurgitation, and aortic stenosis. We achieved the promising result of 99.74% accuracy, confirming the ability of Renyi entropy to select an appropriate basis of the wavelet packet tree and extracting the nonlinear behavior of particular heart sounds. Besides, the superiority of our proposed information measure in comparison with other information measures reported before is shown.

A new picture fuzzy information measure based on Tsallis–Havrda–Charvat concept with applications in presaging poll outcome

The picture fuzzy set (PFS) proposed by Cuong and Kreinovich are well suitable to capture the uncertain information in vague circumstances. The main objective of this communication is to propose a new framework as a criteria of fuzzy entropy for PFSs. Further, a new picture fuzzy information measure based on Tsallis–Havrda–Charvat entropy is proposed and validated in accordance with newly proposed framework. Besides this, some major properties of proposed information measure are also discussed. Apart from this, a new multi-criteria decision-making method using the concept of VIKOR (Vlsekriterijumska Optimizacija i Kompromisno Resenje) based on relative projection is proposed. To show the practical utility of proposed decision-making method, two numerical examples based on election forecast through opinion polls have been discussed.

A novel decision-making method using R-Norm concept and VIKOR approach under picture fuzzy environment

The Picture Fuzzy Sets (PFS) are well suitable to capture inconsistent, imprecise and uncertain information in multiple-criteria decision-making problems. This communication is intended to introduce one such information measure defined on PFSs called R-norm picture fuzzy information measure. Moreover, a new set of axioms is proposed as a criteria for picture fuzzy entropy. Besides establishing the validity of proposed R-norm picture fuzzy information measure, some of its major properties are also discussed. In application part, the proposed information measure is applied in predicting the outcome of elections in a poll bound country through opinion polls and to solve an investment problem.

A Superpixel Boundary Optimization (SBO) Framework Based on Information Measure Function

Superpixel is an essential tool for computer vision. In practice, classic superpixel algorithms do not exhibit good boundary adherence with fewer superpixels, which will greatly hamper further analysis. To remedy the defect, a superpixel boundary optimization framework is proposed in this paper. There are three steps in the framework. Firstly, based on the proposed information measure function, the under-segmented superpixels generated by classic superpixel algorithms are screened out. Secondly, with the two invariant centroids method, these under-segmented superpixels are re-segmented to improve the accuracy in boundary adherence. Finally, smaller superpixels are merged to maintain the same number with initial superpixels. Quantitative evaluations on the BSDS500 exhibit that the performance of the classic superpixel algorithms is improved by employing the framework, especially on the condition of fewer superpixels.

Fractional cumulative residual entropy

Recently, cumulative residual entropy was proposed as an alternative measure of information to Shannon entropy. In this work, we generate the cumulative residual entropy (CRE) to the case of fractional order, named fractional CRE. Some properties of the new quantity are presented. The connections of fractional CRE to the CRE and classic differential entropy are studied. Besides, we show that the proposed information measure can be estimated by the empirical fractional CRE of sample data. A central limit theorem for the empirical fractional CRE for random samples from the exponential distribution is derived. Its property of stability is also discussed. Finally, simulations on logistic map and application in financial data are given to support the validity of fractional CRE.

Impact of Monetary Policy on Financial Markets Efficiency under Speculative Bubbles: a Non-Normal and Non-Linear Entropy-based Approach

This paper examines, through the concept of mutual information based on Shannon’s entropy, the impact of monetary policy on the loss of efficiency in the financial markets due to speculative bubbles. The proposed information measure is useful to quantify the efficiency with which stock markets respond to the implementation of monetary policy. The findings show that an increase in both money supply and credit growth, as well as declining interest rates, lead to strong market inefficiencies during the initial periods of formation of a bubble. Moreover, empirical evidence suggests that when a loose monetary policy (money supply is expanded and is accessible to agents to encourage economic growth) generates inefficiencies, its instruments are not effective to realign the performance of financial markets. JEL Classification: E5, G14, D84, C60.