Fuzzy Entropy Measure Research Articles

A Novel Method Based on the Fuzzy Entropy Measure to Optimize the Fuzziness in Trapezoidal Strong Fuzzy Partitions

Analyzing the uncertainty of outcomes based on estimates of the data’s membership degrees to fuzzy sets is essential for making decisions. These fuzzy sets are often designated by experts as strong fuzzy partitions of the data domain with trapezoidal fuzzy numbers. Some indices of the fuzzy set’s fuzziness provide an assessment of the degree of uncertainty of the results. It is feasible to bring the fuzzy sets’ fuzziness below a tolerable level by suitably redefining the strong fuzzy partition. Significant differences in the original fuzzy partition, however, result in disparities concerning the decision maker’s approximative reasoning and the interpretability of the results. In light of this, we provide in this study a technique applied to trapezoidal strong fuzzy partitions that, while not appreciably altering the original fuzzy partition, reduces the fuzziness of its fuzzy sets. The fuzziness of the fuzzy sets is assessed using the De Luca and Termini fuzzy entropy. An iterative process is then executed, with the aim of modifying the cores of the trapezoidal fuzzy partitions to decrease their fuzziness. This technique is tested on datasets containing average daily temperatures measured in various cities. The findings demonstrate that this approach strikes a great balance between the goal of lessening the fuzziness of the fuzzy sets and the goal of not appreciably altering the original fuzzy partition.

Generalized Parametric Fuzzy Information Measure

Objective: To generalize an existing fuzzy information measure and verify its important properties. Methods: Both objective and descriptive methods have been adopted; problem-solving and problem-posing methods have been used. A collection of properties presented by De Luca and Termini is used as a standard for establishing new fuzzy information measures. Findings: This study has analysed the different features of the parametric measure of fuzzy information that we have presented. The suggested fuzzy entropy measure is a legitimate measure of fuzzy information since it meets all necessary requirements. Its monotonic behaviour has also been studied. Comparisons between the proposed measure of fuzzy information and the corresponding measure of probabilistic information have been discussed. Novelty: The unique quality of the suggested fuzzy information measure is found in its monotonic behaviour corresponding to parameter α. When conducting a multicriteria decision analysis and directing the decision-making process, monotonic fuzzy information measures are more useful. Because the suggested measure satisfies fundamental set features, it can be applied in soft computing for economics, decision-making, and data aggregation. Mathematics Subject Classification: 94 D 05 Keywords: Fuzzy Entropy, Uncertainty, Fuzziness, Measures of Information, Shannon Entropy

Noise-resistant fuzzy multineighbourhood rough set-based feature selection with label enhancement and its application for multilabel classification

Noise pollution in process of feature selection greatly reduces the classification efficacy of multilabel data, and the estimation of label descriptions is insufficient because of the lack of label enhancement for label distribution learning. To overcome the limitations, this work presents a noise-resistant fuzzy multineighbourhood rough set-based feature selection methodology with label enhancement and its application for multilabel classification. First, under the fuzzy T-equivalence relation, to construct new adaptive fuzzy neighbourhood class, the multineighbourhood radius set on feature space is integrated with fuzzy neighbourhood radius via sample interval on label space; then, the adaptive fuzzy multineighbourhood granules are obtained. Second, by integrating the parameterized fuzzy decision of labels and adaptive fuzzy multineighbourhood granules, noise-resistant lower and upper approximations via fuzzy multineighbourhood are constructed. A noise-resistant multilabel fuzzy multineighbourhood rough set model and its noise-resistant approximate accuracy can be proposed. Third, the description degree of label is computed to design label proportion after label enhancement. Certain fuzzy multineighbourhood entropy measures are developed to obtain label enhancement-based mutual information. When the algebraic and information perspectives are fused, label enhancement-based mutual information with fuzzy multineighbourhood via approximate accuracy is presented to evaluate the final association relationship between the features and label sets. Finally, a multilabel feature selection strategy via label enhancement will be constructed to obtain the best feature subset. The experimental results applied to 14 multilabel datasets indicate that this algorithm is significant.

Some Results On Mathai-Haubold Fuzzy Entropy

The concept of entropy, emerged from thermodynamics and statistical mechanics is of fundamental importance in some scientific and technological areas such as communication theory, physics, probability and statistics. Fuzzy entropy is much looked upon concept for measuring fuzzy information. The concept of fuzzy entropy was firstly mentioned by Zadeh way back in 1965 asa measure of fuzziness. In this paper , we introduce Mathai - Haubold fuzzy entropy with the proof of its validity. In addition, the elegant properties are studied of the proposed fuzzy entropy measure.

Assessing Motor Variability during Squat: The Reliability of Inertial Devices in Resistance Training.

Movement control can be an indicator of how challenging a task is for the athlete, and can provide useful information to improve training efficiency and prevent injuries. This study was carried out to determine whether inertial measurement units (IMU) can provide reliable information on motion variability during strength exercises, focusing on the squat. Sixty-six healthy, strength-trained young adults completed a two-day protocol, where the variability in the squat movement was analyzed at two different loads (30% and 70% of one repetition maximum) using inertial measurement units and a force platform. The time series from IMUs and force platforms were analyzed using linear (standard deviation) and non-linear (detrended fluctuation analysis, sample entropy and fuzzy entropy) measures. Reliability was analyzed for both IMU and force platform using the intraclass correlation coefficient and the standard error of measurement. Standard deviation, detrended fluctuation analysis, sample entropy, and fuzzy entropy from the IMUs time series showed moderate to good reliability values (ICC: 0.50-0.85) and an acceptable error. The study concludes that IMUs are reliable tools for analyzing movement variability in strength exercises, providing accessible options for performance monitoring and training optimization. These findings have implications for the design of more effective strength training programs, emphasizing the importance of movement control in enhancing athletic performance and reducing injury risks.

On some new fuzzy entropy measure of Pythagorean fuzzy sets for decision-making based on an extended TOPSIS approach

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.

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

An integrated interval-valued spherical fuzzy Choquet integral based decision making model for prioritizing risk in Fine-Kinney

The Fine-Kinney model has been expanded to serve as a tool for analyzing systemic risk in different industries, including occupational hazards. However, existing models for prioritizing risk in Fine-Kinney fail to account for the interconnectedness of experts’ cognitive information in interval-valued spherical fuzzy situations. This paper creates a new fuzzy compromise ranking of alternatives from distance to ideal solution (CRADIS) method to address the limitations of the Fine-Kinney model in occupational risk analysis. The interval-valued spherical fuzzy numbers are extended into the conventional risk scales in the Fine-Kinney model to generate a processing method for uncertain risk rating data. Then, the weighted averaging operator is developed based on the Choquet integral and interval-valued spherical fuzzy sets to construct the collective risk assessment matrix. This developed operator can capture inter-dependencies among risk data. Next, an enhanced CRADIS method with interval-valued spherical fuzzy sets and entropy measures is presented to address the risk ranking issue in the application of Fine-Kinney. To demonstrate the implementation of the synthesized occupational risk framework, a case study analyzing the occupational hazards in the metro construction process uses numerical methods. The proposed framework undergoes parameter sensitivity analysis to test its rationality. An evaluation compares the enhanced framework with the risk-prioritizing methods used in F–K to assess its advantages. The outcome suggests that the framework offers an appropriate and dependable approach to prioritizing occupational risks in a subjective and ambiguous scenario.

PARKINSON’S DISEASE DETECTION THROUGH VOICE SIGNALS

The primary Parkinsons disease (PD) is a disorder of the central nervous system and about 89% of the people with PD suffering from speech and voice disorders. In this project, we adopted a dynamic feature selection based on fuzzy entropy measures for speech pattern classification of Parkinsons diseases. To investigate the effect of feature selection, XGBoost algorithm was applied to distinguish voice samples between PD patients and health people. The data set of this research is composed of voice signals from 195 people, 147 with Parkinsons disease and 48 healthy people. The results show that various voice samples need different feature selection. We applied dynamic feature selection can get higher rate of classification accuracy than all features selected. KEYWORDS: Parkinsons disease, linear discriminant analysis, similarity measure, fuzzy

Empirical evaluation of Pythagorean fuzzy entropy measures with application in decision making

Empirical evaluation of Pythagorean fuzzy entropy measures with application in decision making

Nonlinear strict distance and similarity measures for intuitionistic fuzzy sets with applications to pattern classification and medical diagnosis

In this paper, we propose a new type of nonlinear strict distance and similarity measures for intuitionistic fuzzy sets (IFSs). Our proposed methods not only have good properties, but also improve the drawbacks proposed by Mahanta and Panda (Int J Intell Syst 36(2):615–627, 2021) in which, for example, their distance value of d_{_{textrm{MP}}}(langle mu , nu rangle , langle 0, 0rangle ) is always equal to the maximum value 1 for any intuitionistic fuzzy number langle mu , nu rangle ne langle 0, 0rangle . To resolve these problems in Mahanta and Panda (Int J Intell Syst 36(2):615–627, 2021), we establish a nonlinear parametric distance measure for IFSs and prove that it satisfies the axiomatic definition of strict intuitionistic fuzzy distances and preserves all advantages of distance measures. In particular, our proposed distance measure can effectively distinguish different IFSs with high hesitancy. Meanwhile, we obtain that the dual similarity measure and the induced entropy of our proposed distance measure satisfy the axiomatic definitions of strict intuitionistic fuzzy similarity measure and intuitionistic fuzzy entropy. Finally, we apply our proposed distance and similarity measures to pattern classification, decision making on the choice of a proper antivirus face mask for COVID-19, and medical diagnosis problems, to illustrate the effectiveness of the new methods.

Decision-Making Techniques Based on q-Rung Orthopair Probabilistic Hesitant Fuzzy Information: Application in Supply Chain Financing

The influence of COVID-19 on individuals, businesses, and corporations is indisputable. Many markets, particularly financial markets, have been severely shaken and have suffered significant losses. Significant issues have arisen in supply chain networks, particularly in terms of financing. The COVID-19 consequences had a significant effect on supply chain financing (SCF), which is responsible for finance supply chain components and improved supply chain performance. The primary source of supply chain financing is financial providers. Among financial providers, the banking sector is referred to as the primary source of financing. Any hiccup in the banking operational systems can have a massive influence on the financing process. In this study, we attempted to comprehend the key consequences of the COVID-19 epidemic and how to mitigate COVID-19’s impact on Pakistan’s banking industry. For this, three extended hybrid approaches which consists of TOPSIS, VIKOR, and Grey are established to address the uncertainty in supply chain finance under q-rung orthopair probabilistic hesitant fuzzy environment with unknown weight information of decision-making experts as well as the criteria. The study is split into three parts. First, the novel q-rung orthopair probabilistic hesitant fuzzy (qROPHF) entropy measure is established using generalized distance measure under qROPHF information to determine the unknown weights information of the attributes. The second part consists of three decision-making techniques (TOPSIS, VIKOR, and GRA) in the form of algorithm to tackle the uncertain information under qROPHF settings. Last part consists of a real-life case study of supply chain finance in Pakistan to analyze the effects of emergency situation of COVID-19 on Pakistani banks. Therefore, to help the government, we chose the best alternative form list of consider five alternatives (investment, government support, propositions and brands, channels, and digital and markets segments) by using proposed algorithm that minimize the effect of COVID-19 on supply chain finance of Pakistani banks. The results indicate that the proposed techniques are applicable and effective to cope with ambiguous data in decision-making challenges.

An improved entropy function for the intuitionistic fuzzy sets with application to cloud vendor selection

This study proposes a novel entropy function for the intuitionistic fuzzy sets to improve the existing fuzzy entropy measure. We introduce an attitude-based entropy measure by methodically calculating the experts’ attitude values through variance approach. We discuss several important properties and present an example to demonstrate the applicability and efficacy of the proposed method. An illustrative example exhibits the effectiveness of the proposed intuitionistic fuzzy entropy functions and measures. We further show the superiority of the proposed intuitionistic fuzzy entropy measures over the existing measures.

Exponential information measures-driven Pythagorean fuzzy MADM method and its application to new energy battery supplier evaluation problem

Under the Pythagorean fuzzy environment, this paper presents a multi-attribute decision-making (MADM) model based on exponential entropy measure and exponential similarity measure to evaluate new energy battery supplier’s performance. In this method, the notion of Pythagorean fuzzy linguistic sets (PFLSs) is first introduced by combining the linguistic fuzzy sets (LFSs) and the Pythagorean fuzzy sets (PFSs). Then, the axiomatic definitions of Pythagorean fuzzy entropy and Pythagorean fuzzy similarity measure are developed to measure the degree of uncertainty and similarity between two Pythagorean fuzzy linguistic values (PFLVs). The PFLVs can be expressed by the linguistic membership degree (LMD) and linguistic non-membership degree (LNMD). In addition, we construct two new information measure formulas based on exponential function. Through a series of proofs, we verify that they satisfy the axiomatic conditions of entropy and similarity measure of Pythagorean fuzzy language respectively. On this basis, we research the relationship between the two information measures. Finally, we present a novel Pythagorean fuzzy linguistic MADM model. An example for evaluating performance of new energy battery supplier is given to explain the effectiveness of the newly-developed approach. The stability and validity of the newly-developed approach is performed by sensitivity analysis and comparative analysis.

Spherical fuzzy hamacher power aggregation operators based on entropy for multiple attribute group decision making

As an improved form of fuzzy sets (FSs), spherical fuzzy sets (SFSs) could provide decision makers (DMs) with more free space to express their preference information. In this article, we first develop some Hamacher power aggregation operators under SFSs by power operators and Hamacher operators, including spherical fuzzy Hamacher power average (SFHPA) operator, spherical fuzzy Hamacher power geometric (SFHPG) operator, spherical fuzzy Hamacher power weighted average (SFHPWA) operator, spherical fuzzy Hamacher power weighted geometric (SFHPWG) operator, spherical fuzzy Hamacher power ordered weighted average (SFHPOWA) operator, spherical fuzzy Hamacher power ordered weighted geometric (SFHPOWG) operator, spherical fuzzy Hamacher power hybrid average (SFHPHA) operator and spherical fuzzy Hamacher power hybrid geometric (SFHPHG) operator. At the same time, some properties of the proposed operators are investigated, and the relationships between these operators and existing operators are discussed. Furthermore, a novel spherical fuzzy entropy measure is introduced to calculate unknown attribute weights. Then, some novel multiple attribute group decision making (MAGDM) methods are established by the proposed operators as well as entropy measure under SFSs. Lastly, the practicability of the presented methods is verified with a numerical case. Moreover, the robustness, availability and superiority for the developed methods are demonstrated via sensitivity analysis and further comparation with the existing methods.

Transformer's frequency response analysis results interpretation using a novel cross entropy based methodology

Transformer defects can be identified by the FRA (frequency response analysis) that is a promising diagnostic technique. Despite the standardization in FRA measuring technique, its results interpretation is yet a research area. Because different faults types can be identified in various frequency bounds of the FRA signatures, it is necessary to identify the possible relationships between specific failures and frequency ranges in this contribution. For this purpose, a real transformer is used to conduct the essential tests, which include both healthy and faulted circumstances (axial displacement (AD), radial deformation (RD), and short-circuits (SC)). To identify efficient characteristics from the produced frequency response traces and improve interpretation accuracy of such traces, a new hyperbolic fuzzy cross entropy (FCE) measure is demonstrated and then utilized for the aim of discrimination and classification of transformer winding defects in pre-defined frequency ranges. After normalizing FRA results of the transformer under healthy and various fault circumstances the lower bounds from such responses have been extracted and then utilized to construct the desired form of the fuzzy sets of healthy and faulted circumstances. Then, a new hyperbolic FCE measure-based discrimination and classification of winding faults methodology is offered on the basis of highest and lowest FCE measure values. The highest FCE measure value between the fuzzy sets of healthy and faulted circumstances such as AD, RD and SC is designated to confirm the occurrence of winding faults in a suitable frequency range. The suggested methodology ensures smart interpretation of FRA signature and accurate classification of winding faults as it can effectively discriminate both healthy and faulted circumstances in the desired frequency ranges. The proposed approaches' performance is tested and compared by applying the experimental data after feature extraction.

Multi-attribute decision-making based on novel Fermatean fuzzy similarity measure and entropy measure.

To deal with situations involving uncertainty, Fermatean fuzzy sets are more effective than Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. Applications for fuzzy similarity measures can be found in a wide range of fields, including clustering analysis, classification issues, medical diagnosis, etc. The computation of the weights of the criteria in a multi-criteria decision-making problem heavily relies on fuzzy entropy measurements. In this paper, we employ t-conorms to suggest various Fermatean fuzzy similarity measures. We have also discussed all of their interesting characteristics. Using the suggested similarity measurements, we have created some new entropy measures for Fermatean fuzzy sets. By using numerical comparison and linguistic hedging, we have established the superiority of the suggested similarity metrics and entropy measures over the existing measures in the Fermatean fuzzy environment. The usefulness of the proposed Fermatean fuzzy similarity measurements is shown by pattern analysis. Last but not least, a novel multi-attribute decision-making approach is described that tackles a significant flaw in the order preference by similarity to the ideal solution, a conventional approach to decision-making, in a Fermatean fuzzy environment.

Some novel q‐rung orthopair fuzzy similarity measures and entropy measures with their applications

AbstractIn this paper, we have introduced some new similarity measures for ‐rung orthopair fuzzy sets and discussed their various features. These similarity measures have been constructed with the help of t‐conorms. The suggested similarity measures are more effective than the available ones in computing the similarity between distinct ‐rung orthopair fuzzy sets. With the help of these suggested similarity measures, we have also developed some novel entropy measures for ‐rung orthopair fuzzy sets. The newly proposed entropy measures are more effective than the existing ones in handling linguistic hedges. The applicability of the suggested similarity measures has been demonstrated in pattern analysis and the findings have been found to be better than due to existing ones. The traditional decision‐making method namely, the technique for order preference by similarity to the ideal solution gives us a compromise solution that is either closest to the positive ideal solution and farthest from the negative ideal solution but not both. So, to overcome this major drawback, we suggest a novel multi‐attribute decision‐making method in the ‐rung orthopair fuzzy environment and apply it to a decision‐making problem.

Development of entropy measure for selecting highly sensitive WPT band to identify defective components of an axial piston pump

This paper proposes a novel tangent hyperbolic fuzzy entropy measure-based method for determining the highly (most) sensitive frequency band to easily identify defective components in an axial piston pump. The validation of proposed scheme was done by experimental and simulation analysis. In the proposed method, initially, the raw vibration signal is decomposed into 16 frequency bands. Second, the energy of the WPT band is computed. Third, lower bounds of energy readings at the 4th level of decomposition are extracted, and thereafter they are normalised and finally converted into the forms of fuzzy sets. Following that, the proposed measure's value is computed. The proposed measure is analogous to the quantity of available information. The WPT4 band with the highest measure value will have the most information and can be designated as sensitive. Finally, envelope demodulation of the sensitive band is computed to identify the defects by evaluating the magnitude of vibration at fundamental frequencies. The superiority of the proposed sensitive band selection technique has been justified by comparing the findings with the widely used Fast-Kurtogram, Protugram, and Spectral-Kurtosis methods. The authenticity of the proclaimed tangent hyperbolic fuzzy entropy measure is accomplished with the existing Deluca and Termini fuzzy entropy measures. The latter entropy measure exhibited some inconsequential and unspecified results and established the superiority of our defect identification methodology.

Fault transient feature extraction method of 66kV transmission line based on improved wavelet threshold and CEEMDAN-FME

In the 66kV transmission line, the compensation effect of the arc suppression coil, so the amplitude of fault zero sequence current is weak after the occurrence of single-phase grounding responsibility. The fault characteristics are not obvious, and there is environmental noise interference during fault signal acquisition, which further increases the difficulty of ground fault feature extraction. To solve the above problems, a fault transient feature extraction method of 66kV transmission line is proposed, based on improved wavelet threshold and Complete Ensemble Empirical Mode Decomposition with adaptive noise (CEEMDAN) - Fuzzy measure entropy (FME). The characteristics of single-phase grounding transient fault in small current grounding system are analyzed. The transient fault signal was preprocessed by an improved wavelet threshold method, and the transient fault characteristics were extracted accurately by CEEMDAN-FME processing. The proposed method has good anti-noise performance through the simulation comparison and verification of denoising processing and transient feature extraction by MATLAB. It can effectively extract fault features when the interference degree is significant.