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Concerning decision support in specific disease areas, making faster and more accurate medical diagnoses has become more challenging. Due to indeterminate, inconsistent, and huge patient data, judging a specific disease may be challenging. Similarity is an effective method to enhance healthcare systems by simplifying medical diagnostic generation compared with illness profiles. This paper proposes a new medical diagnosis algorithm that uses interval type-2 fuzzy similarity measures (IT-2FSMs). This algorithm calculates the degree of similarity between varieties of components of patient data and establishes methods of clustering patients based on close distances between some of their features. The proposed approach will be evaluated on UCI Machine Learning Repository medical datasets. Comparative studies will be done between different IT-2 FSMs (Cherif, Jaccard, Bustince, Mitchell, Gorzalczany, Zeng and Li) to demonstrate the capability of IT-2FSMs to make quick medical diagnoses, even with different noise levels. The proposed IT-2FSMs are utilized as a clustering method and compared against existing clustering algorithms such as type-2 fuzzy c-means, cluster forest, bagged clustering, evidence accumulation, and random projection. The IT-2FSMs demonstrate a pertinent classification accuracy comparable to the other algorithms, as assessed by the clustering quality parameter R. [ABSTRACT FROM AUTHOR]

The Aichi biodiversity targets were established by the UN convention of biological diversity and consist of 20 specific targets to address and mitigate biodiversity loss across the globe. We consider countries in East and South Asia. Countries in East and South Asia are very different in size and level of economic development. As such Sustainable Development Goal challenges vary greatly across countries. The 2022 Environmental Performance Index (EPI) provides a quantitative basis for comparing, analyzing, and understanding environmental performance for 180 countries. The EPI score and rank these countries on their environmental performance using the most recent year of data available and calculate how these scores have changed over the previous decade. We determine the similarity between the country achievement rankings of the Aichi Targets and the EPI rankings. [ABSTRACT FROM AUTHOR]

Biomedical data exhibit high-dimensional complexity in its internal structure and are susceptible to noise interference, making classification tasks in biomedical data highly challenging. Twin support vector machine (TSVM) is a machine learning algorithm that can effectively solve pattern recognition problems. To mitigate the negative impact of noise, researchers have combined fuzzy set theory with TSVM and use fuzzy membership to describe the influence of different samples on constructing the optimal hyperplane, thus, extending TSVM to fuzzy twin support vector machines (FTSVM). In this paper, the dissimilarity measure based on data distribution is innovatively introduced into the fuzzy membership assignment process, and a novel fuzzy membership assignment strategy is designed to effectively reduce the negative impact of noise in biomedical data. Rather than rely on geometric distance, this strategy takes data distribution as the primary factor in measuring dissimilarity between samples and then constructs a heuristic function to assign fuzzy membership to different samples. Combining this strategy with TSVM, this paper proposed a fuzzy twin support vector machine based on dissimilarity measure (DFTSVM), which could effectively solve the classification problem with noise and shows excellent generalization performance in biomedical data. Moreover, DFTSVM employs a coordinate descent strategy with shrinking by active set to reduce computational complexity, which significantly improves the training speed of the model. Experiments are conducted on 14 biomedical datasets to compare the performance of DFTSVM with 10 heterogeneous machine learning classification algorithms and four homology algorithms. The results demonstrate that DFTSVM outperforms other algorithms in terms of classification performance on biomedical data. It exhibits excellent generalization performance in noisy environments, and its advantages in terms of generalization performance and noise robustness become more prominent as the noise rate increases. [ABSTRACT FROM AUTHOR]

In artificial intelligence, decision-making is a widely studied field, and distance measure plays a crucial role in decision science. Several distance measures for Intuitionistic Fuzzy sets (IFSs) have been developed to handle uncertain situations. However, some of these measures lack properties of distance measures or produce unreasonable results. This study introduces a new distance measure between IFSs that satisfies the necessary properties and resolves counter-intuitive cases. The proposed distance measure is verified to be more reasonable through numerical examples, and it is applied to pattern recognition and medical diagnosis problems. [ABSTRACT FROM AUTHOR]

Distinguishing different time series, which is determinant or stochastic, is an important task in signal processing. In this work, a correlation measure constructs Correlation Fuzzy Entropy (CFE) to discriminate Chaos and stochastic series. It can be employed to distinguish chaotic signals from ARIMA series with different noises. With specific embedding dimensions, we implemented the CFE features by analyzing two available online signature databases MCYT-100 and SVC2004. The accurate rates of the CFE-based models exceed 99.3%. [ABSTRACT FROM AUTHOR]

In this work, we explore the impact of adaptive fuzzy measures on edge detection, aiming to enhance how computers interpret images by identifying edges more accurately. Traditional methods rely on analysing changes in image brightness to locate edges, but they often use fixed rules that do not account for the unique characteristics of each image. Our approach differs by adjusting fuzzy measures based on the information within specific areas of an image under a sliding window approach, utilizing a variety of fusion functions and generalizations of the Choquet integral to analyse and combine pixel data. The proposed method is flexible, allowing for the adaptation of measures in response to the image's local features. We put our method to the test against the well‐established Canny edge detector to evaluate its effectiveness. Our experimental results suggest that by adapting fuzzy measures for each image section, we can improve edge detection results. [ABSTRACT FROM AUTHOR]

This longitudinal study explored the impact of COVID‐19 on individuals in romantic relationships. The sample spans three waves: first confinement (n = 52), deconfinement (n = 49), and second confinement (n = 26). The study tested sociodemographic factors, psychological adjustment (anxiety, depression, stress, well‐being), COVID‐19 threat perception, dyadic coping, and relationship quality. Results from repeated measures ANOVA and fuzzy set qualitative comparative analysis (fsQCA) models revealed a decline in anxiety, depression, and stress symptoms, coupled with improved relationship quality over time. Well‐being and dyadic coping remained stable, while COVID‐19 threat perception increased. QCA models emphasized the predictive power of initial mental states (anxiety, depression, stress, and well‐being at W1) on subsequent adjustment. Notably, shorter relationship duration, healthcare worker status, and not having children, when combined with prior mental states, explained increased symptoms and diminished well‐being. The study underscores the significance of addressing these factors in individuals navigating romantic relationships during the pandemic. [ABSTRACT FROM AUTHOR]

The dynamic multiple-criteria decision-making (MCDM) approach has drawn immense attention in the decision analysis domain over recent years. An essential problem of this dynamic process is how to retrieve the utmost from historical data. Although most previous dynamic MCDM studies process historical data only with external representatives, namely scores given to alternatives on each criterion, we argue that internal patterns of historical data are also essential to achieve a more comprehensive evaluation of alternatives. Nevertheless, a data-driven methodology aiming to capture internal patterns of historical data and consequently provide decision-makers with meaningful insights is still lacking. In this paper, we propose a framework that serves as integration within which both external representations and internal patterns are used to make a more comprehensive evaluation. Then we apply our framework to student evaluations and country-level risk assessments in the contexts of additive and fuzzy measures, respectively. Both cases show that either using external representatives or internal patterns alone leads to entirely different and even biased results. On the contrary, integrating external representations and internal patterns can offer more flexibility and higher interpretation power. [ABSTRACT FROM AUTHOR]

In the field of fuzzy sets, distance measures can effectively quantify the relevant uncertainty. Regarding hesitant fuzzy sets (HFSs), improved hesitant fuzzy distance measures have recently been proposed by fusing classical distance measures with hesitation degrees, and the corresponding information enrichment can be probabilistically advanced to pursue new distance measures of probabilistic hesitant fuzzy sets (PHFSs). Aiming at PHFSs, the improved distance measures of HFSs are simulated and extended in this paper, and thus improved distance measures of PHFSs are proposed; the new PHFSs distances are utilized to construct a new method of probabilistic hesitant fuzzy decision-making, called MEREC-TODIM. Firstly, the new probabilistic hesitant fuzzy Hamming distance and Euclidean distance are directly and parametrically established by incorporating hesitation degrees; accordingly, the improved distance measures exhibit a 2 × 2 system on (non-parameter, parameter) and (Hamming, Euclidean), and their distance property, measure size, parameter monotonicity, and promotion degeneration are investigated and acquired. Furthermore, a modified score function is proposed for MEREC to determine attribute weights, and thus a corresponding decision method with TODIM (i.e., MEREC-TODIM) is established for PHFSs applications on evaluation sorting and optimization selection. Finally, MEREC-TODIM is validated through parameter analyses and decision comparisons, and it is effectively applied to two practical examples: Carbon Capture Utilization Storage and PhD Admission Interviews. Highlights: PHF Hamming and Euclidean distances fusing hesitation degrees provide extensions on HFSs and improvements on PHFSs. An improved score function considering deviation degrees emerges to induce MEREC for attribute weight determination. Improved measures-based TODIM and MEREC constitute MEREC-TODIM decision making with validity and performance. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study of the linguistic Z-graph, which is a novel framework designed to analyze linguistic structures within social networks. By integrating concepts from graph theory and linguistics, the linguistic Z-graph provides a detailed understanding of language dynamics in online communities. This study highlights the practical applications of linguistic Z-graphs in identifying central nodes within social networks, which are crucial for online businesses in market capture and information dissemination. Traditional methods for identifying central nodes rely on direct connections, but social network connections often exhibit uncertainty. This paper focuses on using fuzzy theory, particularly linguistic Z-graphs, to address this uncertainty, offering more detailed insights compared to fuzzy graphs. Our study introduces a new centrality measure using linguistic Z-graphs, enhancing our understanding of social network structures. [ABSTRACT FROM AUTHOR]

Sustainable development is crucial for conserving resources and ensuring smooth supply chain operations. In the context of the complex task of supplier selection, the traditional assumptions of attribute independencies are frequently found to be inadequate. The effective interaction between attributes and their weights plays a crucial role in navigating the decision outcomes. This paper presents a Choquet integral-based hybrid interactive decision-making approach to address the two important issues regarding the weights and interaction of criteria. To achieve this aim, first a hybrid weight determination method is proposed, combining the merits of multi-objective optimization and clustering techniques. To comprehensively assess the interactions among attributes, a non-additive measure determination method is introduced, leveraging concepts such as standard deviation and correlation. This approach effectively captures the interdependencies among attributes, leading to a more accurate decision-making process. Then, the Choquet integral incorporates a logarithmic function, which serves to enhance the modeling of uncertainty and effectively address the complexities present in intricate decision-making situations. Furthermore, a comprehensive interactive MCDM model is constructed, serving as a framework for supplier selection. Finally, experimental and sensitivity analysis demonstrate the effectiveness and stability of the proposed approach. [ABSTRACT FROM AUTHOR]

Clustering is a technique of grouping data into a homogeneous structure according to the similarity or dissimilarity measures between objects. In clustering, the fuzzy c-means (FCM) algorithm is the best-known and most commonly used method and is a fuzzy extension of k-means in which FCM has been widely used in various fields. Although FCM is a good clustering algorithm, it only treats data points with feature components under equal importance and has drawbacks for handling high-dimensional data. The rapid development of social media and data acquisition techniques has led to advanced methods of collecting and processing larger, complex, and high-dimensional data. However, with high-dimensional data, the number of dimensions is typically immaterial or irrelevant. For features to be sparse, the Lasso penalty is capable of being applied to feature weights. A solution for FCM with sparsity is sparse FCM (S-FCM) clustering. In this paper, we propose a new S-FCM, called S-FCM-Lasso, which is a new type of S-FCM based on the Lasso penalty. The irrelevant features can be diminished towards exactly zero and assigned zero weights for unnecessary characteristics by the proposed S-FCM-Lasso. Based on various clustering performance measures, we compare S-FCM-Lasso with the S-FCM and other existing sparse clustering algorithms on several numerical and real-life datasets. Comparisons and experimental results demonstrate that, in terms of these performance measures, the proposed S-FCM-Lasso performs better than S-FCM and existing sparse clustering algorithms. This validates the efficiency and usefulness of the proposed S-FCM-Lasso algorithm for high-dimensional datasets with sparsity. [ABSTRACT FROM AUTHOR]

Picture fuzzy sets (PFSs), as a generalization of traditional fuzzy sets and intuitionistic fuzzy sets (IFSs), offer a powerful framework for modeling and dealing with imprecise and uncertain information and have been widely used in various fields. Nevertheless, how to effectively measure the differences or similarities between PFSs is still a challenging and urgent problem. Despite that some distance measures for PFSs have been developed, some of them have counterintuitive and unreasonable results and even partially fail to satisfy the axiomatic definition of distance measures. To handle these limitations, in this paper, we propose two distance measures of PFSs motivated by the merits of Jensen–Shannon divergence. Specifically, the first distance measure of the PFSs considers the positive degree, neutral degree and negative degree. The second distance measure introduces the refusal degree on this basis. Moreover, the proposed distance measures not only satisfy the axiomatic definition but also overcome the counterintuitive results of existing distance measures. Finally, two kinds of applications related to pattern recognition and medical diagnosis are used to verify the performance of the proposed distance measures. [ABSTRACT FROM AUTHOR]

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The global population is at risk from both communicable and non-communicable deadly diseases, including cardiovascular disease. Early detection and prevention of cardiovascular disease require an accurate self-detection model. Therefore, this study introduces a novel fuzzy entropy DEMATEL inference system for accurate self-detection of cardiovascular disease. It combines fuzzy DEMATEL, entropy, and Mamdani fuzzy inference, utilizing innovative strategies like attribute reduction, entropy-based clustering, influential factor selection, and rule reduction. The system achieves high accuracy (98.69%) and sensitivity (98.62%), outperforming existing methods. Validation includes satisfactory factor analysis, performance measures and statistical analysis, demonstrating its effectiveness in addressing complexity and prioritizing factors. [ABSTRACT FROM AUTHOR]

Group decision-making (GDM) is crucial in various components of graph theory, management science, and operations research. In particular, in an intuitionistic fuzzy group decision-making problem, the experts communicate their preferences using intuitionistic fuzzy preference relations (IFPRs). This approach is a way that decision-makers rank or select the most desirable alternatives by gathering criteria-based information to estimate the best alternatives using a wider range of knowledge and experience. This article proposes a new statistical measure in a fuzzy environment when the data is ambiguous or unreliable to solve a decision-making problem. This study uses the variation coefficient measure combined with intuitionistic fuzzy graphs (IFG) and Laplacian energy (LE) to solve a GDM problem that utilizes intuitionistic fuzzy preference relations (IFPRs) to select a reliable alliance partner. Initially, the Laplacian energy determines the weight of individual standards, and the obtained weight average further estimates the overall criterion weight vector. We establish the authority criteria weights using the variation coefficient measure and then ultimately rank the alternatives for each criterion using the same measure. We examine four distinct companies Alpha, Beta, Delta, and Zeta to conduct a realistic GDM to choose which alliance partner would be ideal. We successfully implemented the suggested technique, determining that Alpha satisfies company standards and is ranked first among other companies. Moreover, this technique is useful for all kinds of Intuitionistic fuzzy group decision-making problems to select optimal ones. [ABSTRACT FROM AUTHOR]

In this work, we consider De Luca and Termini's notion of non-probabilistic entropy, and we extend some entropy-like measures of the degree of fuzziness to type-2 fuzzy sets. With this aim, we first study different entropy measures proposed in the frameworks of fuzzy, intuitionistic, and interval-valued fuzzy sets. Then, we propose three possible novel axiomatizations for entropy in type-2 fuzzy sets. The proposed types of entropy measures evaluate how much a type-2 fuzzy set is non-crisp, non-fuzzy, and non-interval-valued fuzzy. This can also be interpreted as how far a type-2 fuzzy set is from a crisp, fuzzy, or interval-valued fuzzy set. The present contribution is also novel, since we considered the interpretation of type-2 fuzzy sets that is closest to Zadeh's original conception. [ABSTRACT FROM AUTHOR]

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]

The fuzziness in the coverage, location, transportation and routing problems models is assumed to take place due to the lack of sufficient objective information on the disaster zone data. In evaluating the required parameters in the model, we use the knowledge and experience of experts (of route network dispatchers, etc.). Given the issues outlined above, we consider the fuzzy multi-objective emergency shelters location and victims evacuation problem (FMOESLVEP) in a disaster-stricken zone with the following objective functions: maximizing the total selection reliability index of opened shelters and minimizing the monotone expectation of total time for victims evacuation. These objective functions are novel and their construction and study are the basic tasks of the present work. [ABSTRACT FROM AUTHOR]

In general, raw image may suffer from various uncertain distortions arising due to many factors like low dynamic range of imaging device, low illumination, bad weather conditions. In this paper, a new idea of fuzzy peer group-based image denoising algorithm has been presented with a novel similarity measure function. Unlikely the Gaussian membership function based conventional similarity measure; here proposed method hired the local spatial information induced similarity measure together with Gaussian membership function by exploiting the significance of both. Using the proposed similarity measure, fuzzy peer group of similar pixels contrived and color image having contamination of mixed noise i.e., impulse noise and Gaussian noise is decontaminated with refashioned form of bilateral filter. The algorithm proposed has been compared with some state-of-the-art methods in studies and other techniques. The experimental performance shows that proposed approach is having leading filtering outcome with edge preserving and color information from existing methods. [ABSTRACT FROM AUTHOR]

In traditional Data Envelopment Analysis (DEA) approaches, inputs and outputs are usually considered as exact and real values. The relative efficiency of the Decision-Making Units (DMUs) is evaluated and it is known that the factors are inputs and/or outputs. However, there are some conditions under which the efficiency of DMUs should be calculated while the data are integer and ambiguous. Therefore, various integer DEA models have been proposed to determine the performance of DMUs when integer data and fuzzy factors are available. In addition, there are cases where the efficiency of DMUs should be determined when integer data and flexible factors are available. Therefore, some integer DEA methods have been proposed to calculate the performance of DMUs and specify the role of flexible measures when some of the data are integer and flexible factors are available. However, there are some situations where there are integer data, fuzzy integer measures and flexible factors. Therefore, this paper sheds light on the nature of the model to determine the efficiency of DMUs when there are integer inputs and/or outputs, flexible factors and fuzzy integer measures, and determines the role of factors with uncertain inputs or outputs. In fact, slacks are addressed and a slack-based efficiency measure (SBM) is defined to compute the performance of DMUs in the presence of flexible factors, integer data and fuzzy integer measures. The proposed approaches are demonstrated and illustrated using an example. [ABSTRACT FROM AUTHOR]

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 as a 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. [ABSTRACT FROM AUTHOR]

Due to the information non-independence of attributes, combined with a complex and changeable environment, the analysis of risks faces great difficulties. In view of this problem, this paper proposes a new three-way decision-making (3WD) method, combined with prospect theory and a non-additive measure, to cope with multi-source and incomplete risk information systems. Prospect theory improves the loss function of the original 3WD model, and the combination of non-additive measurement and probability measurement provides a new perspective to understand the meaning of decision-making, which could measure the relative degree by considering expert knowledge and objective data. The theoretical basis and framework of this model are illustrated, and this model is applied to a real in-service aviation equipment structures risk evaluation problem involving multiple incomplete risk information sources. When the simulation analysis is carried out, the results show that the availability of this method is verified. This method can also evaluate and rank key risk factors in equipment structures, which provides a reliable basis for decisions in aviation safety management. [ABSTRACT FROM AUTHOR]

In this article, we implemented the idea of a fuzzy interval-valued function with the well-known generalized fuzzy fractional operators, associated with different types of convexities and preinvexities. We developed the Prabhakar fuzzy fractional operators using the fuzzy interval-valued function. We presented the novel extensions of Hermite-Hadamard fuzzy-type and trapezoidal fuzzy-type inequalities, based on the h-Godunova-Levin convex and h-Godunova preinvex fuzzy interval-valued functions. [ABSTRACT FROM AUTHOR]

Non-additive measures are important for many applications. In this paper we propose an extension of the non-additive measure using the concept of Kerridge inaccuracy and cumulative Tsallis entropy. Several properties including non-linear transformation, bounds and characterizations are obtained using this measure. We also study different properties of the quantile version of the proposed measure. Finally, we numerically illustrate the usefulness of the measure and its quantile form using kernel density estimators. [ABSTRACT FROM AUTHOR]

The medical diagnosis of many critical diseases is difficult as it usually requires the combined effort of several doctors. At this time, the process of medical diagnosis is actually a group decision-making (GDM) problem. In group medical diagnosis, considering doctors' weight information and fusing the interaction relation of symptoms remain open issues. To address this problem, a group decision-making method for intuitionistic fuzzy soft environments is proposed for medical diagnosis because the intuitionistic fuzzy soft set (IFSS) integrates the advantages of the soft set and intuitionistic fuzzy set (IFS). Intuitionistic fuzzy soft weighted Muirhead mean operators are constructed by combining Einstein operations with the Muirhead mean (MM) operator, and some properties and results are revealed. A group medical diagnosis model with unknown doctor weight information and incomplete intuitionistic fuzzy soft information is proposed. Similarity measures of the intuitionistic fuzzy soft matrix (IFSM) given by the doctors are used to estimate the incomplete information. To take into account the advantages of objective weight and subjective weight, the combined weights of doctors are calculated based on the IFSMs' similarity measure and doctors' grades. The developed operators are then used to combine the evaluation information and handle the correlation of input arguments in the group medical diagnosis process. Finally, a numerical problem is selected to illustrate the superiority of the proposed approach compared to related methods. The combined weights are determined to overcome the shortcomings of the single-weight method to some extent. Meanwhile, the proposed method is more comprehensive, and can provide more flexible and reasonable choices for group medical diagnosis problems. [ABSTRACT FROM AUTHOR]

Multi-criteria decision-making (MCDM) entails a heterogeneous decision-making problem, which poses challenges for decision-makers (DMs) in generating an optimal solution. To address this, we have proposed a heterogeneous evaluation framework. First, a novel picture fuzzy cross-entropy measure was defined with the simultaneous consideration of uncertainty and hesitancy of picture fuzzy information, overcoming the shortcomings of the existing cross-entropy measure in relation to its validity and properties. Next, an optimisation-model for determining the objective weights of criteria was constructed based on the proposed closeness measurement and the step-wise weight assessment ratio analysis (SWARA) method. This model was constituted from both objective and subjective perspectives under the circumstance of completely unknown criterion information. Additionally, the conventional Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method was extended to the picture fuzzy environment, and a normalisation method was developed to transform heterogeneous judgments, including linguistic terms, interval numbers, and picture fuzzy numbers, into a unified representation form. A heterogeneous picture fuzzy SWARA-MARCOS evaluation framework was then established and used to solve a military equipment supplier selection problem. The results demonstrated the validity and feasibility of the proposed evaluation framework, while sensitivity, comparative, and complexity analyses demonstrated the robustness and superiority of it. [ABSTRACT FROM AUTHOR]

This work offers a real-world application for the study of fuzzy dynamic equations. First, we propose the novel concept of granular delta differentiability for fuzzy-valued functions defined on time scales with the help of the relative distance measure fuzzy arithmetic and horizontal membership functions. Then, fundamental foundations of fuzzy calculus on time scales are provided. Discussion on the Malthusian model defined on particular time scales to illustrate the proposed approach is presented. [ABSTRACT FROM AUTHOR]

In the consensus reaching process of group decision making (GDM), consensus measures do not require the consensus opinions of all decision makers. Meanwhile, unit adjustment cost is one of the important and often uncertain factors that affect consensus in GDM. Due to the uncertainty of unit adjustment costs, the moderator may not be able to provide each decision maker with an accurate unit adjustment cost. To overcome these problems, a novel class of group consensus decision models is proposed in this paper. First, fuzzy consensus measures are defined to make the consensus flexible using the specificity and coverage of the consensus granule. Secondly, to describe the uncertainty of the cost of unit adjustment, three uncertainty scenarios are created by the robust optimization approach is introduced. In the end, the feasibility and applicability of the method are verified by taking the classical GDM problem as an example, and sensitivity and comparative analyses are also performed. [ABSTRACT FROM AUTHOR]

Uncertainty in medical diagnosis is the main challenge in medical emergencies (MEs) experienced by triage nurses and physicians in the emergency department (ED). The intuitionistic fuzzy correlation coefficient (IFCC) approach is used to analyze and interpret the relationship between variables in an uncertain environment. Assorted methods that involve applying a correlation coefficient under intuitionistic fuzzy sets (IFSs) were constructed based on Pearson's correlation model with various drawbacks. In this work, we construct two new intuitionistic fuzzy correlation measures (IFCMs) based on Spearman's correlation model. It is demonstrated that the Spearman-based IFCMs are appropriate for measuring correlation coefficients without any drawbacks. In addition, we show that the Spearman-based IFCMs overcome all the shortcomings of the associated IFCC methods. Equally, the Spearman-based IFCMs satisfy the maxims of the correlation coefficient that have been delineated in the classical case of correlation coefficient. Due to the challenges that uncertainty in medical diagnosis pose to MEs and the proficiency of the IFCC approach, we discuss the application of the constructed IFCMs in a triage process for an effective medical diagnosis during an ME. The medical data for the triage process are obtained via a knowledge-based approach. Finally, comparative analyses are carried out to ascertain the validity and authenticity of the developed Spearman-based IFCMs relative to other IFCC approaches. [ABSTRACT FROM AUTHOR]

In this paper, we show a Sandor type inequality for pseudo-integrals. Indeed, we prove a classic version of this inequality for pseudo-integrals. Some illustrative examples are given for the theorems. We continue by proving a strengthened version of Sandor's inequality for pseudo-integral. [ABSTRACT FROM AUTHOR]

Type II fuzzy sets consider the uncertainties involved in the membership function of classical fuzzy set theory. The membership function of a Type II fuzzy set is obtained by blurring the boundaries of the original fuzzy set membership function. The interval-based modified Type II fuzzy set method is presented in this paper to measure the fuzziness present in medical images. Using Hamacher T-conorm as the aggregation operator, the membership functions of the upper and lower intervals have been combined to obtain the contrast-enhanced image. For experimental analysis, quantitative and qualitative metrics have been evaluated for different kinds of medical data sets. To test the efficiency of the proposed technique, the computed results are compared with state-of-the-art techniques. The qualitative and quantitative results clearly demonstrate that the performance of the proposed techniques is much better than the existing techniques for almost all the image data sets. The results evaluated for average values with standard deviation for all the datasets bear witness to the performance of the proposed technique. The mean opinion score and the processing time also support the efficacy of the proposed technique, which is much better than most state-of-the-art techniques except at some of the cases. [ABSTRACT FROM AUTHOR]

Telecommunication is one of the essential necessities of everyday life. In India, the telecommunications sector has seen a significant increase in the day-to-day. Telecommunications service companies hold data about their customers, and crisp graphs are used to depict these records. Examining and selecting the best mobile phone service providers (MPSPs) based on operational restrictions will help determine the best MPSPs. The analysis of MPSPs may be regarded as a difficult decisionmaking issue. The aim of this article is to provide an outline to examine the performance of MPSPs and the selection of the best MPSP for customers in India. The statistical data were obtained from the Telecom Regulatory Authority of India between April 2019 and March 2021. A novel approach for cosine similarity measures (CSM) among hesitancy fuzzy graphs (HFG) and estimating the certified repute scores of the experts by determining the ambiguous information of hesitancy fuzzy preference relations (HFPRs) and the regular cosine similarity grades from one separable HFPR to some others. And consider "objective" and "subjective" information given by experts. According to CSMs, we define the Laplacian energy of an HFG. This research provides a solution to a decision-making problem by applying the newly developed cosine similarity measure and the Laplacian energy of hesitancy fuzzy graphs. The ranking order of all alternatives and the best one is determined by calculating the cosine similarity between each alternative and the ideal alternative. Finally, an illustrated example is provided to show the applicability of the proposed approach to the decisionmaking problem as well as its effectiveness. [ABSTRACT FROM AUTHOR]

Similarity measures on trapezoidal-valued intuitionistic fuzzy numbers (TrVIFNs) are functions that measure the closeness between two TrVIFNs, which has a lot of applications in the area of pattern recognition, clustering, decision-making, etc. Researchers around the world are proposing various similarity measures on the generalizations of fuzzy sets. However, many such measures do not satisfy the condition that "the similarity between two fuzzy numbers is equal to 1 implies that both the fuzzy numbers are equal" and this gives a pathway for the researchers to introduce different similarity measures on various classes of fuzzy sets. Also, all of them try to find out the similarity by using a single function, and in the present study, we try to propose a combined similarity measure principle by using four functions (four similarity measures). Thus, the main aim of this work is to introduce a few sets of similarity measures on the class of TrVIFNs and propose a combined similarity measure principle on TrVIFNs based on the proposed similarity measures. To do this, in this paper, firstly, we propose four distance-based similarity measures on TrVIFNs using score functions on TrVIFNs and study their mathematical properties by establishing various propositions, theorems, and illustrations, which is achieved by using numerical examples. Secondly, we propose the idea of a combined similarity measure principle by using the four proposed similarity measures sequentially, which is a first in the literature. Thirdly, we compare our combined similarity measure principle with a few important similarity measures introduced on various classes of fuzzy numbers, which shows the need for and efficacy of the proposed similarity measures over the existing methods. Fourthly, we discuss the trapezoidal-valued intuitionistic fuzzy TOPSIS (TrVIF-TOPSIS) method, which uses the proposed combined similarity measure principle for solving a multi-criteria decision-making (MCDM) problem. Then, we discuss the applicability of the proposed modified TrVIF-TOPSIS method by solving a model problem. Finally, we discuss the sensitivity analysis of the proposed approaches by using various cases. [ABSTRACT FROM AUTHOR]

Statistical process control (SPC) is widely used to monitor production processes in many industries under certain conditions. When dealing with a quality characteristic for uncertainty, fuzzy numbers are used in the context of the statistical process control (SPC) to monitor a fuzzy production process. The aim of this paper is fourfold. One, a fuzzy X ¯ - R control chart with an α-level cut is used based on trapezoidal fuzzy numbers (TFNs) for detecting the large shifts in the fuzzy process mean. Second, a fuzzy cumulative sum (FCUSUM) control with an α-level cut based on TFNs is firstly developed for detecting the small shifts in the fuzzy process mean. Third, the fuzzy process capability indices (FPCIs) are presented to measure the fuzzy process performance. Finally, an ultra-fine calcite production process is controlled with both the fuzzy X ¯ - R control chart and the proposed FCUSUM control chart. The results of the fuzzy X ¯ - R control charts show that the fuzzy production process is in control, and large shifts in the fuzzy process mean were detected. On the other hand, the results of the FCUSUM charts show that the fuzzy production process is out of control, and small shifts in the fuzzy process mean were detected. FPCIs are also conducted, and the results of fuzzy Cpk indices show that the ultra-fine calcite production process is not capable of meeting specification limits. [ABSTRACT FROM AUTHOR]

The increasing production of electric vehicles (EVs) has boosted the demand for recycling spent lithium-ion batteries (LiBs), as recycling preserves many valuable and useful materials such as cobalt, iron, nickel, and so on, and can lead to sustainable environmental development and public health safety by reducing waste volume. Mining and processing these minerals are both financially and environmentally costly, thus reclaiming and reusing them is prudent, as they can be damaging to the environment if not recycled. To ensure environmental sustainability, it is vital to select the best recycling procedure for wasted LiBs. However, uncertainty and vagueness are associated with the selection of recycling alternatives in real-life scenarios, so the current study aims to develop a multi-criteria group decision-making (MCGDM) model under the Fermatean fuzzy environment (FFE) to identify the optimal spent LiB recycling (LiBR) technique using the FF weighted power average operator (FFWPAO). The notion of Methods based on the Removal Effects of criteria (MEREC) has been extended under FFE with the aid of FFWPAO to identify the importance of influential parameters involved in spent LiB recycling (LiBR) process selection. A new Fermatean fuzzy distance measure (DsM) has been developed, and its significance has been demonstrated using theoretical explanation. Furthermore, a weighted DsM (WDsM), and a novel FFWDsM-based ranking approach have been proposed under FFE to evaluate LiBR processes. Furthermore, to address the constraints of the current Fermatean fuzzy score function (FFSF), an improved FFSF (IFFSF) has been presented that may rank any sort of Fermatean fuzzy numbers (FFNs), regardless of membership or non-membership grades.The envisioned integrated method's homogeneity and dependability have been evaluated by comparisons. The proposed approach has indicated "amalgamation of mechanical shredding (MS), electrolyte extraction (EE), electrode dissolution (ED), and cobalt electrochemical reduction (CECR)" as the best option for recycling spent LiBs. • An improved Fermatean fuzzy (FF) score function is introduced to rank FF numbers. • Novel FF distance measure and weighted distance measure (DM) are introduced. • FFWPAO based MEREC and novel FFWDM based ranking methods are developed and integrated. • Spent LiB recycling technology selection problem has been modelled and solved. • The proposed technique is validated through comparative and sensitivity analyses. [ABSTRACT FROM AUTHOR]

We use a new method to determine a fuzzy similarity measure using fuzzy implication operators. We use this method to determine the fuzzy similarity between the two rankings of countries involving health security and health care. We then find a fuzzy similarity of countries involving the two rankings of countries with respect to national disaster and political disaster. [ABSTRACT FROM AUTHOR]

Automated classification of tumors in breast ultrasound (BUS) using deep learning-based methods has achieved remarkable success recently. The initial performance of the individual convolutional neural networks (CNNs) and vision-Transformer have been encouraging. However, artifacts like shadows, low contrast, speckle noise, and variations in tumor shape and sizes impose a kind of uncertainty that limits the performance of existing methods. The interpretation of classification results with a high confidence rate is strongly required in a real clinical setting. This work proposes an efficient method for predicting breast tumor malignancy (EPTM) in BUS images. EPTM comprises heterogeneous deep learning-based feature extraction models and a Choquet integral-based fusion mechanism. Specifically, EPTM incorporates efficient CNN and vision-Transformer methods to build accurate individual breast tumor malignancy prediction models (IMMs). The heterogeneous IMMs ensure complete feature representation of the breast tumors as each CNN or vision-Transformer captures different textural patterns in BUS images. EPTM applies learnable fuzzy measure-based Choquet integral to fuse the predictions of IMMs, where the gray wolf optimizer is employed for generating fuzzy measures. The experimental results confirm the versatility of the EPTM method evaluated on two publicly available datasets, namely UDIAT BUS and Baheya Hospital. EPTM yielded state-of-the-art results with the area under the curve of 0.932 and 0.98, respectively, in the UDIAT BUS and Baheya Hospital datasets. The source code of the proposed model is publicly available at https://github.com/vivek231/breastUS-classification. [ABSTRACT FROM AUTHOR]

To reflect both fuzziness and hesitation in the evaluation of interactivity between attributes in the identification process of 2-order additive fuzzy measure, this work uses the hesitant fuzzy linguistic term set (HFLTS) to describe and depict the interactivity between attributes. Firstly, the interactivity between attributes is defined by the supermodular game theory. According to this definition, a linguistic term set is established to characterize the interactivity between attributes. Under the linguistic term set, the experts employ linguistic expressions generated by context-free grammar to qualitatively describe the interactivity between attributes. Secondly, through the conversion function, the linguistic expressions are transformed into the hesitant fuzzy linguistic term sets (HFLTSs). The individual evaluation results of all experts were further aggregated with the defined hesitant fuzzy linguistic weighted power average operator (HFLWPA). Thirdly, based on the standard Euclidean distance formula of the hesitant fuzzy linguistic elements (HFLEs), the hesitant fuzzy linguistic interaction degree (HFLID) between attributes is defined and calculated by constructing a piecewise function. As a result, a 2-order additive fuzzy measure identification method based on HFLID is proposed. Based on the proposed method, using the Choquet fuzzy integral as nonlinear integration operator, a multi-attribute decision making (MADM) process is then presented. Taking the credit assessment of the big data listed companies in China as an application example, the analysis results of application example prove the feasibility and effectiveness of the proposed method. This work successfully reflects both the fuzziness and hesitation in evaluating the interactivity between attributes in the identification process of 2-order additive fuzzy measure, enriches the theoretical framework of 2-order additive fuzzy measure, and expands the applicability and methodology of 2-order additive fuzzy measure in multi-attribute decision making. [ABSTRACT FROM AUTHOR]

Although there are many researches on the similarity measure for intuitionistic fuzzy sets, some of them have some defects. To overcome these shortcomings, based on the Euclidean distance between intuitionistic fuzzy set and three special intuitionistic fuzzy sets, a new similarity measure for intuitionistic fuzzy sets is proposed in this paper. The proposed similarity measure is compared with the existing similarity measures in intuitionistic fuzzy environment by numerical examples. Moreover, we apply the proposed similarity measure to pattern recognition problems in intuitionistic fuzzy environment. The experimental results show that the proposed similarity measure for intuitionistic fuzzy sets is reasonable and effective. [ABSTRACT FROM AUTHOR]

The similarity measure of intuitionistic fuzzy sets is a primary method for dealing with uncertainty and fuzzy problems and is commonly used in fuzzy decision-making and pattern recognition. The current mainstream similarity measure is based on the classical fuzzy set with only one negation, which often violates the intuitionistic problem in applications because the actual semantics of multiple negations are not considered. To solve the inconsistency and irrationality problems in the classical similarity methods, we introduce three negations (contradiction negation, opposition negation, and mediation negation) in the intuitionistic fuzzy set to obtain the generalized intuitionistic fuzzy set and prove its related property theorem. On this basis, our similarity measure adopts a mediational negation to represent non-membership, which fully utilizes the multiple negation information of non-membership and hesitancy and avoids the loss of fuzzy information. We verify the method's rationality, validity, and originality through pattern recognition experiments and numerical examples, which improves the performance of intuitionistic fuzzy set similarity in practical applications and provides a new approach for future research on intuitionistic fuzzy inference. [ABSTRACT FROM AUTHOR]

Probabilistic linguistic term sets (PLTSs) provide a flexible tool to express linguistic preferences, and several multi-criteria decision models based on PLTSs have been recently developed. In this framework, distortion risk measures are extensively used in finance and insurance applications, but are rarely applied in fuzzy systems. In this paper, distortion risk measures are applied to fuzzy tail decisions. In particular, three tail risk measurement methods are put forward, referred to as probabilistic linguistic VaR (PLVaR), expected probability linguistic VaR (EPLVaR), and Wang tail risk measure and extensively study their properties. Our novel methods help to clarify the connections between distortion risk measure and fuzzy tail decision-making. In particular, the Wang tail risk measure is characterized by consistency and stability of decision results. The criteria and expert weights are unknown or only partially known during the decision making process, and the maximising PLTSs deviations are showed how to determine them. The theoretical results are showcased on an optimal stock fund selection problem, where the three tail risk measures are compared and analyzed. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy sets (PFSs) are a versatile tool for handling uncertain problems and have proven effective in practical applications. However, many existing Pythagorean fuzzy distance measures have counter-intuitive situations, making it challenging to measure the difference between PFSs accurately. To address this issue, we propose two distance measures for PFSs inspired by the Hellinger distance measure. We also explore the properties of the proposed measures and provide several comparative examples with existing measures for PFSs, illustrating their superior performance in processing fuzzy information from PFSs. Finally, we further develop a new decision-making method on top of the proposed measures and evaluate its performance in two applications. [ABSTRACT FROM AUTHOR]

In general, most of the clustering algorithms deal with high-dimensional data. Therefore, the resulting clusters are high-dimensional geometrical objects, which are difficult to analyse, visualize and interpret. Principal component analysis (PCA) is a widely used classical technique for unsupervised dimensional reduction of datasets which extracts smaller uncorrelated data from the original high dimensional data space. The methodology of classical PCA is based on orthogonal projection defined in convex vector space. Thus, a norm between two projected vectors is unavoidably smaller than the norm between any two objects before implementation of PCA. Due to this, in some cases when the PCA cannot capture the data structure, its implementation does not necessarily confirm the real similarity of data in the higher dimensional space making the results unacceptable. Furthermore, when applied with fuzzy clustering algorithms, it demonstrates its weakness in capturing the data structure what affects the PCA mapping quality. In this research we propose a new fuzzy PCA algorithm (FuzPCA) combining FCM and PCA which builds not only fuzzy similarity measures based on the membership functions calculated by FCM but also a measure corresponding to the rate of dissimilarities between the clustering structures of the dataset objects and their dimensions. We formulated the respective new fuzzy covariance matrix which is processed by the PCA during subsequent iterations. FuzPCA demonstrates higher clustering discriminatory ability and visualization accuracy than regular FCM when applied to high-dimensional datasets, in cases when clusters’ sizes or densities are different as well as in discovering small clusters. The function integrated with FuzPCA Silhouette provides preliminary information and visualization allowing faster choice of number of clusters which is additionally refined after implementation of fuzzy clustering validation metrics. The projected 2- and 3-D topologies of FuzPCA are more reliable, significantly improve the visualization results and demonstrate high mapping quality. [ABSTRACT FROM AUTHOR]

Seismic risk estimation for urban building clusters is essential when developing regional seismic resilience models. A masonry structure is a type of building with a large stock, broad applicability, and simplified construction technology. The traditional seismic intensity measures and fuzzy quantification of structural vulnerability levels result in low accuracy in estimating and predicting seismic damage to masonry structure clusters. This paper proposes a method for evaluating bivariate seismic intensity measure. Nonlinear dynamic and spectral analyses were conducted on real acceleration records monitored by ten stations during the Wenchuan earthquake in Sichuan, China, on May 12, 2008. The outdated seismic vulnerability level of masonry structures is updated, and an optimized structural seismic risk model based on the seismic damage database of 2407 masonry structures in Dujiangyan city under the influence of the Wenchuan earthquake is established. An innovative seismic risk membership index algorithm was developed, and a vulnerability curve was generated for masonry structures considering multiple risk membership indices. An improved seismic risk index calculation function is proposed using the proposed updated vulnerability level, and the seismic risk index curve and stripe model of typical urban masonry building clusters are established. According to the field investigation of the actual structures in Dujiangyan city affected by the Wenchuan earthquake, the typical failure features and disaster mechanism of masonry structures are reported and analysed, and measures and methods to improve and enhance the seismic capacity of such buildings are proposed. The developed seismic risk model for urban masonry structures can contribute positively to the development of relatively accurate seismic resilience models for urban buildings and can improve the accuracy of seismic risk estimation for masonry structures. [ABSTRACT FROM AUTHOR]

Incipient degradation dynamic detection is crucial for preventing serious accidents in the context of rolling bearing online automatic condition monitoring and preventive maintenance. This article presents a novel framework, cyclostationarity-sensitive spectrum fuzzy entropy-assisted Bayesian online anomaly inference (CSFE-BOAI), to address this challenge. A new health index, CSFE, is first defined by performing the fuzzy entropy measure on the extracted cyclostationarity-sensitive spectra to promote incipient-degradation sensitivity and robustness to interferences. Next, the BOAI procedure for detecting anomalies in continuously arriving CSFEs is derived using the robust generalized T-distribution as the underlying predictive distribution. Eventually, the CSFE-BOAI framework is constructed for bearing incipient degradation dynamic detection, which possesses double confirmation of valid anomalies through the Pauta criterion and cyclostationarity-sensitive spectrum. Experimental verifications are performed on two typical bearing degradation data and one healthy-to-incipient defect data. Results show that CSFE-BOAI enables effective and timely incipient degradation alarm and identification of rolling bearings. The comparisons with the eight advanced health indexes and four anomaly detection approaches demonstrate that CSFE-BOAI has the lowest false and missed alarms and therefore has good deployment potential for practical applications. • CSFE is defined to improve incipient-degradation sensitivity and robustness to interferences. • BOAI with the generalized T-distribution is derived for detecting anomalies in continuously arriving CSFEs. • CSFE-BOAI framework with double confirmation of valid anomalies enhances dynamic detection of bearing incipient degradation. • Verification and comparison results demonstrate the superiority of CSFE-BOAI in the lowest false and missed alarms. [ABSTRACT FROM AUTHOR]

The concept of q-rung orthopair fuzzy set (q-ROF) defined as generalization of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PyFS) has more flexible structure according to several clusters. Therefore, it is a benefit tool to obtain various results for different values of q. The basic benefit of generalized concepts is to rate level of truth and falsity and reduce to error margin. Thus, while the final decision is decided by experts, the most accuracy finding is to present. Aczel-Alsina t-norm (AA-TN) and t-conorm (AA-TCN) structures were defined by Aczel and Alsina in 1982. The both concepts include parameters changing according to prefer, decision, and request of experts. In this paper, q-rung orthopair fuzzy Aczel-Alsina weighted geometric operator (q-ROFAAWG) is produced and also ordered and hybrid concepts (q-ROFAAOWG, q-ROFAAHWG) are obtained using Aczel-Alsina operators (AAOs). Hence, this operator is expanded to generalized q-rung orthopair fuzzy Aczel-Alsina weighted geometric operator (Gq-ROFAAWG), ordered and hybrid concepts (Gq-ROFAAOWG, Gq-ROFAAHWG) using single parameter. Finally, group-based generalized q-rung orthopair fuzzy Aczel-Alsina weighted geometric operator (GGq-ROFAAWG), ordered and hybrid concepts (GGq-ROFAAOWG, GGq-ROFAAHWG) are proposed and their properties are worked. Moreover, an algorithm-based multi-criteria decision-making is given and applied over a numerical example to illustrate the effective of the proposed method. The results are evaluated for different values of parameters. In addition to, comparative analysis is developed to show the superiority of proposed approach than existing methods. [ABSTRACT FROM AUTHOR]

Automatic term extraction from a biomedical text is a well-known problem in the area of natural language processing. It is carried out by employing four kinds of measures: linguistic and rule-based, dictionary-based, statistical, and machine learning. Automatic term extraction indicates whether or not two or more words come together in the text more often than by chance to form a biomedical term that is automatically extracted using an automated system. A fuzzy set-theoretic approach is presented in this article and compares with the existing statistical measures. The experimental result shows that the fuzzy measure offers better precision than the popular statistical measures for extracting biomedical terms, especially when we have compared more than 60% ranked list of extracted terms. [ABSTRACT FROM AUTHOR]

Summary: The internet of things (IoT) refers to the interconnection of various devices through the internet. With the help of IoT, different applications and devices can interact with each other and even with humans through the internet. However, the widespread use of IoT in homes, offices, and private companies has raised concerns about privacy and security. The theft of user information by hackers is a major challenge that has hindered the adoption of IoT. This paper proposes a method for improving security on two levels: intra‐cluster and inter‐cluster. In the intra‐cluster phase, the cluster head uses fuzzy logic to measure the trust level of nodes. If the node is trusted, the information is received and sent to the destination. In the inter‐cluster phase, data between cluster heads is encrypted using column transposition encryption. The encryption is hop by hop, and the encryption key is changed at each hop. The proposed method is simulated using NS‐2 software. A comparison of the proposed method's performance with conventional methods shows that the proposed method results in better packet delivery rate, throughput, and prevention of link spoofing attacks. [ABSTRACT FROM AUTHOR]