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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]

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]

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]

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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 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]

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]

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]

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]

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]

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]

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 similarity measure (SM) of fuzzy numbers is vital in decision-making, ranking, and risk analysis, particularly when dealing with qualitative information and fuzzy mathematical models. Traditional set theory struggles with such applications due to the significant presence of uncertainties. Although a wide array of methods are available for SMs applied to fuzzy numbers (FNs), some shortcomings persist. Few recent approaches involving magnitude, distance, and coordinates to measure similarity have demonstrated certain drawbacks when applied to arbitrary trapezoidal fuzzy numbers (TZFNs). These existing measures frequently fail to capture human intuitions, encounter division by zero issues, and account for the unique properties of TZFNs. The proposed work introduces a method to determine the center of gravity (CoG) of TZFNs, which is then utilized along with information on areas, perimeter, weights, and geometric distances of TZFNs to formulate a comprehensive SM. This new approach overcomes the limitations observed in the existing SMs for TZFNs. The mathematical properties of the proposed method are discussed, and the performance of the model is evaluated and compared with recent works. It demonstrates its superior handling of a standard set of 32 TZFNs and for various other special cases, shown numerically in the results section. Additionally, three case studies that involve risk assessment analysis applying the proposed SM are done. A specific scenario concerning service level agreement (SLA) violation in Fog-integrated Cloud is thoroughly explored. [ABSTRACT FROM AUTHOR]

Fuzzy set theory has extensively employed various divergence measure methods to quantify distinctions between two elements. The primary objective of this study is to introduce a generalized divergence measure integrated into the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approach. Given the inherent uncertainty and ambiguity in multi-criteria decision-making (MCDM) scenarios, the concept of the fuzzy α -cut is leveraged. This allows experts to establish a broader spectrum of rankings, accommodating fluctuations in their confidence levels. To produce consistent criteria weights with the existence of outliers, the fuzzy Method based on the Removal Effects of Criteria (MEREC) is employed. To showcase the viability and effectiveness of the proposed approach, a quantitative illustration is provided through a staff performance review. In this context, the findings are compared with other MCDM methodologies, considering correlation coefficients and CPU time. The results demonstrate that the proposed technique aligns with current distance measure approaches, with all correlation coefficient values exceeding 0.9. Notably, the proposed method also boasts the shortest CPU time when compared to alternative divergence measure methodologies. As a result, it becomes evident that the proposed technique yields more sensible and practical results compared to its counterparts in this category. [ABSTRACT FROM AUTHOR]

This article produces a blend between the fields of time discounting and fuzzy integrals. By exploiting the mathematical properties of the Sugeno capacities, we can produce a Choquet integral that simultaneously is subadditive and coincides with either the exponential or hyperbolic discounting additive formulas in the evaluation of individual time moments. Numerical analyses guarantee that the new valuation procedures are different from their additive counterparts. [ABSTRACT FROM AUTHOR]

This paper mainly studies and proves the roughness bound of disturbation fuzzy sets. Firstly, based on the theory of determining self-increment and uncertain self-decrement operators, the problem that the execution subsets are not equal sets is effectively solved, which hinders the quantitative study of disturbed fuzzy sets and lays a foundation for the quantitative study of the related properties of disturbed fuzzy sets in the future. The boundary of roughness measure of disturbing fuzzy set is further studied and proved. The new territories proposed in this paper can effectively avoid the unnecessary calculation space outside the boundary in the calculation process, so as to improve the work efficiency. [ABSTRACT FROM AUTHOR]

This paper's aim is to extend and generalize the classic results regarding spectral radii and the corresponding resolvent sets for some different classes of bounded operators acting on fuzzy normed spaces. In this context, the fuzzy norm definition introduced giving shape to a new topology for a fuzzy space, namely a fuzzy topology, also gives the opportunity to study the behavior of various types of operators defined between fuzzy normed spaces, along with their spectral properties. There are several definitions for resolvent sets and consequently, several corresponding definitions of spectral radii that will be considered in this work, since these are non-equivalent ways of defining such notions. Spectral radii are calculated for a fuzzy Volterra type operator acting between fuzzy normed spaces. [ABSTRACT FROM AUTHOR]

Copyright of Serbian Journal of Management is the property of Serbian Journal of Management and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The key objective of this article is to introduce the innovative idea of a complex intuitionistic hesitant fuzzy set (CIHFS), which blends the intuitionistic hesitant fuzzy set with the complex fuzzy set to address the uncertain information in real-life complex problems. In CIHFS, the range of the membership functions is extended from the subset of the real number to the unit disc under the hesitant environment. To determine how well the CIHFSs can be distinguished from one another, we first propose generalized distance measures and weighted generalized distance measures based on the Hamming, Euclidean, and Hausdorff metrics. Some interesting properties and their relationships are thoroughly discussed. Furthermore, a decision-making framework for selecting the optimal option from the feasible set has been proposed, which is grounded in these distance metrics. For the purpose of proving the method's efficacy, we included examples from pattern recognition and medical diagnostics. [ABSTRACT FROM AUTHOR]

Due to the barriers of finance, talent, and technology, small and medium-sized enterprises (SMEs) have faced uncertainty and risks if they fail to engage in digital transformation (DT). A good choice is for SMEs to choose solutions already on the market, provided by professional DT solutions suppliers. However, how to choose the most suitable DT solution remains a major challenge for SMEs. Thus, to help SMEs to select an appropriate DT solution, we proposed a novel, prospect theory-based evidential reasoning (ER) assessment method under a hesitant picture fuzzy linguistic sets (HPFLSs) environment. First, the novel distance measures of picture fuzzy sets (PFSs) and HPFLSs are proposed, then, based on the proposed distance measures of HPFLSs, novel, prospect theory formula are constructed. Additionally, a novel HPFLS ER method was developed to aggregate the evaluation information. Afterward, an assessment and selection decision approach for DT solutions for SMEs, based on the prospect theory-based ER of HPFLSs, was conducted. Finally, actual examples of DT solutions for SMEs to illustrate the decision-making approach were used to verify the effectiveness of the proposed method, and the conclusions were summarized. [ABSTRACT FROM AUTHOR]

In the present manuscript, it is our utmost aim and objective to comprehensively and extensively expound upon two highly innovative and remarkably novel information measures that have been adeptly and appropriately extended to encompass fuzzy sets. These measures have undergone a rigorous and meticulous scrutiny and examination with regard to axiomatic principles, and have evinced numerous and manifold advantageous properties, thus providing a compelling and highly persuasive validation of their reliability, credibility, and overall effectiveness. It is of paramount importance to note that the measures in question have been meticulously and painstakingly designed with the express aim and purpose of effectively quantifying the extent of information that is inextricably embedded and enmeshed within fuzzy sets, and are firmly grounded in the foundational and bedrock principles of information theory, which is an indisputably and irrefutably significant and substantial academic discipline. Our contributions to the field of study are truly and incontestably unparalleled, and offer a fresh, innovative, and unprecedented perspective on the study of fuzzy sets and their associated information content, which is of immense and inestimable value to the overall advancement and progress of the academic discipline. [ABSTRACT FROM AUTHOR]

A particularly useful assessment tool for evaluating uncertainty and dealing with fuzziness is the Fermatean fuzzy set (FFS), which expands the membership and non-membership degree requirements. Distance measurement has been extensively employed in several fields as an essential approach that may successfully disclose the differences between fuzzy sets. In this article, we discuss various novel distance measures in Fermatean hesitant fuzzy environments as research on distance measures for FFS is in its early stages. These new distance measures include weighted distance measures and ordered weighted distance measures. This justification serves as the foundation for the construction of the generalized Fermatean hesitation fuzzy hybrid weighted distance (DGFHFHWD) scale, as well as the discussion of its weight determination mechanism, associated attributes and special forms. Subsequently, we present a new decision-making approach based on DGFHFHWD and TOPSIS, where the weights are processed by exponential entropy and normal distribution weighting, for the multi-attribute decision-making (MADM) issue with unknown attribute weights. Finally, a numerical example of choosing a logistics transfer station and a comparative study with other approaches based on current operators and FFS distance measurements are used to demonstrate the viability and logic of the suggested method. The findings illustrate the ability of the suggested MADM technique to completely present the decision data, enhance the accuracy of decision outcomes and prevent information loss. [ABSTRACT FROM AUTHOR]

The authors develop the theory of discrete differentiation and, on its basis, solve the problem of detecting trends in records, using the idea of the connection between trends and derivatives in classical analysis but implementing it using fuzzy logic methods. The solution to this problem is carried out by constructing fuzzy measures of the trend and extremum for a recording. The theoretical justification of the regression approach to classical differentiation in the continuous case given in this work provides an answer to the question of what discrete differentiation is, which is used in constructing fuzzy measures of the trend and extremum. The detection of trends using trend and extremum measures is more stable and of higher quality than using traditional data analysis methods, which consist in studying the intervals of constant sign of the derivative for a piecewise smooth approximation of the original record. The approach proposed by the authors, due to its implementation within the framework of fuzzy logic, is largely focused on the researcher analyzing the record and at the same time uses the idea of multiscale. The latter circumstance provides a more complete and in-depth understanding of the process behind the recording. [ABSTRACT FROM AUTHOR]

In this paper, we prove some inequalities for Riemann–Lebesgue integrable functions when the considered integration is obtained via a non-additive measure, including the reverse Hölder inequality and the reverse Minkowski inequality. Then, we generalize these inequalities to the framework of a multivalued case, in particular for Riemann–Lebesgue integrable interval-valued multifunctions, and obtain some inequalities, such as a Minkowski-type inequality, a Beckenbach-type inequality and some generalizations of Hölder inequalities. [ABSTRACT FROM AUTHOR]

To make a decision to select a suitable approximation for the solution of a functional inequality, we need reliable information. Two useful information ideas are quality and certainty, and the measure of quality and certainty approximation of the solution of a functional inequality helps us to find the optimum approximation. To measure quality and certainty, we used the idea of the Z-number (Z-N) and we introduced the generalized Z-N (GZ-N) as a diagonal matrix of the form diag(X,Y,X*Y), where X is a fuzzy set time-stamped, Y is the probability distribution function and the third part is the fuzzy-random trace of the first and the second subjects. This kind of diagonal matrix allowed us to define a new model of control functions to stabilize our problem. Using stability analysis, we obtained the most suitable approximation for functional inequalities. [ABSTRACT FROM AUTHOR]

G. Klir proposed to describe the behavior of complex systems using behavior functions (BFs) - invariant constraints on the set of system states. BFs are one of the most productive tools for studying the functioning of systems. To study systems, it is necessary to have a metric for measuring of the difference between two BFs. To describe BFs modern researchers do not use distributions other than probability or possibility. But these distributions can be considered as special cases of Sugeno fuzzy measures, the use of which greatly expands the possibilities in the study of systems. However, metrics to measure the difference between fuzzy measures have not been developed. Therefore, in this article, the authors proposed a new metric and an algorithm for its calculation for the case when BFs are described by Sugeno fuzzy measures. This metric is based on the Cartesian product of fuzzy measures and the use of our proposed concentration function. The metric makes it possible to compare the behavior of systems in the case of describing BFs by Sugeno fuzzy measures with different modalities, as well as to ensure the priority of taking into account the set of the most significant states of the system. [ABSTRACT FROM AUTHOR]

Diagnosing and finding the disease in medical sciences is a complex procedure. The basic steps involved in finding starts with signs, symptoms, and test. This study is based on the diagnosis of a skin disorder. The identification of a disease has been made on the basis of symptoms that sometimes show bipolarity. To address this bipolarity, the bipolar fuzzy sets are used as bipolar fuzzy sets cover the positive as well as negative aspects of a specific symptom. It is combined with the idea of soft sets, which gives more precise results. We have proposed a new technique in which a correlation coefficient is used to measure bipolar fuzzy soft set, which has been applied for diagnosis. The BFSSs deal most effectively with dual and fuzzy information. The correlation coefficient and the weighted correlation coefficient of BFSSs are suggested in this research. Based on said techniques, the decision-making method is suggested under a bipolar fuzzy environment to resolve ambiguous and unclear information. The implementation and effectiveness of the proposed and existing strategy has been checked by numerical computation. [ABSTRACT FROM AUTHOR]

is research paper introduces a comprehensive study on /xed points in orthogonal fuzzy metric spaces.,e primary objective is to establish the existence and uniqueness of /xed points for self-mappings satisfying implicit relation criteria in complete orthogonal fuzzy metric spaces. By doing so, our proven results extend and generalise well-known /ndings in the /eld of /xedpoint theory. To demonstrate the signi/cance of the established results, several related examples are provided, serving to support and validate the theoretical /ndings in orthogonal fuzzy metric spaces.,e implications of these results are discussed, shedding light on their potential applications in various practical scenarios. In addition to theoretical advancements, the paper also demonstrates a practical application of our established results in solving integral equations.,is application exempli/es the e7ectiveness and versatility of the proposed approach in real-world problem-solving scenarios. [ABSTRACT FROM AUTHOR]

Measure theory is used in physics, not just to capture classical probability, but also to quantify the number of states. In previous works, we found that state quantification plays a foundational role in classical mechanics, and, therefore, we set ourselves to construct the quantum equivalent of the Liouville measure. Unlike the classical counterpart, this quantized measure is non-additive and has a unitary lower bound (i.e., no set of states can have less than one state). Conversely, requiring that state quantification is finite for finite continuous regions and that each state counts as one already implies non-additivity, which in turn implies the failure of classical theory. In this article we show these preliminary results and outline a new line of inquiry that may provide a different insight into the foundations of quantum theory. Additionally, this new approach may prove to be useful to those interested in a quantized theory of space-time, as we believe this requires a quantized measure for the quantification of the independent degrees of freedom. [ABSTRACT FROM AUTHOR]

In 1991, Gerstenkorn and Manko introduced a correlation coefficient similarity measure for intuitionistic fuzzy sets, aiming to investigate statistical relationships between objectives. However, their proof of the upper bound for the correlation coefficient similarity measure is overly complex and can be simplified. In 1995, Bustince and Burillo developed a similar correlation coefficient similarity measure for interval-valued intuitionistic fuzzy sets, but their proof of the upper bound closely resembles that of Gerstenkorn and Manko. Both proofs utilized the Schwarz inequality, yet failed to fully harness its power as a tool. In this paper, we begin by simplifying the intricate computations presented in the works of Gerstenkorn and Manko (1991) and Bustince and Burillo (1995). Subsequently, we demonstrate that their proofs can be directly derived by applying the Schwarz inequality. For a related transit bus model, we derive a new approximated solution that is very closed to the approximated solution of Wang et al. (2023) with the relative error less than 5%. We also consider an inventory model to show a possible new direction to locate the formulated closed-form optimal solution. [ABSTRACT FROM AUTHOR]

We consider capacity (fuzzy measure, non-additive probability) on a compactum as a monotone cooperative normed game. Then it is natural to consider probability measures as elements of core of such game. We prove a topological version of the Bondareva--Shapley theorem that non-emptiness of the core is equivalent to balancedness of the capacity. We investigate categorical properties of balanced capacities and give characterizations of some fuzzy integrals of balanced capacities. [ABSTRACT FROM AUTHOR]

A new measure for intuitionistic fuzzy numbers (IFNs) is proposed to reflect the magnitude of IFNs, and a novel ranking approach for IFNs is presented based on this measure. Furthermore, the theoretical basis of the ranking method is investigated, and several intuitionistic fuzzy monotonic dependent ordered weighted averaging (IFMDOWA) operators are developed, such as the conservative IFMDOWA (COV-IFMDOWA) operator, positive intuitionistic fuzzy monotonic DOWA (POS-IFMDOWA) operator, conservative intuitionistic fuzzy hybrid monotonic dependent order weighted averaging (COV-IFHMDOWA) operator, and positive intuitionistic fuzzy hybrid monotonic dependent order weighted averaging (POS-IFHMDOWA) operator. Finally, a numerical example is given to illustrate the flexibility of our proposed monotonic dependent order weighted averaging operators in a practical decision making process. [ABSTRACT FROM AUTHOR]

Picture fuzzy sets (PFSs) are a versatile generalization of fuzzy sets and intuitionistic fuzzy sets (IFSs), providing a robust framework for modeling imprecise, uncertain, and inconsistent information across various fields. As an advanced extension of PFSs, interval-valued picture fuzzy sets (IvPFSs) offer superior capabilities for handling incomplete and indeterminate information in various practical applications. Distance measures have always been an important topic in fuzzy sets and their variants. Some existing distance measures for PFSs have shown limitations and may yield counterintuitive results under certain conditions. Furthermore, there are currently few studies on distance measures for IvPFSs. To solve these problems, in this paper we devised a series of novel distance measures between PFSs and IvPFSs inspired by the Hellinger distance. Specifically, all the distance measures were divided into two parts: One considered the positive membership degree, neutral membership degree and negative membership degree, and the other added the refusal membership degree. Moreover, the proposed distance measures met some important properties, including boundedness, non-degeneracy, symmetry, and consistency, but also showed superiority compared to the existing measures, as confirmed through numerical comparisons. Finally, the proposed distance measures were validated in pattern recognition and medical diagnosis applications, indicating that the proposed distance measures can deliver credible, reasonable results, particularly in similar cases. [ABSTRACT FROM AUTHOR]

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 MP (⟨ μ , ν ⟩ , ⟨ 0 , 0 ⟩) is always equal to the maximum value 1 for any intuitionistic fuzzy number ⟨ μ , ν ⟩ ≠ ⟨ 0 , 0 ⟩ . 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. [ABSTRACT FROM AUTHOR]

Covering granular reduction is an important issue in multi-covering information systems. The main methods to solve this problem are set operators. How to solve this problem by quantitative analysis is an interesting topic. Furthermore, as a type of nonlinear fuzzy aggregation function (which is a quantitative tool), Choquet-like integrals with fuzzy measures are widely used in many files. However, the corresponding fuzzy measures in Choquet-like integrals are given by man, not by data. In this work, we present two types of multi-neighborhood approximation numbers in multi-covering information systems, which are used to establish Choquet-like integrals. Furthermore, they are applied to deal with the problem of granular reduction in multi-covering information systems. First, the notions of lower and upper multi-neighborhood approximation numbers are presented in a multi-covering information system, as well as their properties. Furthermore, some conditions under which multi-covering information systems induce the same lower and upper multi-neighborhood approximation numbers are presented. Second, two covering granular reduction methods based on multi-neighborhood approximation numbers are presented in multi-covering information systems. Third, multi-neighborhood approximation numbers are used to establish Choquet-like integrals, which are applied in covering granular reduction. Finally, these methods are compared with existing methods through experiments, which are used to demonstrate the effectiveness and benefits of our methods. [ABSTRACT FROM AUTHOR]

As we all know, when describing knowledge measures in the context of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets, it is always considered as dual measures of entropy. However, information content and information clarity is closely related with the amount of knowledge. Motivated by this fact, in this study, we focus on a new axiomatic definition of knowledge measures for intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets. First, we present the formulas of the knowledge measures using different abstract functions, and we proved these functions satisfy the axioms. On the basis of mathematical analysis and numerical examples, we further analyze the characteristics of the suggested knowledge measure. Finally, in order to demonstrate how rational and useful the system we developed is, we provide medical diagnoses and specific multi-attribute decision problems. [ABSTRACT FROM AUTHOR]

Under uncertainty, the analytical behaviour of fractional partial differential equations is frequently puzzling and challenging to predict. Therefore, in order to address these problems, it is essential to create a proper, extensive, and highly effective theory. The theory of fuzzy fractional partial differential equations is a relatively new idea with applications in applied mathematics and engineering. In this article, we examined the different types of fuzzy fractional-order Korteweg-de-Vries (KdV) equations along with their analytical fuzzy solutions. To construct a series-type solution under a fuzzy notion for the relevant research, we utilise the fractional reduced differential transform method (FRDTM) in the Caputo sense. The solutions of various kinds of fuzzy fractional KdV equations that have been developed are more broadly applicable. The fuzzy concept is used to overrule the uncertainty in physical models based on the parametric form of the fuzzy number. The numerical and graphical presentation demonstrates the symmetry between the lower and upper cut representations of the fuzzy solutions and may be helpful in improving understanding of automatic control models, measure theory, physics, biology, computer science, quantum optics, economics, artificial intelligence, and other domains, as well as non-financial analysis. [ABSTRACT FROM AUTHOR]

In image processing, data extraction from any image with deviation is difficult to pursue. Especially in identification of radiological images, many issues have been involved in the choosing of right image from the available images. In this paper, new similarity measure model for images is proposed that have application in the identification of the images of plant diseases. The application of the similarity measures is compared with existing models. The results reports that the proposed Pythagorean entropy measures have application in the detection of plant diseases. Even, the quality ofextraction of data from images is enhanced. Further, the study concludes that the proposed measures are better than the existing measures in case of image processing problems. [ABSTRACT FROM AUTHOR]

Background: The purpose of this article is to present a model of process maturity assessment dedicated to service enterprises. The model developed is validated in a company in the development services sector. Methods: The implemented research methodology includes literature analysis, expert research, fuzzy set theory, and a case study. Results: The results indicate that the developed model provides a solid and practical diagnostic tool, based on a fuzzy index to measure the process maturity of a service company. Conclusions: The proposed model may have practical implications for the assessment of process maturity in the service sector. It will allow a diagnosis of the current state and will indicate the direction of further improvement in process management. From an epistemological perspective, the proposed model fills the research gap in the field of maturity models dedicated to service enterprises and extends knowledge on adapting fuzzy set theory to assessing process-orientated maturity of enterprises. The originality of the proposed approach results mainly from the research object that was used to validate the model. [ABSTRACT FROM AUTHOR]

Pandemics are well-known as epidemics that spread globally and cause many illnesses and mortality. Because of globalization, the accelerated occurrence and circulation of new microbes, the infection has emerged and the incidence and movement of new microbes have sped up. Using technological devices to minimize the visit durations, specifying days for handling chronic diseases, subsidy for the staff are the alternatives that can help prevent healthcare systems from collapsing during pandemics. The study aims to define the efficient usage of optimization tools during pandemics to prevent healthcare systems from collapsing. In this study, a new integrated framework with fuzzy information is developed, which attempts to prioritize these alternatives for policymakers. First, rating data are assigned respective fuzzy values using the standard singleton grades. Later, criteria weights are determined by extending Cronbach´s measure to fuzzy context. The measure not only understands data consistency comprehensively, but also takes into consideration the attitudinal characteristics of experts. By this approach, a rational weight vector is obtained for decision-making. Further, an improved Weighted Aggregated Sum Product Assessment (WASPAS) algorithm is put forward for ranking alternatives, which is flexibly considering criteria along with personalized ordering and holistic ordering alternatives. The usefulness of the developed framework is tested with the help of a real case study. Rank values of alternatives when unbiased weights are used is given by 0.741, 0.582, 0.640 with ordering as R 1 ≻ R 3 ≻ R 2 . The sensitivity/comparative analysis reveals the impact of the proposed model as useful in selecting the best alternative for the healthcare systems during pandemics. [ABSTRACT FROM AUTHOR]

In fuzzy set theory, the concept of a non-membership function and the hesitation margin were not considered while these two concepts have been included along with the membership function for intuitionistic fuzzy sets. It is also to be noted that the intuitionistic fuzzy set is re ected as an extension of the fuzzy set accommodating both membership and non-membership functions together with a hesitation margin. In the intuitionistic fuzzy set theory, the sum of the membership function and the non-membership function is a value between 0 and 1. In recent times, intuitionistic fuzzy rough set theory has emerged as a powerful tool for dealing with imprecision and uncertain information in relational database theory. Measures of similarity between fuzzy rough sets as well as intuitionistic fuzzy rough sets provide wide applications in real-life problems and that is why many researchers paid more attention to this concept. Intuitionistic fuzzy rough set theory behaves like an excellent tool to tackle impreciseness or uncertainties. In this paper, we propose a new approach of similarity measure on an intuitionistic fuzzy rough set based on a set-theoretic approach. The proposed measure is able to give an exact result. In the application part, we consider a real-life problem for selecting a fair play award-winning team in a cricket tournament and describe the algorithm. [ABSTRACT FROM AUTHOR]