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Type-2 fuzzy information systems (TFISs-2), one interesting form of complex data, are extensions of fuzzy information systems. Uncertainty measurement and attribute reduction of TFISs-2 are key issues when describing and analyzing complex fuzzy data. However, existing researches mainly focus on the traditional fuzzy data, and seldom consider type-2 fuzzy data. This paper focuses on finding an effective indicator to measure the uncertainty of TFISs-2, and carries out the research of attribute reduction based on this indicator. Firstly, the weighted membership distance and the weighted membership similarity are defined, which are used to describe the relation between two objects in TIFSs-2, and σ similarity relations are introduced. Secondly, a fuzzy neighborhood structure is defined based on σ similarity relations. The classical rough set model is extended on TFISs-2, and the definitions of upper and lower approximation, accuracy and roughness are given. Then, a novel indicator called σ self-information is used to describe the uncertainty of TFISs-2, and a heuristic greedy selection attribute reduction algorithm is proposed. Finally, the experimental results show that the constructed uncertainty measurement indicator is suitable for TFISs-2, and the proposed attribute reduction method is effective. This study is beneficial to promote the understanding of complex fuzzy data, and contributes to the data analysis and processing of TFISs-2. [ABSTRACT FROM AUTHOR]

Spherical fuzzy sets are more powerful in modelling the uncertain situations than picture fuzzy sets, fermatean fuzzy sets, Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. In this paper, we first define the variance and covariance of spherical fuzzy sets. Then, using variance and covariance, we define the unique spherical fuzzy set correlation metric in line with the statistical coefficient of correlation. Two spherical fuzzy sets are correlated in both direction and strength using the provided measure of correlation. We discussed its many characteristics. We compared the measure of correlation with the current ones through linguistic variables. We established its validity by showing its application in bidirectional approximate reasoning. We also resolve a pattern identification issue in the spherical fuzzy environment using the provided correlation function, and we compare the results with several current measurements. [ABSTRACT FROM AUTHOR]

The probabilistic rough set (PRS) model, through the incorporation of error levels, represents a quantitative extension of the classical rough set model. It serves as a fundamental expansion that enables robust fault tolerance capabilities by employing relative quantitative description. However, when confronted with interval-valued fuzzy data, the PRS model is rendered ineffective. The primary reason for this lies in the absence of a unique equivalence relation in interval-valued decision systems. This paper presents a novel approach to address this limitation. In this paper, we first propose a fuzzy similarity relation based on diversity function, which establishes a viable foundation for constricting models of probabilistic rough fuzzy set and multi-granularity probabilistic rough set models for interval-valued fuzzy decision systems. Then the decision rules are derived from the presented three kinds of multi-granularity probabilistic rough fuzzy sets, respectively. In order to elucidate the concepts of interval-valued probabilistic rough fuzzy sets and multi-granularity probabilistic rough fuzzy sets, a case study is considered, which is helpful for applying these theories to deal with practical issues. [ABSTRACT FROM AUTHOR]

The adequacy of mathematical models of economic systems is reduced by the complexity of their structures, the number of parameters and influencing factors. The mathematical regression model assumes that the structure and functional dependence of the input and output variables of the modeled system is precisely defined. However, real systems are complex and indeterminate, and their adequate models must formalize their vague phenomenon. Artificial intelligence methods use fuzzy set mathematics and fuzzy logic approaches to synthesize models of indeterminate systems. We provided our research of defined fuzzy linear regression models using data series of economic variables, namely the evolution of the discount rate, inflation rate and the rate of unemployment between 2019 and 2021. These data series were chosen with regard to the selected economic cycle before, during and after the Covid-19 pandemy. It is precisely due to the cyclical development of the economy that some level of uncertainty and vagueness of data of monitored variables is manifested. Results of the work reflect outputs of the proposed fuzzy regression model of indeterminate variables during the selected time series. These confirmed the assumptions of the authors that there is a mutual interdependence between the selected economic variables, in particular the amount of the discount rate in relation to the inflation rate, the amount of the inflation rate in relation to the rate of unemployment and thus the amount of discount rate in relation to the rate. The existence of time lags in deciding on economic policy measures and their subsequent implementation was also confirmed in all cases, even during the analyzed time series of three years. Only variable unemployment behaved less standardly, as its essence in many respects lies outside of purely pure market mechanism and is under the influence of market inelasticity, legal measures, free movement of labor in the EU, etc. [ABSTRACT FROM AUTHOR]

A new area of research called intuitionistic fuzzy soft expert set is expected to overcome the drawbacks of an intuitionistic fuzzy soft set in terms of eligibility for soft expert-argument approximate function. This type of function views the power set of the universe as its co-domain and the cartesian product of attributes, experts, and their opinions as its domain. The domain of this function is larger as compared to the domain of a soft approximation function. It can manage a situation in which several expert opinions are taken into account by a single model. For the soft expert-argument approximate function with intuitionistic fuzzy setting, concepts such as set inclusion, (α , v) -convexity(concave) sets, strongly (α , v) -convexity (concave) sets, strictly (α , v) -convexity (concave) sets, convex hull, and convex cone are conceived in this paper. Some set-theoretic inequalities are established with generalized properties and results on the basis of these specified notions. Additionally, by using a theoretic cum analytical approach, various elements of computational geometry, such as convex hull and convex cone, are theorized and some pertinent results are generalized. [ABSTRACT FROM AUTHOR]

Twin support vector machine (TSVM) is a contemporary machine learning technique to tackle classification and regression problems. However, TSVM lacks the ability to differentiate between support vectors and noises since it neglects the positional information of input data samples, and hence it is sensitive to noises. Additionally, it fails to consider uncertainties associated with the data, which reduces its capacity for generalization. To address these drawbacks, we propose a novel fuzzy hyperplane based intuitionistic fuzzy twin proximal support vector machine. The first significant feature of the proposed approach is that it gives an intuitionistic fuzzy number based on the relevance to each data vector. This efficiently reduces the impact of noise and outliers by leveraging the local neighborhood information within the data points by incorporating membership and non-membership weights. Secondly, all the parameters present in the model are fuzzy variables, including the offset term and the elements of the normal vector. The suggested fuzzy hyperplane successfully reflects the inherent ambiguity prevalent in real-world categorization problems by reflecting vagueness in the input data through the use of fuzzy variables. The model's efficiency is enhanced by solving two systems of linear equations to obtain two non-parallel classifiers rather than solving two quadratic programming problems as in standard TSVM. Utilizing non-linear kernel functions within the feature space enables the method to effectively identify complex patterns or non-linear relationships within the datasets. In order to demonstrate the effectiveness of the suggested approach, extensive computer experiments have been conducted on a set of eighteen benchmark datasets with both linear and non-linear kernels. In addition, rigorous statistical analysis, including Friedman and post-hoc Nemenyi tests, have been employed to assess the significance of the observed performance differences. Furthermore, we also performed numerical experiments utilizing linear, Gaussian, and polynomial kernels to classify electroencephalogram (EEG) signals. The outcomes of the experiment are analyzed in terms of average accuracy, processing time, and F -measure. The results demonstrate that the proposed method outperforms existing methods and achieves better generalization. • Intuitionistic fuzzy twin proximal SVM with fuzzy hyperplane is proposed. • Assigned weights to training set based on their significance for better learning. • Generalization performance is significantly improved using L2-norm regularization. • Extensive empirical analysis is performed on 18 benchmark datasets. • Applied proposed model to EEG datasets for efficient EEG signal classification. [ABSTRACT FROM AUTHOR]

The environmental, social, and economic challenges associated with the massive activities of the oil and gas industry require analysis and evaluation of companies' sustainability priorities. Evaluating the environmental performance of oil companies requires the application of strict mathematical tools and models that provide rigorous results. Multi-criteria decision-making (MCDM) is a rigorous tool that evaluates the performance and practices of oil and sustainable energy companies. However, classical multi-criteria decision analysis has problems related to inconsistency because of the subjective nature of pairwise comparisons. This study responded to the literature call by utilizing the weight fuzzy judgment method (WFJM) to determine the weight coefficients of criteria with zero consistency. Such a method employed criteria values and expert judgment for decision-making to create a bridge between the mathematical approach and the human approach. This study aims to develop a solid decision support system by evaluating and benchmarking 11 companies utilizing the fuzzy judgment method based on fuzzy theory and the VIekriterijumsko KOmpromisno Rangiranje (VIKOR) method to determine sustainability priorities for oil and gas companies. The oil companies' criteria were efficiently weighted by the fuzzy judgment method, and the organizational capabilities represented the greatest weight value of 0.128, whilst the low-weight criteria were the high costs of technologies at 0.080. Besides, the benchmarking results for oil companies revealed that COM 8 was the best, whilst COM 11 was the worst. The fuzzy judgment technique is a unique approach to solving complicated decision-making problems, and its influence can be significant. Furthermore, this method can be applied in sectors other than energy, including banking, medical services, and engineering, where decision-making is not straightforward and requires a systematic approach. [Display omitted] • We developed a novel method called the weight fuzzy judgment method (WJSM). • This study arised the decision matrix based on 9 main criteria and 11 alternatives. • This study evaluated oil and gas companies' sustainability behaviors. • A comparison analysis was conducted between WJSM and BWM methods. [ABSTRACT FROM AUTHOR]

Fuzzy set theory constitutes the theoretical background for abstractly formalizing the vague phenomenon of complex systems. Vague data are defined herein as specialized fuzzy sets, i.e., fuzzy numbers, and a fuzzy linear regression model is described as a fuzzy function with such numbers as vague parameters. We applied a generic algorithm to identify the associated coefficients of the model, and provide both analytically and graphically, a linear approximation of the vague function, together with description of its potential application. We also provide an example of the fuzzy linear regression model being employed in a time series with economic indicators, namely the evolution of the unemployment, agricultural production, and construction between 2009 and 2011 in the Czech Republic. We selected this period since it represents the period when the financial and economic crisis started, and a certain degree of uncertainty existed in the evolution of economic indicators. Results take the form of fuzzy regression models in relation to variables of the time-specific series. For the period 2009-2011, analysis confirmed assumptions held by the authors on the seasonal behaviour of such variables and connections between them. In 2010, the system behaved in a fuzzier manner; hence, relationships between variables were vaguer than otherwise, brought about by factors such as difference in the elasticity of demand, state interventions, globalization, and transnational impacts. [ABSTRACT FROM AUTHOR]

This study proposes a fuzzy multi-criteria model to assess the risk of unemployment among professionals in the communication sector in Turkey, prompted by the rapid development and evolution of artificial intelligence (AI) technologies. The method integrates Fuzzy The Decision Making Trial and Evaluation Laboratory (F-DEMATEL) and Fuzzy Logarithm Methodology of Additive Weights (F-LMAW) procedures. Data were collected from 20 experts representing professions such as public relations, advertising, journalism, and design through a 12-question survey. In the analysis, the F-DEMATEL procedure was initially employed to determine attitudes towards AI technologies, followed by the application of the F-LMAW procedure to assess the magnitude of AI's impact on occupational groups. Findings reveal a nuanced stance: while professionals acknowledge the necessity of AI for their work, they are unwilling to accept unemployment due to more advanced AI. This newly identified structure, termed Post-Luddism, highlights concerns over technological unemployment, particularly pronounced in professions like journalism where job prospects are limited and creative thinking is paramount. In other communication fields, the intensive use of technology mitigates fears of AI harm. However, even in journalism, there exists a propensity to perceive AI as detrimental. These insights shed light on communication professionals' apprehensions and attitudes towards AI's effects. Policymakers and stakeholders can leverage this understanding to formulate strategic measures, considering the divergent perspectives among professional groups regarding AI, towards mitigating potential unemployment risks and fostering AI-adaptive strategies. • The evaluation is performed with the fuzzy-based DEMATEL-LMAW model. • The concept of Post-Luddism is presented in the literature for the first time. • The assessment of unemployment anxiety is used for the first time in the fuzzy MCDM literature. [ABSTRACT FROM AUTHOR]

In the classical EOQ model, acquiring cost of an order would be usually paid while receiving its receipt. Sometimes, the supplier may offer the retailer to pay the entire amount or the fraction of acquiring cost in advance as equal number of payments. The present research discusses the EOQ model with substandard products under fuzzy situation. This model deals with the advance payment on acquiring cost, products with substandard quality, and misclassification errors under repair option without scarcity by providing two models. The first model hypothesizes a remittance situation where the advance payment should be paid before the cycle time with some rate of interest which incurred by the supplier while the second model scrutinizes a situation where the prepayment occurs during the time length of the prior cycle which leads the supplier who would offer some price rebate on prepaid quantities. The proportion of improper items and the two kinds of screening errors are considered as the pentagonal fuzzy numbers [PFNs]. A fuzzy EOQ is framed for analyzing the sample, which can obtain the optimal solution. The impact of fuzziness on fraction of substandard products and investigation errors are illustrated for two models with appropriate examples. [ABSTRACT FROM AUTHOR]

Predicting or deducing war outcomes is the basis of military strategy formulation. Considering the high information uncertainty and complex influencing factors of modern wars, we applied a fuzzy influence diagram (FID) to realize the macroscopic prediction of war outcomes. In particular, we identified multidimensional factors that influence war outcomes in a relatively comprehensive and practical manner, thereby obtaining a relatively complete FID containing 24 nodes, with the value node "combat outcome" as the core. Subsequently, we performed a simulation analysis for a hypothetical war scenario to demonstrate the specific application and applicability of the proposed FID model. This study expands the prediction methods of war outcomes, and demonstrates that an FID can be feasibly applied in an uncertain battlefield environment to realize the prediction and risk assessment of war outcomes. Moreover, this approach can be used to analyze prewar decision making. The findings highlight that combat participants should attempt to further improve their military technology and combat effectiveness to gain combat advantage. [ABSTRACT FROM AUTHOR]

Automatic detection of crop yield ripeness is a tedious task because of the presence of various intensities of color in crops. One of the solutions to this problem is the monitoring of those crops by performing segmentation operations. This operation can help to distinguish the ripe and non-ripe regions among the crop images. For this purpose, this study presents a new hybrid crop image segmentation method utilizing type-2 fuzzy set (T2FS), K-means clustering algorithm, and modified quantum optimization algorithm (MQOA). The proposed method fully utilizes the indispensable qualities of these three techniques by (a) using T2FS to represent each color component of crop images in terms of secondary memberships, (b) applying K-means clustering algorithm to extract the similar features from the set of type-2 entropy values obtained from the secondary memberships, and (c) exploiting MQOA to optimize the distance function used in K-means clustering algorithm to obtain the optimal clusters. The performance of the proposed method is assessed based on the experiments carried out on color images of cherry tomatoes. Evidence of experimental results suggests that the proposed method produces extremely effective segmented images relative to those well-known color image segmentation methods available in the literature of pattern recognition and computer vision domains. [ABSTRACT FROM AUTHOR]

One of the essential features of project management is the novelty of work and uncertainty in the estimation of activities which will, in turn, result in uncertainty in project scheduling. In this study, a multi-objective multi-skill project scheduling problem is examined in terms of fuzzy time with two main objectives including: minimizing the project's makespan and minimizing the total cost of labor allocation. Besides, a Multi-Objective Imperialist Competitive Algorithm (MOICA) is adopted to solve the problem. In order to evaluate the performance of the algorithm, the suggested algorithm is compared with the Non-d ominated Solutions Genetic Algorithm (NSGA-II) based on three indicators. Apart from these, the parameters were optimized using the Taguchi algorithm in order to optimize the performance of the proposed algorithm. The results indicate the good performance of the MOICA. [ABSTRACT FROM AUTHOR]

The practical applications of engineering designs are often concerned by the presence of interrelated decisions. Naturally, these decisions are induced by solving many conflicting and incommensurable objectives. To deal with the interlinked decisions as well as the paradox natures among objectives, this paper presents an integrated approach based on dynamic programming approach (DPA) and intuitionistic fuzzy set (IFS) denoted as DPA-IFS for solving multi-objective optimization problem (MOOP). In DPA-IFS, the principle of DPA aims to generate an efficient solution of MOOP. In contrast, IFS aims to handle conflicting natures among the objective functions by means of the satisfaction (maximization the degree of membership) and dissatisfaction (minimization the degree of non-membership) concepts. The illustration is investigated by numerical illustrations taken from the literature. Furthermore, a new closeness strategy-based distance function is introduced to measure the worth of a satisfactory solution. The proposed methodology is validated on the IEEE 30-bus with six generators as a real test paradigm in the electrical power system. The results obtained by the DPA-IFS show the superior results than those obtained by different approaches. [ABSTRACT FROM AUTHOR]

Multi-attribute group decision making (MAGDM ) can be considered as the process of ranking alternatives or selecting an optimal alternative by many decision makers based on multiple criteria. By comparing any two alternatives pairwise, preference relations provide efficient ways to represent the preference degrees of decision makers. The aim of this paper is to introduce the notions of upward intuitionistic fuzzy preference relations from fuzzy information system and to study some properties of these relations. Further the series of upward intuitionistic fuzzy preference aggregation operators including the upward intuitionistic fuzzy preference weighted averaging UIFPWA operator, upward intuitionistic fuzzy preference ordered weighted averaging UIFPOWA operator and upward intuitionistic fuzzy preference hybrid averaging UIFPHA operator and their related results are also investigated. We developed a MAGDM method based on the proposed operators under the fuzzy environment and illustrated with a numerical example to study the applicability of the new approach on a candidate selection decision-making problem. [ABSTRACT FROM AUTHOR]

Fuzzy approaches that are proposed to describe uncertain, impressive or vague concepts, are based on the construction of membership function (MF), which reflects what is known about the linguistic variables in the application domain. However, a non-trivial problem exists in how to construct the most appropriate MF that has the best-fit representation of the analysed problem. Therefore, many authors propose their own ways to construct MF using a certain technique in a particular application domain. Consequently, the need for a general approach for constructing MF led us to systematise and to generalise the analysed approaches into a general methodological framework (GMF) of constructing MF. The novelty of this paper is that the proposed GMF is general, domain independent and free of a chosen understanding of fuzziness (i.e., similarity (imprecision), preference (vagueness), and uncertainty). To verify the proposed GMF, it was applied for the enterprise business service quality (QoSEBS) planning problem. The obtained results showed that a semi-automatic MF construction for QoSEBS planning was more sensitive, less subjective and more precise than a manual construction. Moreover, illustrative examples showed that our proposed GMF is applicable and implementable. The reliability of the results was assessed using experts and users' experience, which is based on general guidelines of the "acceptable" response time limits for various activities. [ABSTRACT FROM AUTHOR]

Fuzzy hidden Markov model is the efficient way of finding an optimized path among the states where uncertainty exists. Aggregation operators replaced the conventional operators in the fuzzy environment and play a vital role in real-world problems. Here, the aggregation operators namely trapezoidal interval type-2 weighted arithmetic (TpIT2FFWA) and trapezoidal interval type-2 weighted geometric (TpIT2FFWG) operators have been derived and their desired properties also have been proved based on Frank triangular norms. Using the proposed operators and Viterbi algorithm, decision-making process has been analyzed to choose the best medicine company. [ABSTRACT FROM AUTHOR]

A co-location pattern is a subset of spatial objects whose instances are frequently located together in geography space. The traditional co-location mining algorithms treated the spatial proximity relationship between the instances as unanimous by binary logic, which weakened the accuracy and effectiveness of the results. In this paper, the co-location pattern mining based on fuzzy neighbor relationship is studied. Firstly, fuzzy neighbor relationship (FNR) is defined to measure the proximity level between instances, and then the fuzzy participation ratio and the fuzzy participation index are defined. Secondly, the algorithm for spatial co-location pattern mining based on FNR (CPFNR) is proposed by the basic idea of the Join-less algorithm. Moreover, optimizing strategy is adopted for the CPFNR algorithm. Finally, the effectiveness of the CPFNR algorithm is verified by experiments on the real datasets, and the performance of our algorithm is evaluated on the synthetic datasets. [ABSTRACT FROM AUTHOR]

As an extension of wearable technology devices, smart jewelry has grasped the attention of women looking for both stylish and smart devices. Though smart jewelry is designed for women desiring to use wearable technologies without sacrificing their style, extant studies on smart jewelry lack a women-centered approach. Moreover, in the face of accelerated race in the launch of new smart jewelry in the marketplace, current approaches in the relevant literature on determining key evaluation criteria regarding smart jewelry and selecting the best alternative for women remain incapable. In this research, therefore, three main criteria, including jewelry-related, technology-related, and producer-related criteria, are initially determined, and seventeen sub-criteria are identified based on a review of relevant literature and experts~ opinions and knowledge. Then, four smart jewelry alternatives, including Bellabeat-Ivy Health Tracker, Totwoo We Bloom Smart Bracelet, Ringly Luxe Smart Bracelet, and Ringly Go Smart Bracelet, are chosen for analysis due to their technology and aesthetic design. Unlike prevailing studies, this study adopts the base-criterion method (BCM) and measurement of alternatives and ranking according to the compromise solution (MARCOS) with fuzzy ZE-numbers. The findings reveal that technology-related criteria are the most prioritized criteria by women. Further, activity tracking, price, and mobile alert are the first three critical sub-criteria in smart jewelry preference. Based on the overall evaluation, Ringly Luxe Smart Bracelet is the best smart jewelry for women. This research strongly contributes to extant literature as follows: (i) It provides a practical contribution to women in their smart jewelry selection processes and guides industrial practitioners, including smart jewelry designers and producers, in their design of smart jewelries that better satisfies the technological and aesthetic needs of women, and (ii) in terms of methodology, the proposed framework allows for the consideration of the degree of reliability of two different groups of decision-makers and experts for the decision-making process. [Display omitted] • Identified crucial criteria influencing women~s smart jewelry preferences • Proposed a new model to evaluate the criteria and alternatives for smart jewelry • Developed tool utilizes BCM and MARCOS methods with fuzzy ZE-numbers • Technology-related criteria are the most prioritized criteria by women. • Activity tracking, price, and mobile alert are the first three critical factors. [ABSTRACT FROM AUTHOR]

As a three-way approximation scheme to deal with fuzzy set, shadowed set approximately divides fuzzy objects with uncertainty into elevated, reduced, and shadow areas by a pair of decision thresholds α , β , thus effectively reducing the uncertainty of information. However, the current construction of shadowed set is all based on a single principle, lacking the comprehensive consideration of multiple principles, and these construction principles focus on the rationality of semantic interpretation of model construction process and threshold determination, and lack of consideration of the validity of partition results. To resolve these issues, this paper proposes a new shadowed set model through the game analysis between uncertainty and decision cost (UC-GTSS). First, Combining shadowed set construction with game theory, UC-GTSS is proposed based on game competition mechanism. Through the game analysis of uncertainty and decision cost, the optimal α , β is found, and a game payoff fusion algorithm based on Topsis is proposed. Second, the definition of UC-GTSS model expression, game player, strategy, payoff function, equilibrium analysis, optimization α , β determination and the influence of model parameters are analyzed and discussed. Third, the UC-GTSS model is extended and discussed based on the validity of the partition results, such as the game between approximate classification accuracy and coverage, the game between the Gini coefficient of the partition areas. Finally, through the analysis of algorithms, instances and data experiments, the construction process, validity, and rationality of UC-GTSS and its extended model are demonstrated. • This paper proposes a new shadowed set model through the game analysis between uncertainty and decision cost (UC-GTSS). • First, Combining shadowed set construction with game theory, UC-GTSS is proposed based on game competition mechanism. Through the game analysis of uncertainty and decision cost, the optimal threshold is found, and a game payoff fusion algorithm based on Topsis is proposed. • Second, the definition of UC-GTSS model expression, game player, strategy, payoff function, equilibrium analysis, optimization threshold determination and the influence of model parameters are analyzed and discussed. • Third, the UC-GTSS model is extended and discussed based on the validity of the partition results, such as the game between approximate classification accuracy and coverage, the game between the Gini coefficient of the partition areas. • Finally, through the analysis of algorithms, instances and data experiments, the construction process, validity, and rationality of UC-GTSS and its extended model are demonstrated. [ABSTRACT FROM AUTHOR]

The automatic and accurate arrhythmia diagnosis in the electrocardiogram (ECG) signals is significant for cardiac health. Typically, the arrhythmia diagnosis is automatically detected depending on single-lead signals or a simple combination of multilead signals from the ECG. However, it ignores the inter-lead correlation and the significance of different leads for different heart beats detection, which decreases the performance of arrhythmia diagnosis. In this paper, arrhythmia diagnosis is converted to a problem of multigranulation computing in the view of granular computing, and thus different lead signals can be captured to improve the effectiveness of abnormal heart beats detection. To this end, multilead ECG signals are firstly granulated into different fuzzy information granules by the fuzzy equivalence relation. An objective decision-making model based on fuzzy set theory is then proposed for describing and analyzing these granulated multilead ECG signals, which brings a self-adaptive and unsupervised decision making. As a result, the significance and correlation of different leads are analyzed by granularity selection and granular structures to make a better decision for arrhythmia diagnosis. Extensive experimental results show that the proposed algorithm can significantly improve the performance of arrhythmia diagnosis, especially better robustness to several types of cardiac arrhythmia. • Automatic arrhythmia diagnosis in ECG signals is modeled via multigranulation computing. • A self-adaptive and unsupervised decision making is brought by fuzzy granulation. • The significance of different leads is analyzed by granularity selection. • The inter-lead correlation is analyzed by granular structures. • Different multigranulation rough computing is studied for different granular structures. • The effectiveness and robustness of arrhythmia diagnosis are improved. [ABSTRACT FROM AUTHOR]

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With the rapid application of the new radar system, radar signal sorting based on conventional parameters has not achieved the desired results. Therefore, new features need to be extracted for signal sorting. In response to this problem, the paper proposes to use the entropy theory to extract the fuzzy entropy characteristics of the radar signal to determine the uncertainty of the radar source signal. Experiments with test signals show that the fuzzy entropy characteristics are less affected by noise over a wide range of SNR. [ABSTRACT FROM AUTHOR]

Abstract The development of alternative-fuel vehicles has been recognized as a promising way for emissions reduction from transportation. This study aims to develop a fuzzy group decision supporting framework for sustainability prioritization of alternative-fuel based vehicles. A criteria system which consists of thirteen evaluation criteria in environmental, economic, technological and social aspects was developed for sustainability assessment of alternative-fuel vehicles. The linear goal programming priority based Fuzzy Analytic Hierarchy Process was employed to determine the weights of the evaluation criteria for sustainability assessment of alternative-fuel vehicles, and Fuzzy Group Multi-Attribute Decision Analysis which allows multiple groups of stakeholders to participate in the decision-making process for rating the alternative-fuel vehicles with respect to the evaluation criteria was developed for sustainability prioritization of alternative-fuel vehicles. Three alternative-fuel based vehicles including compressed natural gas based, liquid petroleum gas based, and biodiesel based vehicles were studied by the developed method, and the sustainability sequence of these three scenarios from the most sustainable to the least is biodiesel based vehicle, compressed natural gas based vehicle and liquid petroleum gas based vehicle, thus, China's administration should give the first priority to biodiesel based vehicle under the current context of China. The results were validated by the fuzzy TOPSIS method, and sensitivity analysis was also carried out to test the effects of the weights of the evaluation criteria on the sustainability order of the three alternative-fuel based vehicles. Highlights • Fuzzy group decision supporting method was developed for ranking the alternative-fuel vehicles. • A four-dimensional criteria was developed for sustainability ranking of alternative-fuel vehicles. • LGPPFAHP method was employed for determining the weights of the evaluation criteria. • FGMADA was developed for ranking the alternative-fuel vehicles. [ABSTRACT FROM AUTHOR]

Nowadays, databases expand rapidly due to electronically generated information from different fields like bioinformatics, census data, social media, business transactions, etc. Hence, feature selection/attribute reduction in databases is necessary in order to reduce time, cost, storage and noise for better accuracy. For this purpose, the rough set theory has been played a very significant role, but this theory is inefficient in case of real-valued data set due to information loss through discretization process. Hybridization of rough set with intuitionistic fuzzy set successfully dealt with this issue, but it may radically change the outcome of the approximations by adding or ignoring a single element. To handle this situation, we reconsider the hybridization process by introducing intuitionistic fuzzy quantifiers into the idea of upper and lower approximations. Supremacy of intuitionistic fuzzy quantifier over VPRS and VQRS is presented with the help of some examples. A novel process for feature selection is given by using the degree of dependency approach with intuitionistic fuzzy quantifier-based lower approximation. A greedy algorithm along with two supportive examples is presented in order to demonstrate the proposed approach. Finally, proposed algorithm is implemented on some benchmark datasets and classification accuracies for different classifiers are compared. [ABSTRACT FROM AUTHOR]

In this paper we discussed the problem of generation and efficient software- and hardware-based implementation of branches of fuzzy logic parametric operations that can be used as basic operations of reconfigurable fuzzy systems (embedded fuzzy controllers). The ways of design of strict t -norms and t -conorms on fuzzy systems in presented paper based on the mathematical theory of geometrical aggregation operations from the Rvatchev constructive geometry. Presented theoretical results may be implemented for a new branches of membership functions design and in the hardware-based units of analytical fuzzy inference systems. [ABSTRACT FROM AUTHOR]

Train timetable plays an important role in the passenger train operations, which is typically developed or adjusted from the draft train timetable (DTT). The DTT serves as the basic framework and the core component of the train timetable to generate the rough plan of passenger trains, and eventually impacts the performance of the train operations. The paper attempts to develop a draft passenger train timetable under the constrained capacities of arrival-departure tracks and servicing tracks for the passenger train coaching stocks in a passenger railway network. The goals of the DTT are to satisfy the expected arrival/departure time, reduce the number of passenger coaching stocks, and avoid the closely spaced arrival/departure times. We propose a heuristic optimization algorithm based on the node importance to calculate the optimal train arrival and departure times at each arrival/departure station. The proposed model and algorithm are demonstrated in an experimental network with 11 stations and 73 trains in China; the results show that 93.06% of the trains can utilize the minimum passenger coaching stocks, and the equilibrium among passenger trains of the same route daily are improved approximately 20% compared to the actual timetable. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • We develop a comprehensive structure for weighting FMEA team members with respect to each risk factor based on proximity entropy weight and similarity entropy weight. • We develop a risk factor weighting approach based on fuzzy best-worst method. • The fuzzy VIKOR method is used to obtain the risk priorities of potential failure modes. Abstract In general, analysis of failure modes and their effects requires a group of experts to tackle substantial uncertainties associated with the risk evaluation process. To date, to overcome one or more of the uncertainty-related issues, an increasing number of failure mode and effects analysis (FMEA) models based on multi-criteria decision-making (MCDM) methods have been developed. However, most of the improvements have not cautiously considered the process of assigning importance weights to risk factors and FMEA team members during FMEA. This study aims to enhance the performance of the classic FMEA and to propose an integrated fuzzy MCDM approach for FMEA. First, a fuzzy best-worst method is used to obtain the weights of risk factors. Second, an integrated structure based on fuzzy proximity and fuzzy similarity entropy weights is developed to obtain the weights of FMEA team members with respect to different risk factors. Finally, a fuzzy VIKOR (VIsekriterijumska optimizacija i KOm-promisno Resenje) approach is employed to obtain the risk priorities of failure modes. The applicability and effectiveness of the proposed approach is validated through an illustrative example concerning risk analysis of a grinding wheel system. The results of sensitivity and comparative analyses show that the proposed approach is valid and can provide valuable and effective information in assisting risk management decision-making. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Neutrosophic sets (NSs) extend fuzzy and intuitionistic fuzzy sets to. • NSs can model complex situations characterized by uncertain multi-source multi-spectra information. • We design a NS-based algorithm to aggregate multiple expert opinions in multi-criteria decision making. • Single-valued NSs yield criteria and alternatives priorities reflecting expert opinions reliability. • Independent multi-source reliability measures ensure maximum reliability of decision outcomes. Abstract We develop a novel method that uses single-valued neutrosophic sets (NSs) to handle independent multi-source uncertainty measures affecting the reliability of experts’ assessments in group multi-criteria decision-making (GMCDM) problems. NSs are characterized by three independent membership magnitudes (falsity, truth and indeterminacy) and can be employed to model situations characterized by complex uncertainty. In the proposed approach, the neutrosophic indicators are defined to explicitly reflect DMs’ credibility (voting power), inconsistencies/errors inherent to the assessing process, and DMs’ confidence in their own evaluation abilities. In contrast with most of the existing studies, single-valued NSs are used not only to formalize the uncertainty affecting DMs’ priorities, but also to aggregate them into group estimates without the need to define neutrosophic decision matrices or aggregation operators. Group estimates are synthesized into crisp evaluations through a two-step deneutrosophication process that converts (1) single-valued NSs in fuzzy sets (FSs) using the standard Euclidean metric and (2) FSs in representative crisp values using defuzzification. Theoretical and practical implications are discussed to highlight the flexibility of the proposed approach. An illustrative example shows how taking into account the uncertainty inherent to the experts’ evaluations may deeply affect the results obtained in a standard fuzzy environment even when dealing with very simple ranking problems. [ABSTRACT FROM AUTHOR]

Abstract Pattern Classification involves formulating a method that maps the input feature variables to output space of binomial class. In this paper a modified fuzzy hypersphere neural network (MFHSNN) is proposed for pattern classification. MFHSNN utilizes fuzzy set hypersphere as a pattern cluster and classes are represented by a combination of fuzzy set hypersphere. The major factors which improve the learning algorithm of MFHSNN are:a new hypersphere created based on using supervised clustering and patterns of each class decided by its modified fuzzy membership function. If the new input pattern is outside of generated hypersphere then the radius is expanded to include the pattern based on expansion criteria. The presented model tested on three benchmark pattern data-sets and its performance is found to be superior than existing models. The obtained results show that the proposed membership function is able to improve MFHSNN for representation of pattern classification. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • New solution method to non-homogeneous fuzzy system of differential equations. • Introducing the concept of triangular fuzzy function. • Visual explanation of the difference between two types of fuzzy functions. • Constructing a solution as a fuzzy set of real vector-functions. • Proving the theorem of existence and uniqueness of the solution. Abstract In this paper, we propose a new solution method to non-homogeneous fuzzy linear system of differential equations. The coefficients of the considered system are crisp while forcing functions and initial values are fuzzy. We assume each forcing function be in a special form, which we call as triangular fuzzy function and which represents a fuzzy bunch (set) of real functions. We construct a solution as a fuzzy set of real vector-functions, not as a vector of fuzzy-valued functions, as usual. We interpret the given fuzzy initial value problem (fuzzy IVP) as a set of crisp (classical) IVPs. Such a crisp IVP is obtained if we take a forcing function from each of fuzzy bunches and an initial value from each of fuzzy intervals. The solution of the crisp IVP is a vector-function. We define it to be an element of the fuzzy solution set and assign a membership degree which is the lowest value among membership degrees of taken forcing functions and initial values in the corresponding fuzzy sets. We explain our approach and solution method with the help of several illustrative examples. We show the advantage of our method over the differential inclusions method and its applicability to real-world problems. [ABSTRACT FROM AUTHOR]

In this paper, we present a surrogate-assisted multi-objective genetic algorithm to mine a small number of linguistically interpretable fuzzy rules for high-dimensional classification task in the realm of data mining. However, the difficulties like (1) handling of high-dimensional problems by fuzzy rule-based systems (i.e., the exponential increase in the number of fuzzy rules with the number of input variables), (2) the deterioration in the comprehensibility of fuzzy rules when they involve many antecedent conditions, and (3) the optimization of multiple objectives in fuzzy rule-based system may stand as pertinent issues. Hence, to combat with the aforesaid issues, we design the problem as a combinatorial optimization problem with three objectives: to maximize the number of correctly classified training patterns, minimize the number of fuzzy rules, and minimize the total number of antecedent conditions. We optimize these objectives of the fuzzy rule-based system by using a multi-objective genetic algorithm. Further to reduce the number of required evaluations to approximate the Pareto front of computationally expensive multi-objective genetic algorithm for fuzzy rule-based system, a radial basis neural network surrogate model is adapted. This approach searches for non-dominated rule sets with respect to these three objectives. The performance of the surrogate-assisted model is evaluated through a few benchmark datasets obtained from knowledge extraction based on evolutionary learning data repository. The experimental outcome confirm that this model is competitive compared to the non-surrogate-assisted model. However, the performance of the model has drawn a clear edge over rule mining approaches like Decision Table, JRip, OneR, PART, and ZeroR. [ABSTRACT FROM AUTHOR]

In this paper, a new hierarchical method of contour analysis is proposed. The first stage of the analysis is based on the syntactic approach in which elementary segments of the contour are extracted by using geometric features. As a result, each extracted segment belongs to one of the equivalence classes which make the set of primitives. The contour is described as a string of primitives. The applied syntactic approach is a generalization of a classical shape language. Such description enables to classify some cases, but not all. Therefore, the second stage of the classification is applied. It consists in analysing other local geometric features of the contour in the context of the syntactic description obtained at the first stage of the analysis. The values of these features are used to define the arguments of the membership functions of the family of fuzzy sets which is the basis for the contour classification at the second stage of the analysis. The proposed formalism has been applied effectively to the recognition of bone contours in X-ray images. Healthy bones, the bones with erosions and the bones with osteophytes have been classified correctly. The proposal described in this paper turned out to be effective in the classification of contours of bones. [ABSTRACT FROM AUTHOR]

This study presents a model to forecast the Indian summer monsoon rainfall (ISMR) (June–September) based on monthly and seasonal time scales. The ISMR time series data sets are classified into two parts for modeling purposes, viz., (1) training data set (1871–1960), and (2) testing data set (1961–2014). Statistical analyzes reflect the dynamic nature of the ISMR, which couldn't be predicted efficiently by statistical and mathematical based models. Therefore, this study suggests the usage of three techniques, viz., fuzzy set, entropy and artificial neural network (ANN). Based on these techniques, a novel ISMR time series forecasting model is designed to deal with the dynamic nature of the ISMR. This model is verified and validated with training and testing data sets. Various statistical analyzes and comparison studies demonstrate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

As an extension of classical sets, fuzzy sets allow their containing elements to have continuous membership, which broadens its applications in various domains. In order to visualize the uncertain owner–member relationship, we design an intuitive diagram to visualize fuzzy sets. The diagram has a freeform boundary, which allows a clear layout of the data. In addition, the opacity of the diagram reveals the uncertainty of the membership. Physical simulation and bi-harmonic interpolation are introduced to generate the proposed diagram. We test our method with different fuzzy sets. The results show that our method is efficient to generate intuitive visualization of fuzzy sets. [ABSTRACT FROM AUTHOR]

This paper proposes a fuzzy l -complete approximation technique based on Willems’ behavioural systems theory for a class of hybrid system with symbolic inputs and quantized measurements. The discrete controller (or supervisor) is designed based on the abstracted (or approximated) system and high-level specifications. Furthermore, we show that the set of external behaviour (i.e., state set) of the fuzzy l -complete approximation based on the notion of ‘ guardian states ’ contains or at least equal to the behaviour set generated by traditional l -complete discrete abstraction. Finally, several simulation examples are presented to show the effectiveness of the proposed method for supervisory control of a special class of hybrid systems. [ABSTRACT FROM AUTHOR]

An attempt for exertion is made to utilize the capacity of fuzzy arbitrariness in dealt with instabilities to develop a generic approach for strength based administration life plan of fortified cement basic individuals. In the proposed procedure, convection and surface chloride focus are handled as irregular variable and subsequently the diffusion coefficient is characterized as a fuzzy arbitrary variable. The present work, dealt about the service life in sea-side location that lacks region of support due to limited distinction plan is evaluated using fuzzy probabilistic approach and fractal analysis. A case issue is also discussed to outline the adequacy of the proposed approach. [ABSTRACT FROM AUTHOR]

The subject of this paper is a procedure for the identification (detection, discovery) of atypical elements, understood in the sense that they occur rarely. A result of the procedure is the generation of a rating as to whether an examined observation should be classed as atypical, given in classic two-values form (deterministic, sharp), as well as fuzzy or intuitionistic fuzzy. Moreover, the task of identifying atypical elements, unsupervised in its basic formula, can − as a result of the procedure − be brought to a supervised form, which allows well-developed diverse methods of supervised classification to be used. The investigated method is independent of distribution existing in a population and enables the detection of atypical elements not only occurring in the tails, but also − e.g. for multimodal distributions with more distant factors − potentially located inside. The procedure is presented in ready-to-use form and does not require laborious research or literary study. The correctness of its functioning has been examined in practical medical problems. [ABSTRACT FROM AUTHOR]

By the concept of the Bloch ball we mean a three-dimensional shape that includes the sphere as well as all of the interior points (3-ball enclosed by 2-sphere). The Bloch ball is a geometric representation of qubit states. In this article we suggest a new sight on the Bloch ball considering this one via fuzzy set. A C++ style algorithm computes the value of a hash function using the von Neumann entropy of a density matrix. This value is transformed into the value of the linguistic variable. We get the possibility to express our knowledge on quantum states in linguistic terms. [ABSTRACT FROM AUTHOR]

To detect and evaluate the possible anomalous in IP-packets the fuzzy forecasting methods of network traffic is considered. In the context of network traffic control system it is offered several fuzzy models allowing to approximate the network traffic and, thus, to obtain short-term forecasts of volumes of IP-packets. [ABSTRACT FROM AUTHOR]

The solution of the problem of optimization of the university organization is proposed on the base of using a fuzzy model of nonlinear mathematical programming. This fuzzy approach allows to aggregate the expert estimates of influence obtained at the initial stage and, thereby, to more accurately evaluate the measures of effectiveness of the university organization. [ABSTRACT FROM AUTHOR]

For the evaluation and the subsequent ranking of universities for the quality of educational services provided by them it is proposed two approaches: statistical based on weighted estimates of key indicators of universities, and verbal based on the application of fuzzy inference engine. By applying these methods to the evaluation of five randomly selected universities (hypothetical alternatives), it is obtained their aggregate estimations (ratings) and corresponding two ways of ranking. [ABSTRACT FROM AUTHOR]

To increase the validity of positional-binary recognition of cyclic signals it is proposed to use the mathematical apparatof fuzzy sets theory that allows taking into account additional informative attributes of these signals. Recognition of cyclic signals is carried out by comparing their fuzzy interpretations with the corresponding fuzzy interpretations of etalon signals reflecting the time location of the position-binary components. [ABSTRACT FROM AUTHOR]

Today, many common activities have been transformed to electronic and online based environments because of the increased usage of technology and the Internet. Education is one of the sectors that is using computer technologies for training and delivering learning information to learners. Learning management systems (LMS) applications are some of the frequently used applications. There are different LMSs with different feature specifications available on the Internet, which can be accessed at anytime, anywhere and by anyone who wants to use them. Making an appropriate evaluation of the LMS and identifying the most important features should be considered before the evaluation of the LMS can be a complex process because the increasing number of features that are now available. The Multi-Criteria Decision Making (MCDM) method is now widely used by researchers to solve various problems that involve different criteria. This study suggests a fuzzy DEMATEL model to determine the interrelations between LMS evaluation criteria, their effects on each other as well as which criteria are the most important. Twelve criteria selected as the most important by experts will be considered in the study. Ten LMS experts made decisions based on the pairwise comparison of the criteria to be used in the DEMATEL method. Based on the case study, the result demonstrates that the three most important criteria are user satisfaction, learnability and usability among the 12 criteria considered. The research proposes a combination of this method and other MCDM techniques in the future to evaluate and select an alternative based on selected criteria, the research also suggested developing an application to substitute the manual evolution process. [ABSTRACT FROM AUTHOR]

The article considers the issues of applying the methodology of "soft computing" to analyze transients in gas pipelines. The gas pipelines have to operate in the transient regime before an exit to new steady-state flow regime. A set of values for the pressure of gas within the interval of output at the new steady-state flow regime was considered as fuzzy set, when with sufficient accuracy can only be determined values for the gas pressure to shut-down and after the new flow regime. On the basis of the computational experiments was obtained time series for changes in the basic parameters of the gas stream and constructed the corresponding curves. These curves were processed by methods of fractal geometry and the basic laws of their behavior. An effective apparatus to diagnose structural changes of the gas flow in case of emergency situations in gas pipelines is developed. The results of these studies can be recommended for use by services operating gas pipelines. [ABSTRACT FROM AUTHOR]

Building upon the national innovation system perspective and using a fuzzy set qualitative comparative analysis approach (fsQCA), we propose an integrating framework to determine the conditions that lead to high levels of national innovation capability outcomes. We discriminate between five conditions, viz. , building national institutions, developing human capital and research systems, improving infrastructures, and facilitating business and market conditions. We do so by analyzing data collected from the Global Innovation Index database containing 74 indicators and 133 countries between 2012 and 2015. The results show no singular path leading to high levels of innovation capability but there are three configurations of conditions. Two configurations highlight that the combination of three distinct conditions is sufficient for a country to reach a high innovation capability (one in which market conditions ‘are not necessary’ and one in which institutions ‘are not necessary’ conditions). The third configuration highlights that the combination of all five conditions is necessary for a country to reach a very high innovation capability. Some crucial implications of these findings for theory and practice are discussed. [ABSTRACT FROM AUTHOR]

This paper examines conditions and pathways that explain variation in the adoption of renewable energy (RE) in Nigeria's 36 states based on a fuzzy set qualitative comparative analysis. Using three analytical lenses proposed by the multi-level socio-technical theory (niches, regimes, and landscapes), we examine RE adoption in these states. While all three lenses explain variation to some extent, a combination of regime and landscape characteristics, enables states to overcome dependence on oil while triggering the adoption of RE. States with high income and a regime featuring institutions and coalitions supporting transitions establish themselves as pioneers. States with medium/low income and a regime characterised by a weak pro-RE political coalition support emerge as laggards. Hence we conclude that the role of the regime and particularly political actors therein, is central in energy transition processes among Nigerian states. This has implications for future transition attempts in Nigeria and developing (rentier) countries, generally. [ABSTRACT FROM AUTHOR]

Fuzzy set just past its 50-year anniversary and different fuzzy associations and organizations hold different forms of conferences and activities to celebrate this epoch-making scientific discovery. As an important branch of fuzzy theory, fuzzy decision has attracted scholars from almost all fields from psychologists, economists, to computer scientists. In this paper, we conduct a bibliometric analysis on fuzzy decision-related research to find out some underlying patterns and dynamics in this research direction. A total of 13,901 fuzzy decision-related publication records from Web of Science are analyzed with the aid of the text-mining software Vantage Point. Many interesting results with regard to the annual trends, the top players in terms of country level, time dynamic as well as institutional level, the publishing journals, the highly cited papers, and the research landscape are yielded and explained in-depth. It is observed that some small or developing economies (such as China, Iran, Taiwan, and Turkey) are quite active in fuzzy decision research. The fuzzy decision theories and methods have increasingly be utilized in various fields evidenced by the growing number of disciplines involved in the fuzzy decision research. [ABSTRACT FROM AUTHOR]

Used aircraft acquisition is one of the most important issues for airline companies, with multiple factors affecting the results. However, there is a lack of research on which criteria and to what extent these criteria affect the used aircraft acquisition operation. To this end, focusing on the identification and prioritization of used aircraft acquisition criteria, this paper presents a fuzzy best–worst method (BWM)-based approach. Firstly, by using the grounded theory analysis, 55 initial criteria that affect the used aircraft acquisition operation are identified based on the literature review. Then, an empirical analysis is conducted through a questionnaire survey, and 40 criteria are finally determined to be important to used aircraft acquisition based on the judgments of industry experts. Finally, the fuzzy BWM is adopted to rank the identified criteria with respect to the relative importance of these criteria, it is found that the physical situation of the aircraft is the most important criterion for used aircraft acquisition. The results presented in this paper could assist decision-makers to focus on the crucial criteria for used aircraft acquisition. • Criteria for used aircraft acquisition are identified. • Empirical analysis is conducted to validate the identified criteria. • Fuzzy BWM is adopted to rank the used aircraft acquisition criteria. • 40 criteria are identified and prioritized for used aircraft acquisition. [ABSTRACT FROM AUTHOR]