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This paper deals with the problem of sampled-data-based H ∞ control design for nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine system (WTS) subject to actuator failures. First, the Takagi-Sugeno (T-S) fuzzy system is employed to handle the nonlinearities of presented model. Next, by employing a Bernoulli stochastic variable, the general scenario of switched coupling memory sampled-data control (CMSDC) is designed which contains the sampled-data control (SDC) and memory SDC scheme as special cases. By combining the membership function-dependent (MFD) asymmetric looped-type Lyapunov-Krasovskii functional (LKF) and employing the available information of membership functions in H ∞ performance, the delay-dependent stabilization conditions of considered PMSG-based WTS are derived through the switched CMSDC technique. Meanwhile, the disturbances of considered systems are attenuated by taking the advantage of the newly proposed MFD H ∞ performance. Eventually, the simulation results are given to demonstrate the efficacy and applicability of the proposed CMSDC technique. [ABSTRACT FROM AUTHOR]

This article investigates type-2 fuzzy initial value problems and introduces a novel strategy that capitalises on granular differentiability. Incorporating type-2 fuzzy numbers to depict the problem's uncertainty may be advantageous from a practical standpoint. This work employs triangularly perfect quasi type-2 fuzzy numbers (TPQT2FNs) and defines the granular differentiability of TPQT2FN-valued functions. In addition, the solution approach for initial value problems with type-2 fuzzy initial conditions is discussed in the context of granular differentiability by transforming the type-2 fuzzy problem into a type-1 fuzzy problem using the lower membership function (LMF) and upper membership function (UMF) concepts. A couple of numerical examples are then examined to determine the applicability of the proposed method, and comparisons are made with existing type-2 fuzzy results and, in a special case, type-1 fuzzy results. In order to aid readers' comprehension and study the behaviour of the numerical solution, three-dimensional graphical results are also shown. [ABSTRACT FROM AUTHOR]

To investigate factors influencing the seed germination of Sichuan pepper (Zanthoxylum armatum DC.) and determine the optimal germination method, this study used an L16(4³) orthogonal test. The effects of compound treatments, including 2.5% sodium carbonate degreasing time, indole acetic acid (IAA) concentration, and IAA soaking time on seed germination were examined. The results indicated that 2.5% sodium carbonate degreasing time was the primary factor affecting the germination rate and vigor index of the seeds. IAA concentration primarily affected the germination index and the duration of germination, whereas IAA soaking time primarily influenced the time lag of germination. In addition, the 2.5% sodium carbonate degreasing time had a significant effect on the germination rate; IAA concentration significantly impacted the germination index; and IAA soaking time had a significant effect on both the germination index and the time lag of germination. Through the analysis and evaluation of the membership function, the optimal treatment combinations for seed germination were determined to be a 24-hour degreasing time with 2.5% sodium carbonate, an IAA concentration of 200 mg•L-1, and an IAA soaking time of 12 hours. This study provides a valuable reference for the future propagation of Zanthoxylum armatum DC. [ABSTRACT FROM AUTHOR]

An input–output finite-time filtering design problem for a class of delayed Takagi–Sugeno fuzzy systems with external disturbance input is discussed in this paper. Specifically, the filter design uses the imperfect premise matching scheme that relaxes the requirement that the filter and system membership functions be the same. This method can improve the flexibility of the filter design by incorporating membership function information into the input–output finite-time stability analysis. Using the system and filter states, an augmented filtering system is obtained. The required stability criteria are then derived using the Lyapunov–Krasovskii stability theorem and a few recent inequality approaches. Following that, the desired filter gain matrices are determined. The developed filtering design method is validated through some demonstrative examples. [ABSTRACT FROM AUTHOR]

• The bio-economic SSMJSs is formulated using T-S fuzzy modeling, in which the commodity price is governed by a semi-Markov process, and an event-triggered controller is proposed for this system using an affine membership-based approach. • The required sufficient conditions to ensure the admissibility of the addressed system over a specified finite-time interval are obtained using dissipative theory and the Lyapunov-Krasovskii functional method. • The eel seedling harvesting model is used to demonstrate the effectiveness and utility of the developed controller design. An event-triggered scheme-based admissibilization problem of bio-economic singular semi-Markovian jump systems over a finite-time interval is investigated in this study, where the commodity price is assumed to follow a semi-Markov process. To facilitate analysis, the addressed system is expressed using Takagi-Sugeno fuzzy modeling with two fuzzy rules, which is then generalized to a finite number of fuzzy rules. Following that, an affine membership-based event-triggered controller is proposed for the system under consideration to ensure the desired admissibility within a given finite-time interval. A new set of conditions that adequately guarantees the aforementioned problem is derived using the Lyapunov-Krasovskii stability theory, parameterized linear matrix inequality technique and dissipative theory. A numerical example based on the eel seedling harvesting model is considered to validate the developed theoretical findings, where the significance of the proposed control design method is clearly demonstrated. [ABSTRACT FROM AUTHOR]

Purpose: The paper aims to introduce a novel concept to solve the bi-level multi-criteria nonlinear fractional programming (BL-MCNFP) problems. Bi-level programming problem (BLPP) is rigorously flourished and studied by several researchers, which deals with decentralized decisions by comprising a sequence of two optimization problems, namely upper and lower-level problems. However, on the other hand, many real-world decision-making problems involve multiple objectives with fraction aspects, called fractional programming problems that reflect technical and economic performance. Design/methodology/approach: This paper introduces a VIKOR ("VlseKriterijumska Optimizacija I Kompromisno Resenje") approach to solve the BL-MCNFP problem. In this approach, an aggregating function based on LP metrics is formulated on the basis of the "closeness" scheme from the "ideal" solution. The three steps perform the solution process: First, a new concept is attempted to minimize and maximize of the numerators and denominators from their respective ideal solutions and anti-ideal values simultaneously. Second, for each level, the K-dimensional objective space of each level is converted to a one-dimensional space by an aggregating function. Third, to obtain the final solution, all levels are combined into single-level model where the decision variables of upper levels are interrelated with other levels through fuzzy strategy-based linear and nonlinear membership functions. Findings: The effectiveness of the proposed VIKOR is demonstrated by numerical examples, where the reported results affirm that the extended VIKOR method provides superior results in comparison with the same methods in the literature, and it is a good alternative to BL-MCNFP problems. Originality/value: In terms of the assistance-based right decision, a parametric analysis for the weight of the majority is provided to exhibit a wide range of compromise solutions for the decision-maker. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of stability and stabilization for interval type-2 (IT2) fuzzy systems with time-varying delays and external disturbances using the extended dissipative theory. In particular, our approach is to develop a new type of IT2 fuzzy controller that uses affine parameter-based weighting variables. Based on appropriate augmented Lyapunov-Krasovskii functionals and recently developed integral inequalities, some less conservative sufficient conditions are derived in the existence of the zeros equations. Specifically, the required conditions for co-design of affine matched membership functions-based IT2 fuzzy control law are provided such that the generalized performance index, the L 2 − L ∞ , H ∞ , passivity and (Q , S , R) − γ -dissipative problems are investigated. Finally, four examples are represented to verify the advantages of the developed method by comparing it with some existing results. [ABSTRACT FROM AUTHOR]

For nonlinear space-varying parabolic distributed parameter systems, this paper introduces an H ∞ fuzzy intermittent boundary control, where the output measurements are only available at some specified boundary position (i.e., boundary measurements). Initially, a Takagi–Sugeno fuzzy parabolic partial differential equation is used to precisely describe the nonlinear space-varying parabolic distributed parameter system. Then, under boundary measurements, an H ∞ fuzzy intermittent boundary control design based on the Takagi–Sugeno fuzzy parabolic partial differential equation model ensuring the exponential stability with an H ∞ performance for closed-loop space-varying distributed parameter system is subsequently obtained via spatial linear matrix inequalities by employing inequality techniques and piecewise switching-time-dependent Lyapunov function. Furthermore, in order to solve the H ∞ fuzzy intermittent boundary controller design of nonlinear space-varying parabolic distributed parameter systems under boundary measurements, we express spatial linear matrix inequalities as linear matrix inequalities and further present some linear matrix inequality based fuzzy intermittent boundary control design conditions respecting the property of membership functions. Finally, two simulation examples are offered to demonstrate the effectiveness of the proposed H ∞ fuzzy intermittent boundary control method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of adaptive event-triggered (AET) based optimal fuzzy controller design for nonlinear networked control systems (NCSs) characterized by Takagi–Sugeno (T–S) fuzzy models. An improved AET communication scheme with a memory adaptive rule is proposed to enhance the utilization of the state response vertex data. Different from the existing ET based results, the improved AET scheme can save more communication resources and acquire better system performance. The sufficient criteria of performance analysis and controller design are presented for the closed-loop control system subject to mismatched membership functions (MFs) and AET scheme. And then, a new MFs online learning algorithm on the basis of the gradient descent approach is employed to optimize the MFs of fuzzy controller and obtain optimal fuzzy controller for further improving system performance. Finally, two simulation examples are presented to verify the advantage and effectiveness of the provided controller design technique. [ABSTRACT FROM AUTHOR]

In this paper, a new two-dimensional gaussian hierarchical priority fuzzy system (TGHPFS) is proposed to handle interval-valued data. TGHPFS first performs hierarchical clustering of the average value of interval-valued data in each dimension to generate two-dimensional gaussian membership functions of two-level rules. The two levels of rules are associated by calculating the activation strength of the second-level rules to the first-level rules and setting the connection threshold. The regularized least squares method is used to optimize the consequents of the second-level rules. The two-dimensional gaussian membership function designed in this paper is used to model the antecedents of interval-valued data, solving the correlation problem between the left and right values of interval-valued data. The effectiveness of TGHPFS is validated using real-world datasets, and the proposed method is compared with other latest methods to show the superiority of TGHPFS. [ABSTRACT FROM AUTHOR]

This work concentrates on the control design of interval type-2 (IT2) T–S fuzzy systems under probabilistic saturation constraints. The actual control signals are allowed to exceed some preset thresholds with a certain frequency. Meanwhile, the sensors are governed by the multi-node round-robin scheduling protocol, which permits more than one sensors to transmit their information at every moment. The main objective is to synthesize a fuzzy controller such that the closed-loop system is locally stochastically stable under probabilistic saturated constraints and the multi-node round-robin scheduling protocol. To this end, the probabilistic saturation constraints are characterized by a Bernoulli-distributed stochastic process, and the received state at the controller side is formulated based on an updating rule and a compensation strategy. By constructing new membership functions, a token-dependent control law is subsequently designed. The stability analysis is facilitated by a modified sector condition dealing with the saturation nonlinearities. With suitable selection of initial states, sufficient conditions are derived to achieve the local stochastic stability of the closed-loop IT2 T–S fuzzy system. A larger domain of stochastic stability can be obtained via a searching algorithm. Finally, the proposed method is illustrated via a simulation example. [ABSTRACT FROM AUTHOR]

Witnessing the growth of inaccurate data with uncertainty and ambiguity, the belief rule base system is attracting increasing research interest because of its usage in decision-making problems as a disjunctive paradigm particularly when there is incomplete information. In this paper, we devise a novel method that employs fuzzy association rules to optimize disjunctive belief rule base (DBRB) systems regarding incomplete information in decision-making and achieve a significant performance improvement compared to the existing ones. First, we devise a method for constructing a fuzzy representation base from history data by using the triangular membership functions to blur history information. Then, a method is proposed to construct association rules based on the fuzzy representation base, in which the association rules are found regarding the missing input information by carrying out reasoning to complete the data and then making decisions on the data filled with DBRB system. Lastly, we evaluate the effectiveness of our proposed method against the public test data set, demonstrating that our method outperforms other baselines for decision-making with incomplete information. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of mixed actuator failures for discrete-time interval type-2 (IT-2) fuzzy systems with time-varying delays and external disturbances. Applying the non-parallel compensation strategy, the IT-2 fuzzy controller is designed. Considering the nonlinear fault factors of actuator, the linear fault model is expanded, which is more general than the conventional mixed actuator failure model. The information of membership function is introduced by staircase function approximation. Based on Lyapunov stability theory and a series of matrix inequality scaling techniques, a membership function dependent stability criterion with H ∞ performance is obtained. Then, the effectiveness of the proposed conclusion is verified by two simulation examples. [ABSTRACT FROM AUTHOR]

In the real word, due to the existence of uncertainty in decision-making information, it is often difficult to accurately evaluate utility values of alternatives. Recently, a series of discrete choice models based on fuzzy subjective utility have been proposed. Specifically, utility evaluation of each alternative has been expressed by fuzzy membership grades. However, traditional fuzzy membership function has only considered supporting degree, but has not considered the degrees of opposition and indeterminacy involved in decision makers' evaluations. In this paper, a series of novel discrete choice models based on Atanassov-type intuitionistic fuzzy set are proposed, in which membership degrees, non-membership degrees, and hesitation degrees are simultaneously taken into account to jointly express the utility evaluations. Moreover, the attitudinal character of decision makers and relative weights of attributes are also considered to further extend the proposed models. Compared with existing discrete choice models, these new models are more flexible and general, which increase the applicability of discrete choice models for decision-making under an uncertain and imprecise environment. Two real-world case studies are given to illustrate the effectiveness and rationality of the new models. [ABSTRACT FROM AUTHOR]

Formation control of multi-agent systems has a wide range of applications, but it has not been paid much attention in Takagi–Sugeno (T-S) fuzzy systems. In this paper, an event-triggered sampling strategy is designed for the formation control of T-S fuzzy systems, which allows the fuzzy controller and the fuzzy model not to share the same membership functions. The control strategy reduces the transmission frequency of sampling states by setting event conditions for information transmission. By means of Lyapunov stability theory, a set of formation conditions based on LMI is established. Less conservative and more efficient conditions are also obtained based on the properties of membership functions. Numerical examples show the validity of the proposed formation conditions, and the conservatism of the two criteria is compared. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to investigate a reliability-level demand-oriented pharmaceutical supply chain design with maximal anticipated demand coverage. Different hospitals with the particular reliability value associated with the various pharmaceutical items (PIs) are considered. An inter-connected multi-period supply chain comprising manufacturers, distribution centers, hospitals and patients is assumed for the smooth flow of health-care items, enhancing supply chain reliability. A reliability index for PIs is depicted to highlight product preference and facilitate hospitals' service levels for patients. Design/methodology/approach: A mixed-integer multi-objective programming problem that maximizes maximal demand coverage minimizes the total economic costs and pharmaceutical delivery time is depicted under intuitionistic fuzzy uncertainty. Further, a novel interactive neutrosophic programming approach is developed to solve the proposed pharmaceutical supply chain management (PSCM) model. Each objective's marginal evaluation is elicited by various sorts of membership functions such as linear, exponential and hyperbolic types of membership functions and depicted the truth, indeterminacy and falsity membership degrees under a neutrosophic environment. Findings: The proposed PSCM model is implemented on a real case study and solved using an interactive neutrosophic programming approach that reveals the proposed methods' validity and applicability. An ample opportunity to generate the compromise solution is suggested by tuning various parameters. The outcomes are evaluated with practical managerial implications based on the significant findings. Finally, conclusions and future research scope are addressed based on the proposed work. Research limitations/implications: The propounded study has some limitations that can be addressed in future research. The discussed PSCM model can be merged with and extended by considering environmental factors such as the health-care waste management system, which is not included in this study. Uncertainty among parameters due to randomness can be incorporated and can be tackled with historical data. Besides, proposed interactive neutrosophic programming approach (INPA), various metaheuristic approaches may be applied to solve the proposed PSCM model as a future research scope. Practical implications: The strategy advised is to provide an opportunity to create supply chains and manufacturing within India by helping existing manufacturers to expand, identifying new manufacturers, hand-holding and facilitating, teams of officers, engineers and scientists deployed and import only if necessary to meet timelines. Thus, any pharmaceutical company or organization can adopt the production and distribution management initiatives amongst hospitals to strengthen and enable the pharmaceutical company while fighting fatal diseases during emergencies. Finally, managers or policy-makers can take advantage of the current study and extract fruitful pieces of information and knowledge regarding the optimal production and distribution strategies while making decisions. Originality/value: This research work manifests the demand-oriented extension of the integrated PSCM design with maximum expected coverage, where different hospitals with pre-determined reliability values for various PIs are taken into consideration. The practical managerial implications are explored that immensely support the managers or practitioners to adopt the production and distribution policies for the PIs to ensure the sustainability in supply chain design. [ABSTRACT FROM AUTHOR]

The article discusses the development of a Severity Index (SI) for Oral Epithelial Dysplasia (OED) using a fuzzy group decision-making algorithm to address uncertainties and imprecision in OED grading. Oral onco-pathologists provided weights for different histopathological features, which were aggregated using a fuzzy logic-based algorithm. The SI was found to be statistically different for different grades of dysplasia, with the methodology offering potential applications in other medical decision-making contexts. This preprint has not been peer-reviewed and more information can be found on biorxiv.org. [Extracted from the article]

This paper introduces the foundational theory of fuzzy calculus on time scales, utilizing granular arithmetic operations between fuzzy intervals. These operations are developed based on the concept of the horizontal membership function (HMF), which is applied in multidimensional fuzzy arithmetic (MFA). Furthermore, the paper explores the existence of a unique solution and the continuous dependence of the solution to fuzzy dynamic equations on initial data, employing the Banach fixed-point theorem under a new metric for fuzzy functions in time scales involving the generalized exponential function. Finally, to highlight the practical significance of these results and their potential applications, the paper presents mathematical models relevant to nuclear physics and biology. [ABSTRACT FROM AUTHOR]

Due to objects described by a linguistic value with unsharp or fuzzy boundary, meaning of a linguistic value means different things to different people, the relation between the linguistic value and membership functions as its meaning is one-to-many rather than one-to-one. How to precisiate meaning of a linguistic value and even determine the truth values of fuzzy propositions remain open problems in computing with words (CW). In the paper, label of a linguistic value in its universe of discourse is proposed to formalize a possible position of objects described by the linguistic value, which is determined by a part of objects that can be and can not be described by the linguistic value via a group of users' commonsense knowledge. Then confidence degree of a membership function relative to a linguistic value is presented by measuring " the membership function is close to label of the linguistic value ", which can be used to precisiate meaning of a linguistic value and determine the truth values of fuzzy propositions. Finally, the truth value approximate reasoning of fuzzy propositions in the framework of the generalized modus ponens is provided and employed to evaluate the students' educational achievement. Comparative analysis with educational achievement based on Aliev's Z -interpolation approach and Zadeh's compositional rule of inference show that label of a linguistic value and confidence degree of a membership function relative to the linguistic value are effective and useful tools for CW. [ABSTRACT FROM AUTHOR]

A fuzzy series–parallel stochastic configuration networks (F-SPSCN) is proposed based on the application of nonconvex optimization in fuzzy systems. Firstly, the kernel density estimation method is used to fit the distribution of original input data to generate dynamic nonconvex membership functions, which enhances the fuzzy system ability to handle uncertain industrial data. Then the parameters of the nonconvex membership functions are optimized based on Majorization-Minimization algorithm and Generalized Projective Gradient Descent algorithm. The optimized membership matrices and fuzzy outputs are used as inputs of the serial-parallel stochastic configuration networks to improve the overall prediction accuracy of the model. Finally, the prediction accuracy of the F-SPSCN model has been verified by performing prediction experiments with two different functions and four benchmark datasets. The F-SPSCN model demonstrates superior performance compared to other models in predicting the magnetic separation recovery ratio (MSRR) of hydrogen-based mineral phase transformation (HMPT) process for refractory iron ore. [ABSTRACT FROM AUTHOR]

This paper presents a Type-3 Fuzzy Neural Network (T3FNN) for dynamic system control. The structure of the T3FNN controller, which is based on the compositional rule of inference of interval type-3 fuzzy systems, is proposed. TSK-type fuzzy rules, employing three-dimensional membership functions (MFs) in the antecedent part and linear functions with coefficients represented as interval sets in the consequent part, are utilized to design T3FNN. Gaussian functions with uncertain centers are employed to describe the type-3 membership functions. By employing three-dimensional MFs, type-3 fuzzy logic rules can accurately model a high degree of uncertainty and effectively handle uncertain information. The design of the T3FNN was accomplished by integrating the type-3 fuzzy logic system (T3FLS) with neural networks. The learning of the T3FNN was conducted using the genetic algorithms and gradient descent algorithm. As a result, the type-3 rule base of the system was effectively developed. The learning algorithms are presented and the proposed T3FNN structure is employed for the development of dynamic system control. The simulations of the T3FNN system for the control of the nonlinear and time-varying dynamic systems were carried out. The results obtained from the simulations indicate the suitability of using the T3FNN in controlling dynamic systems. [ABSTRACT FROM AUTHOR]

Interval type-2 fuzzy neural network systems (IT2 FNNSs) own the advantages of IT2 fuzzy logic systems (FLSs) and NN. The paper designs a kind of IT2 FNNSs for permanent magnetic drive (PMD) forecasting. For each rules of IT2 FNNSs, whose antecedents, consequents and input measurements are chosen as Gaussian IT2 membership functions (MFs). The proposed hybrid backpropagation (BP) algorithms and recursive least square (RLS) algorithms are adopted to tune all the parameters simultaneously. Simulation instances on the basis of data of permanent magnetic drive (PMD) torque and revolutions per minute (rpm) are adopted for testing the performances of proposed hybrid optimized IT2 FNNSs for forecasting. Convergence analysis illustrates that the IT2 FNNSs have excellent generalization capability compared with both singleton and non-singleton T1 FNNSs. [ABSTRACT FROM AUTHOR]

The fault detection issue for discrete-time nonlinear complex dynamical networks (CDNs) with Markov jump topology is investigated. Firstly, an interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model is used to approximate discrete-time nonlinear CDNs with the lower and upper membership functions (MFs) to capture nonlinear parameters. Secondly, both the H ∞ robust performance and the H _ fault sensitivity index are proposed to minimize the effect of external disturbance and maximize that of some faults on the generated residual, respectively. Moreover, based on the lower and upper MFs, the H _ / H ∞ fault detection observer mechanism consisting of IT2 T–S observers and residual systems is designed to detected some faults, which can trigger alarm by evaluation function when fault occurs. Finally, the numerical result of the presented method is shown by applying two simulation examples, which show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The intuitionistic fuzzy set theory is recognized as an effective approach for attribute reduction in decision information systems containing numerical or continuous data, particularly in cases of noisy data. However, this approach involves complex computations due to the participation of both the membership and non-membership functions, making it less feasible for data tables with a large number of objects. Additionally, in some practical scenarios, dynamic data tables may change in the number of objects, such as the addition or removal of objects. To overcome these challenges, we propose a novel and efficient incremental attribute reduction method based on α , β -level intuitionistic fuzzy sets. Specifically, we first utilize the key properties of α , β -level intuitionistic fuzzy sets to construct a distance measure between two α , β -level intuitionistic fuzzy partitions. This extension of the intuitionistic fuzzy set model helps reduce noise in the data and shrink the computational space. Subsequently, we define a new reduct and design an efficient algorithm to identify an attribute subset in fixed decision tables. For dynamic decision tables, we develop two incremental calculation formulas based on the distance measure between two α , β -level intuitionistic fuzzy partitions to improve processing time. Accordingly, some important properties of the distance measures are also clarified. Finally, we design two incremental attribute reduction algorithms that handle the addition and removal of objects. Experimental results have demonstrated that our method is more effective than incremental methods based on fuzzy rough set and intuitionistic fuzzy set approaches in terms of execution time and classification accuracy from the obtained reduct. • A distance measure between two α , β -level intuitionistic fuzzy partitions is proposed. • A novel attribute reduction algorithm is proposed for finding an optimal reduct on the fixed decision table. • Two incremental attribute reduction algorithms are also proposed for dynamic decision tables. • Experiments on the benchmark datasets demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Researchers at Queen's University Belfast have developed a modified fuzzy logic system to predict cortical bone drilling temperature, aiming to address the challenge of controlling temperature during bone drilling procedures to prevent thermal damage. The interval type-2 fuzzy logic system predicts temperature with a maximum error of 7%, taking into account drill bit geometry and drilling parameters. This system simplifies temperature modeling in surgical drilling processes, potentially improving surgical outcomes. The study was published in Fuzzy Information and Engineering and can be accessed for free online. [Extracted from the article]

This paper investigates the event-triggered sliding mode control (SMC) problem for networked T–S fuzzy delayed systems subject to random injection attacks, where the event-triggered mechanism (ETM) is introduced to alleviate data congestion and improve network efficiency. Under an open network environment, malicious attackers may randomly inject false information into the controller–actuator channel to compromise the integrity of the data. A new fuzzy sliding mode controller is constructed based on a non-parallel distributed compensation strategy, which introduces the distribution information of the attack probability. Then, the membership function dependent (MFD) analysis technique is adopted to reconstruct the membership functions in order to reduce the conservatism caused by the mismatch between the membership functions of fuzzy model and controller. Furthermore, the co-design conditions for the ETM and the fuzzy sliding mode controller are provided, which can ensure that the resulting closed-loop fuzzy system is mean-square exponentially ultimately bounded (EUB) and the sliding surface is reachable. Finally, a simulation experiment with tunnel diode circuit application is utilized to demonstrate the validity of the proposed SMC scheme. • A common sliding function is designed to facilitate subsequent analysis. • The mismatch problem of membership functions caused by asynchronous premise variables is discussed. • A new asynchronous fuzzy SMC law is constructed to ensure satisfactory performance. [ABSTRACT FROM AUTHOR]

In real-world problems, uncertainty may not be ignored. Because in the actual scenario, the parameters involved may vary depending on a variety of factors. Accordingly, fuzzy numbers rather than crisp parameters may be used to deal with these uncertainties. It may be noted that the use of Type-2 fuzzy numbers (T2FN) over Type-1 fuzzy numbers (T1FN) is advantageous as the value of the membership function varies from observer to observer. There are several practical problems whose governing equations are initial value problems. The main goal of this investigation is to solve ordinary differential equations with type-2 fuzzy uncertain initial conditions in order to deal with such situations. This article presents an analytical method for solving type-2 fuzzy differential equations using Triangular Perfect Quasi Type-2 Fuzzy Numbers (TPQT2FN). A newly defined triple parametric form of the type-2 fuzzy number is used in this case. Finally, the proposed method is demonstrated using a few numerical examples and application problems. [ABSTRACT FROM AUTHOR]

In this paper, a new approach is proposed for parameter identification in seismically excited structures based on synchronization method and fuzzy logic. The main contribution of this paper is providing a general solution for the estimation of the identifier coefficients using fuzzy logic. These identifier coefficients adjust the convergence rate and accuracy of the identification. The fuzzy controller uses triangular membership functions as input and output. The input parameters to the fuzzy controller are functions of displacement and velocity of the top story subjected to earthquake excitation. By using appropriate fuzzy rules the results are obtained for identifier coefficients. Additionally, a novel and simple formulation to identify structural unknown parameters based on synchronization is presented. The performance of the proposed approach is investigated using different shear frames under various excitations. The sensitivity of the proposed method to different noise levels and modeling uncertainties is analyzed. Numerical examples indicate that the presented method can identify the unknown parameters of the structure with high accuracy and reasonable computational time. [ABSTRACT FROM AUTHOR]

• A new BN model for risk assessment was developed. • The BN model is based on CM, IT2FSs, and the improved D-S evidence theory. • A new BPA function and a new evidence fusion rule algorithm were defined. • D-S evidence theory was improved under the IT2FSs environment. • The BN model could be used to predict the risk and analyze the sensitivity. Traditional Bayesian network (BN) model is established by crisp sets and probabilities, and its effectiveness and applicability are restricted. In order to solve this problem, a new BN model for risk assessment based on cloud model (CM), interval type-2 fuzzy sets (IT2FSs) and the improved Dempster-Shafer (D-S) evidence theory was developed in the following route. Firstly, CM and IT2FSs were used to define a new solution for the digital characteristics, and the standard and index cloud membership functions for the IT2FSs-CM were established. Then, the index cloud membership function for the IT2FSs-CM was defined as the basic probability assignment (BPA) function, a new evidence fusion rule algorithm was defined, and the improved D-S evidence theory was proposed. Furthermore, the improved D-S evidence theory was used to transform the BPA function into the IT2FSs based prior probability, and a new BN model for risk assessment was developed. Finally, the BN model was applied to a nuclear power plant (NPP) construction project, its risk was assessed at level I (very low risk), and the results by IT2FSs-CM and Bayesian reasoning were compared with those by common methods. The findings show that the new BN model is effective and applicable in risk assessment. [ABSTRACT FROM AUTHOR]

In this paper, the problem of observer-based model predictive control (MPC) for a multi-channel cyber-physical system (CPS) with uncertainties and hybrid attacks is investigated via interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model. Both denial-of-service (DoS) and false data injection (FDI) attacks are studied due to the vulnerability of wireless transmission channels. The objective of the addressed problem is to improve the security performance of the multi-channel CPS under malicious attacks, which has not been adequately investigated in the existing MPC algorithms. Moreover, uncertainties which appear not only in the membership functions but in both state and input matrices are considered. In this paper, different from the method that FDI attacks are handled by the bounded functions, an off-line observer is designed to actively defend against the FDI attacks. Meanwhile, an on-line MPC optimization algorithm, which minimizes the upper bound of objective function respecting input constraints, is presented to obtain the secure controller gains. Finally, an illustrative example is provided to verify the effectiveness and superiority of presented approach. [ABSTRACT FROM AUTHOR]

• Granular convexity of interval type-2 fuzzy functions is defined. • Properties of granular convex interval type-2 fuzzy functions are investigated. • Two kinds of granular solutions are presented for interval type-2 fuzzy optimization. • Optimality conditions are established for interval type-2 fuzzy optimization. Interval type-2 fuzzy optimization models have become increasingly attractive and useful in various practical applications. Nonetheless, there israre discussion on the optimality conditions of granular solutions for the problem of interval type-2 fuzzy optimization. In response to this, we introduce two kinds of granular solutions and endeavor to ascertain the conditions under which a feasible solution becomes granular-efficient in this study. Firstly, we put forth the concept of granular convexity for interval type-2 fuzzy functions, and investigate some fundamental properties. Secondly, we present the concepts of granular-efficient solutions and weakly granular-efficient solutions for optimization problems under an interval type-2 fuzzy setting. Finally,we obtain the optimality conditions for interval type-2 fuzzy optimization. Furthermore, several examples arepresented to demonstrate the proposed concepts and main results. [ABSTRACT FROM AUTHOR]

Time series forecasting becomes important due to its wide application in many fields. A variety of methods have been developed to address this problem based on different information in the time series. In this paper, a novel approach is proposed to accurately forecast the time series based on the visibility graph. The similarity between nodes is measured by the topological structure information based on the Jensen-Shannon divergence. The information from top- φ most similar nodes is considered to determine the final predicted value with the weighting coefficient obtained by the Gaussian membership function. Two real-world time series data sets are applied to demonstrate the applicability of our proposed model, and results show that our proposed method can achieve lower error indicators compared to other existing network-based approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a method for aggregating the information contained in sets of Time Series (TS) into a Fuzzy Time Series (FTS). First, an aggregation technique is defined, which is based on the algorithm known as Kernel Density Estimation (KDE) which reconstructs the probabilistic density function of a set of points, in this case a TS. Second, to operate with FTS, an algebraic framework is created based on Zadeh's extension principle and as a result of operating with FTS, a new FTS is obtained, which allows obtaining richer information and operating under conditions of uncertainty. Finally, the operations needed to compute the membership function of any TS in the aggregated FTS are introduced too. As a use case, it is proposed to work with sets of TS in the supply and demand domain, in such a way that information regarding the satisfaction of demand over time can be extracted. The specific application domain chosen will be that of the electricity market, analysing the consumption of buildings and their self-generation of energy to obtain information about the dependence on the electricity grid. [ABSTRACT FROM AUTHOR]

The manifold hypothesis states that the shape of the observed data is relatively simple and that it lies on a low-dimensional manifold embedded in a high-dimensional space. We contribute to the problem of data-driven modeling by treating it as an inverse problem where the model defines a Euclidean space with a Riemannian manifold structure. In particular, our contribution shows that a fuzzy set on a bounded support defines a Riemannian manifold that can be embedded in a multidimensional space where dimension is a model parameter. A noticeable advantage of the proposed approach is its connection with the values of the membership function and independence from the dimension of the data being modeled. Last but not least, we have found various formal representations of the Laplace-Beltrami operator and use its values as an estimate of the quality of the approximate solution to the inverse problem. [ABSTRACT FROM AUTHOR]

This paper presents the memory-based Takagi–Sugeno (T-S) fuzzy state feedback controller (SFC) for switched nonlinear systems based on the admissible edge-dependent average dwell time (AEDADT) rule. Different from the existing studies, the fuzzy dependent exponential Lyapunov–Krasovskii functional (LKF) is introduced for switched nonlinear systems, which include the notion of the derivative of membership functions based on the switching idea. Besides that, when compared to the traditional SFC framework, a time-varying delay is involved with the AEDADT switching rule in control gain matrices that are considered for the first time to tackle the stabilization problem. Further, the AEDADT switching property is considered for proposed nonlinear systems, and it contributes to getting more information about previous modes. Based on the proposed membership function dependent exponential LKF, new sufficient conditions are carried out to stabilize the proposed nonlinear systems in terms of the linear matrix inequalities (LMIs) technique. To support the applicability and efficacy of the proposed controller scheme, the tunnel diode circuit system model is illustrated. Also, the feasibility of the obtained results is verified by the numerical example. [ABSTRACT FROM AUTHOR]

The article shows that solving singular interval linear equations systems (ILESs) of the type A ˇ X = Y ˇ T , with a determinant containing zero, is possible and that it can be done without the need to invert the matrix A ˇ of the system. The method presented in the article can also be used to solve non-singular ILESs and ILESs with any ratio of the number of variables n and the number of equations k , where the values of n and k are not limited to 2 and may be greater. The method allows the detection of the optimal tolerance control vector X opt characterized by the highest degree of satisfaction with the tolerance requirements specified by the Y ˇ T vector. Calculations are carried out separately for subsequent equations of the system and not for the entire system at the same time, so they do not require the use of matrix arithmetic. Determination of the solution is implemented using the Shifted Membership Function (SMF) method, which the authors developed and published earlier. The article presents several examples to facilitate understanding of the method. [ABSTRACT FROM AUTHOR]

Researchers at the University of Technology in Bahrain have conducted a study on Polycyclic Aromatic Hydrocarbons (PAHs) in food products, which can be carcinogenic and occur due to various processes. Traditional methods of detecting PAHs in food are expensive and time-consuming, leading the researchers to develop a Fuzzy Logic System to create a harmfulness index based on PAH values. The study found that 89.72% of food samples were accurately classified based on their degree of harmfulness using this system. For more information, the research article can be accessed in the Journal of Intelligent & Fuzzy Systems. [Extracted from the article]

The type-2 fuzzy number (T2 FN) is a special type-2 fuzzy set whose all secondary membership functions are fuzzy numbers. This paper proposes a new defuzzification method and ranking method for T2 FNs. The defuzzification method can be expressed in a closed-form formula or can be divided into two computational steps. The first step computes the centroid of each secondary membership function to obtain a type-reduced set using the method derived from generalizing the existing alpha-cut defuzzification methods by introducing a parameter that controls the importance of secondary membership degrees, and the second step calculates the centroid of the type-reduced set. The defuzzified values are used to provide position information of T2 FNs. Secondly, we define a function to calculate the area enclosed by the image of the type-reduced set and the coordinate axes, and prove that this function is continuous. The values of this function are used to provide shape information of T2 FNs. Finally, to rank T2 FNs, we define a family of quasi-orders based on their position and shape information, and illustrate the validity and rationality of these quasi-orders through examples. [ABSTRACT FROM AUTHOR]

A recent study conducted by researchers from Donghua University in Shanghai, China, focused on the thermal risks faced by occupational workers in hot environments. The study found that workers face heat strain during temperature up-steps and cardiovascular strain during temperature down-steps. The researchers developed a comprehensive evaluation model that assessed both heat strain and cardiovascular strain using physiological and psychological parameters. The study emphasized the importance of transitional spaces and appropriate clothing choices in mitigating thermal risks and promoting human health and comfort in environments with substantial temperature variations. [Extracted from the article]

The main goal of this paper is to develop a new less conservative linear matrix inequality (LMI) condition for the asymptotic stability of continuous-time Takagi-Sugeno fuzzy systems. A key advantage of this new condition is its independence from the bounds on the time-derivatives of the membership functions (MFs), a requirement that presents in the existing approaches. This is achieved by introducing a novel fuzzy Lyapunov function that incorporates an augmented state vector. Notably, this augmented state vector includes MFs and allows their dynamics to be integrated into the proposed LMI condition. This inclusion of additional information about MFs reduces the conservativeness of the suggested stability condition. Finally, examples are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• Novel implementation technique of T1 and IT2 rule-based fuzzy systems. • Decomposition based on first-order rule partitions for singleton and non-singleton fuzzifiers. • Proposed technique outperforms the traditional method regarding computational and memory efficiency. • Case of identical partitions shows that execution time and memory costs remain unaffected by fuzzy sets increase. Rule-based fuzzy systems are widely adopted in various fields for their effectiveness in reducing uncertainties. However, large rule bases present significant computational and memory challenges, especially for real-time applications. To overcome this limitation, this paper introduces a novel first-order rule partitions-based decomposition technique (FORPs-DT) for type-1 (T1) and interval type-2 (IT2) fuzzy logic systems (FLSs). This method involves decomposing the universe of discourse, membership functions (MFs), and fuzzy sets (FSs) by defining conditions for non-zero firing levels (intervals). Significantly, this approach allows the construction of subfuzzy systems with separate knowledge bases while maintaining the input–output relationship. The paper provides detailed explanations and visual representations of FORPs-DT and proposes a case of identical FORPs to illustrate its simplicity and resource optimization benefits. Extensive experiments demonstrate the superiority of this technique, showcasing not only reduced execution time and memory usage but also enhanced performance through identical partitions, which allows an increase in the number of FSs without additional computational or memory overhead. [ABSTRACT FROM AUTHOR]

In the design process of traditional L ∞ methods, a common performance index is often considered in different fuzzy rules. This may introduce a certain conservatism when most of the whole fuzzy system operates under a certain fuzzy rule or a few fuzzy rules. Therefore, this paper focuses on robust interval estimation problems for discrete-time Takagi–Sugeno fuzzy systems, and a new membership function-dependent L ∞ performance index is proposed. The proposed L ∞ performance can ensure better results in practical engineering applications by using the priori knowledge that the model works most of the time on some specific fuzzy systems to design performance index. By means of fuzzy basis-dependent Lyapunov functions, a membership function-dependent L ∞ performance based interval estimation strategy applied to fault detection is presented. Through simulation analysis, the L ∞ index in this paper is better than the conventional one and a tighter interval estimation is obtained leading to more accurate and faster fault detection effects. Meanwhile, the simulation results of this method also reflect the membership function-dependent property well. • A novel time-varying L ∞ performance index dependent on the membership function is proposed. • It can utilize the a priori knowledge to design the weights to adjust the newly time-varying performance index to get better performance of the T-S fuzzy system as a whole. • An interval estimation method for discrete-time T-S fuzzy systems is proposed for fault detection by means of a novel MFD L ∞ performance index. • The proposed interval estimation strategy has a low computational load and requires only simple matrix operations. [ABSTRACT FROM AUTHOR]

In this paper, a new switching sequence convex optimization (SSCO) algorithm is proposed for solving non-convex optimization problem with complex time-varying relaxation matrix structures that arises during output feedback design. Firstly, the introduced time-varying relaxation matrix combines the membership functions and the designed switching mechanism to adjust the positive and negative terms of the inequality constraints. As a result, relaxed controller design conditions with complex matrix structures are established. The proposed SSCO algorithm employs switching optimization variables and inner approximation strategy, which is able to compute non-convex optimization problems with complex matrix structures more flexibly and converge quickly. It is worth noting that the implementation of the SSCO algorithm requires a set of strictly feasible initial solutions. Therefore, an initialization iterative algorithm is proposed, which overcomes the difficulties of transforming the solving problem into a typical non-convex optimization problem and linearizing multiple different concave parts, by which a set of optimized feasible solutions are obtained. Finally, simulation examples are used to demonstrate the superiority of the design scheme proposed in this paper. [ABSTRACT FROM AUTHOR]

In this study, an interval information granulation-based fuzzy partition (InterIG-FP) method is established to define fuzzy items in the framework of fuzzy decision tree induction. The proposed method first employs the principle of justifiable granularity to build information granules in terms of different classes on different condition attributes, where the number of information granules is equal to the number of classes. Then, the average values of the representative samples determined by each information granule are utilized to define the membership functions of fuzzy items for each condition attribute. Finally, an interval information granulation-based fuzzy decision tree (InterIG-FDT) is constructed based on the predefined fuzzy items in a top-down recursive way. The experiments illustrate the effectiveness, comparability and immunity capability of the proposed method. The effectiveness is verified by some comparative analysis with several traditional no-fuzzy decision trees. Furthermore, under the same constructing framework, some fuzzy decision trees with different fuzzy partition methods are studied to show the comparability on classification accuracies and the immunity capability on noise data, respectively. [ABSTRACT FROM AUTHOR]

Purpose: This paper proposes an integrated IT2F-FMEA model under a group decision-making setting. In risk assessment models, experts' evaluations are often aggregated beforehand, and necessary computations are performed, which in turn, may cause a loss of information and valuable individual opinions. The proposed integrated IT2F-FMEA model aims to calculate risk priority numbers from the experts' evaluations and then fuse experts' judgments using a novel integrated model. Design/methodology/approach: This paper presents a novel failure mode and effect analysis (FMEA) model by integrating the fuzzy inference system, best-worst method (BWM) and weighted aggregated sum-product assessment (WASPAS) methods under interval type-2 fuzzy (IT2F) environment. The proposed FMEA approach utilizes the Mamdani-type IT2F inference system to calculate risk priority numbers. The individual FMEA results are combined by using integrated IT2F-BWM and IT2F-WASPAS methods. Findings: The proposed model is implemented in a real-life case study in the furniture industry. According to the case study, fifteen failure modes are considered, and the proposed integrated method is used to prioritize the failure modes. Originality/value: Mamdani-type singleton IT2F inference model is employed in the FMEA. Additionally, the proposed model allows experts to construct their membership functions and fuzzy rules to capitalize on the experience and knowledge of the experts. The proposed group FMEA model aggregates experts' judgments by using IT2F-BWM and IT2F-WASPAS methods. The proposed model is implemented in a real-life case study in the furniture company. [ABSTRACT FROM AUTHOR]

This article investigates the sampled-data control design for single-master multi-slave teleoperation systems with stochastic actuator faults and time-varying delays. At first, the nonlinear bilateral teleoperation systems are modeled as Takagi–Sugeno (T–S) fuzzy systems through membership functions. The decentralized sampled-data control technique is proposed with actuator faults occurring in both master and slave robots. Here, the stochastic faults satisfy certain probability conditions and the forward and backward delays between the master and slaves are time-variant and asymmetric. Next, the delay-dependent Lyapunov–Krasovskii functionals (LKFs) are constructed for the proposed fuzzy model to obtain sufficient stability conditions in terms of linear matrix inequality (LMI). Finally, the reliability and superiority of the proposed method are illustrated by numerical results. • Sampled-data control is applied for the single-master multi-slave bilateral systems. • General time-varying forward and backward delays are studied for the proposed system. • The random variables are introduced to represent the stochastic actuator fault. • A novel sampling and delay-dependent LKF are constructed for the T-S fuzzy systems. • Theoretical results are verified by the single-link flexible joint robot model. [ABSTRACT FROM AUTHOR]

This work investigates the self-triggered control issue for interval type-2 (IT2) fuzzy systems. The transmission of the system state is determined via a self-triggered scheme. Instead of continuously monitoring the prespecified triggering condition, the self-triggered scheme can calculate the next triggering instant by the latest triggered state information. Then, by means of the triggered state, a self-triggered IT2 fuzzy controller is designed, whose fuzzy rules and membership functions (MFs) can be flexibly selected independent of the controlled fuzzy system. Under the constraint of imperfectly premise matching, the relationship between the triggered state and the system state is explicitly established, and the boundaries of MFs in the local operation region are given. Meanwhile, the local boundary information is utilized to obtain the relaxed feasible conditions. Finally, the simulation examples are give and the comparison with other triggered schemes are also made. [ABSTRACT FROM AUTHOR]