Showing papers on "Membership function published in 2021"
TL;DR: This paper introduces in detail a fault identification method based on multi-information fusion, which can consolidate the complementary advantages of different types of judgment in fault identification and prevents electrical fires in green buildings more comprehensively and accurately.
Abstract: Building management systems are costly for small- to medium-sized buildings. A massive volume of data is collected on different building contexts by the Internet of Things (IoT), which is then further monitored. This intelligence is integrated into building management systems (BMSs) for energy consumption management in a cost-effective manner. Electric fire safety is paramount in buildings, especially in hospitals. Facility managers focus on fire protection strategies and identify where system upgrades are needed to maintain existing technologies. Furthermore, BMSs in hospitals should minimize patient disruption and be immune to nuisance alarms. This paper proposes an intelligent detection technology for electric fires based on multi-information fusion for green buildings. The system model was established by using fuzzy logic reasoning. The extracted multi-information fusion was used to detect the arc fault, which often causes electrical fires in the low-voltage distribution system of green buildings. The reliability of the established multi-information fusion model was verified by simulation. Using fuzzy logic reasoning and the membership function in fuzzy set theory to solve the uncertain relationship between faults and symptoms is a widely applied method. In order to realize the early prediction and precise diagnosis of faults, a fuzzy reasoning system was applied to analyze the arcs causing electrical fires in the lines. In order to accurately identify the fault arcs that easily cause electrical fires in low-voltage distribution systems for building management, this paper introduces in detail a fault identification method based on multi-information fusion, which can consolidate the complementary advantages of different types of judgment. The results demonstrate that the multi-information fusion method reduces the deficiency of a single criterion in fault arc detection and prevents electrical fires in green buildings more comprehensively and accurately. For the real-time dataset, the data results are presented, showing disagreements among the testing methods.
86 citations
TL;DR: In this article, a deep learned recurrent type-3 (RT3) fuzzy logic system (FLS) with nonlinear consequent part is presented for renewable energy modeling and prediction. And the proposed method is applied for modeling both solar panels and wind turbines.
65 citations
TL;DR: Simulation results show that GSO outperforms FA in the optimal design of interval type-2 fuzzy controllers, which has a greater capability for managing uncertainty than a type-1 fuzzy controller.
Abstract: This paper presents a comparative study between the firefly algorithm (FA) and the galactic swarm optimization (GSO) method, where the performance of both methods is observed and tested in the optimization of a fuzzy controller for path tracking of an autonomous mobile robot. The main contribution of this work is finding the best method that generates an optimal vector of values for the membership function optimization of the fuzzy controller. This with the goal of improving the performance of the controller and thus the trajectory generated by the autonomous robot is closer to the desired trajectory. It should be noted that the fuzzy controller that is optimized is an interval type-2 fuzzy controller, which has a greater capability for managing uncertainty than a type-1 fuzzy controller. In this case, the limiting membership functions in the interval type-2 fuzzy sets are themselves type-1 fuzzy sets that define the footprint of uncertainty. Type-2 fuzzy controllers have been shown in previous works to handle better the control of robotic systems under noisy and dynamic conditions and this is why their optimal design is very important. Simulation results show that GSO outperforms FA in the optimal design of interval type-2 fuzzy controllers.
58 citations
TL;DR: A novel type-2 adaptive weighted spatial FCM (AWSFCM) clustering algorithm for MR brain tissue segmentation is suggested and the incorporation of adaptive weights into the cluster center update function improves the accuracy of the final cluster centers, thereby reducing the effect of IIH.
Abstract: The fuzzy $C$ -means (FCM) clustering procedure is an unsupervised form of grouping the homogenous pixels of an image in the feature space into clusters. A brain magnetic resonance (MR) image is affected by noise and intensity inhomogeneity (IIH) during the acquisition process. FCM has been used in MR brain tissue segmentation. However, it does not consider the neighboring pixels for computing the membership values, thereby misclassifying the noisy pixels. The inaccurate cluster centers obtained in FCM do not address the problem of IIH. A fixed value of the fuzzifier ( ${m}$ ) used in FCM brings uncertainty in controlling the fuzziness of the extracted clusters. To resolve these issues, we suggest a novel type-2 adaptive weighted spatial FCM (AWSFCM) clustering algorithm for MR brain tissue segmentation. The idea of type-2 FCM applied to the problem on hand is new and is reported in this article. The application of the proposed technique to the problem of MR brain tissue segmentation replaces the fixed fuzzifier value with a fuzzy linguistic fuzzifier value ( ${M}$ ). The introduction of the spatial information in the membership function reduces the misclassification of noisy pixels. Furthermore, the incorporation of adaptive weights into the cluster center update function improves the accuracy of the final cluster centers, thereby reducing the effect of IIH. The suggested algorithm is evaluated using T1-w, T2-w, and proton density (PD) brain MR image slices. The performance is justified in terms of qualitative and quantitative measures followed by statistical analysis. The outcomes demonstrate the superiority and robustness of the algorithm in comparison to the state-of-the-art methods. This article is useful for the cybernetics application.
57 citations
TL;DR: The main motivation of this paper is that the practical system subject to positivity and abrupt changes can be described by positive nonlinear S-MSSs, which always needs to consider the external disturbance.
Abstract: This paper concerns a positive $\mathcal {L}_{1}$ observer for positive nonlinear semi-Markovian switching systems (MSSs) via the expansion of Taylor formula and the fuzzy Lyapunov function approach, in which semi-Markovian switching parameters, positivity, Takagi–Sugeno (T–S) fuzzy, and external disturbance are all considered in a unified framework. A fuzzy Lyapunov function approach with less conservativeness is introduced into the research of positive systems. In the system under consideration, positive S-MSSs with the semi-Markovian process can describe more complex systems in a practical control process. The main motivation of this paper is that the practical system subject to positivity and abrupt changes can be described by positive nonlinear S-MSSs, which always needs to consider the external disturbance. First, by using the normalized membership function approach, positive nonlinear S-MSSs can be represented by local positive T–S fuzzy S-MSSs. Second, by constructing the fuzzy Lyapunov function, some sufficient conditions are proposed for stochastic stability and $\mathcal {L}_{1}$ -gain performance analysis, respectively. Then, a positive $\mathcal {L}_{1}$ observer in a novel standard linear programming condition is designed to guarantee the resulting closed–loop augmented system is positive and stochastically stable with a required $\mathcal {L}_{1}$ -gain performance. Finally, a practical example about the epidemiological model is introduced to show the effectiveness of the main theory.
52 citations
TL;DR: The simulations show that the introduced SO-IT3FLS and learning algorithm result in better accuracy in contrast to the other kind of fuzzy neural networks and conventional learning techniques.
51 citations
TL;DR: This paper presents an adaptive optimal fuzzy logic based energy management solution to develop appropriate day-ahead fuzzy rules for real-time energy dispatch adaptively in the presence of operational uncertainties.
46 citations
TL;DR: In this paper, a positive L₁ filter design was investigated for positive nonlinear stochastic switching systems subject to the phase-type semi-Markov jump process. But the problem was not addressed in this paper.
Abstract: In this article, the issue of positive L₁ filter design is investigated for positive nonlinear stochastic switching systems subject to the phase-type semi-Markov jump process. Many complicated factors, such as semi-Markov jump parameters, positivity, T-S fuzzy strategy, and external disturbance, are taken into consideration. Practical systems under positivity constraint conditions and unpredictable structural changes are characterized by positive semi-Markov jump systems (S-MJSs). First, by the key properties of the supplementary variable and the plant transformation technique, phase-type S-MJSs are transformed into Markov jump systems (MJSs), which means that, to an extent, these two kinds of stochastic switching systems are mutually represented. Second, with the help of the normalized membership function, the associated nonlinear MJSs are transformed into the local linear MJSs with specific T-S fuzzy rules. Third, by choosing the linear copositive Lyapunov function (LCLF), stochastic stability (SSY) criteria are given for the corresponding system with L₁ performance. Some solvability conditions for positive L₁ filter are constructed under a linear programming framework. Finally, an epidemiological model illustrates the effectiveness of the theoretical findings.
41 citations
TL;DR: The 3WD method-based MADM with HF information is proposed and the membership function of an objective HFS is given and the effectiveness of the proposed method is verified by solving an infectious disease diagnosis problem.
41 citations
TL;DR: In this article, the authors proposed novel distance measures for the intuitionistic fuzzy set (IFS) to discuss the decision-making problems, which are based on four different notions of centers, namely centroid, orthocenter, circumcenter and incenter of the triangle.
Abstract: The paper aims at introducing novel distance measures for the intuitionistic fuzzy set (IFS) to discuss the decision-making problems. The current work exploits four different notions of centers, namely centroid, orthocenter, circumcenter and incenter of the triangle. First, we mold knowledge embedded in IFSs into isosceles TFN (triangular fuzzy number). Hence, based on these TFNs, we design four-novel distance/similarity measures for IFSs using the structures of the four aforementioned centers and inspect their properties. To avoid the loss of information during the conversion of IFSs into isosceles TFNs, we included the degree of hesitation (t) between the pairs of the membership function in the process. The compensations and authentication of the proposed measures are established with diverse counter-intuitive patterns and decision-making obstacles. Further, a clustering algorithm is also given to match the objects based on confidence levels. The performed analysis shows that the proposed measures give distinguishable and compatible results as contrasted to existing ones.
40 citations
TL;DR: A new method is proposed to generate generalized basic probability assignment (GBPA) based on the triangular fuzzy number model under the open world assumption and can not only be used in different complex environments simply and flexibly, but also have less information loss in information processing.
Abstract: The process of information fusion needs to deal with a large number of uncertain information with multi-source, heterogeneity, inaccuracy, unreliability, and incompleteness. In practical engineering applications, Dempster–Shafer evidence theory is widely used in multi-source information fusion owing to its effectiveness in data fusion. Information sources have an important impact on multi-source information fusion in an environment with the characteristics of complex, unstable, uncertain, and incomplete. To address multi-source information fusion problem, this paper considers the situation of uncertain information modeling from the closed-world to the open-world assumption and studies the generation of basic probability assignment with incomplete information. A new method is proposed to generate the generalized basic probability assignment (GBPA) based on the triangular fuzzy number model under the open-world assumption. First, the maximum, minimum, and mean values for the triangular membership function of each attribute in classification problem can be obtained to construct a triangular fuzzy number representation model. Then, by calculating the length of the intersection points between the sample and the triangular fuzzy number model, a GBPA set with an assignment for the empty set can be determined. The proposed method can not only be used in different complex environments simply and flexibly, but also have less information loss in information processing. Finally, a series of comprehensive experiments basing on the UCI data sets is used to verify the rationality and superiority of the proposed method.
TL;DR: The results showed that the proposed method more accurately identified the weak links in the safety system, providing a theoretical basis for the risk prevention and control.
TL;DR: A novel membership-function-dependent (MFD) analysis approach is presented that does not need to increase the number of slack variables to reduce conservatism, and some new fuzzy Lyapunov–Krasovskii functionals (FLKFs) that do not require the restrictions of positive definiteness imposed on LyAPunov matrices are proposed.
Abstract: Robust stability and stabilization problems for a class of discrete-time nonlinear systems are studied in this article. The control signal is transmitted to the nonlinear systems through a lossy communication channel in which time-varying network-induced delay occurs. A Takagi–Sugeno (T–S) fuzzy model is used to represent the nonlinear systems. Using membership function boundary information, a novel membership-function-dependent (MFD) analysis approach is presented. Unlike most previous results, the proposed MFD analysis approach does not need to increase the number of slack variables to reduce conservatism. Combining auxiliary matrices and this approach, we propose some new fuzzy Lyapunov–Krasovskii functionals (FLKFs) that do not require the restrictions of positive definiteness imposed on Lyapunov matrices. Using the FLKF and MFD analysis approach, a sufficient condition in the form of linear matrix inequalities (LMIs) is developed to guarantee the stability of T–S fuzzy time-varying delay systems. Based on the results for stability, less conservative stabilization conditions are also derived. Finally, numerical examples show that less conservative results can be obtained by the proposed approach. The inverted pendulum system with state delay or network-induced delay is also studied to verify the effectiveness of the suggested approach.
TL;DR: A hybrid method encompassing interval type-2 semi-supervised possibilistic fuzzy c-means clustering (IT2SPFCM) and Particle Swarm Optimization (PSO) to form the proposed IT2 SPFCM-PSO is proposed.
TL;DR: It is shown that an α-plane represented a GT2-FLC is easily designed via baseline type-1 and interval type-2 FLCs and two design parameters (DPs).
Abstract: This article aims to provide a new perspective on how the deployment of general type-2 (GT2) fuzzy sets affects the mapping of a class of fuzzy logic controllers (FLCs). It is shown that an α -plane represented a GT2-FLC is easily designed via baseline type-1 and interval type-2 FLCs and two design parameters (DPs). The DPs are the total number of α planes and the tuning parameter of the secondary membership function that are interpreted as sensitivity and shape DPs, respectively. We provide a clear understanding and interpretation of the sensitivity and shape DPs on controller performance through various comparative analyses. We present design approaches on how to tune the shape DP by providing a tradeoff between robustness and performance. We also propose two online scheduling mechanisms to tune the shape DP. We explore the effect of the sensitivity DP on the GT2-FLC and provide practical insights on how to tune the sensitivity DP. We present an algorithm for tuning the sensitivity DP that provides a compromise between computational time and sensitivity. We validate our analyses, interpretations, and design methods with experimental results conducted on a drone. We believe that this article provides clear explanations on the role of DPs on the performance, robustness, sensitivity, and computational time of GT2-FLCs.
TL;DR: Results show that the proposed algorithm has a higher generalization capability and provides accurate forecasting results even in the case of medium-term load forecasting, and outperforms other methodologies by achieving a mean absolute percentage error as low as 2.66%.
Abstract: For optimal utilization of power generation resources, load forecasting plays a vital role in balancing the load flow in a power distribution network. There are several drawbacks associated with existing forecasting techniques for load flow balancing. Neural network (NN) based forecasting techniques are unable to consider the actual states of a power system, while weighted least squares state estimation (WLS) fails to counter nonlinearity in the demand profile. In this article, a hybrid approach is proposed for short term load forecasting. The hybrid technique, comprised of a WLS, NN, and adaptive neuro-fuzzy inference system (ANFIS), is termed WLANFIS. ANFIS itself is the combination of an NN and fuzzy logic. It takes a refined data set obtained through NN and WLS, which helps in determining the optimal number and types of membership functions. It also helps in determining the effective fuzzy set ranges for an individual membership function that is used by the fuzzy system. WLS provides estimated states in the real-world scenario while the NN models the nonlinearity in the demand profile and is tested on IEEE 14 and 30 bus systems as well on real-world data sets. Results show that the proposed algorithm has a higher generalization capability and provides accurate forecasting results even in the case of medium-term load forecasting. It outperforms other methodologies by achieving a mean absolute percentage error as low as 2.66%.
TL;DR: The efficient model-predictive control (EMPC) problem of a class of nonlinear systems in the framework of interval type-2 Takagi–Sugeno (IT2 T–S) fuzzy is investigated and sufficient conditions are presented to rigidly guarantee the feasibility of the proposed EMPC algorithm and the mean-square stability of the underlying IT2 T-S fuzzy system.
Abstract: In this article, the efficient model-predictive control (EMPC) problem of a class of nonlinear systems in the framework of interval type-2 Takagi–Sugeno (IT2 T–S) fuzzy is investigated In order to improve the reliability of the data transmission while reducing the network communication burden, a so-called stochastic communication protocol (SCP) governed by a Markov chain is adopted to orchestrate the data transmission order from the controller to the actuator The purpose of the addressed problem is to design a set of desired EMPC controllers so as to guarantee the mean-square system stability and obtain a good balance among the computation burden, initial feasible region, and the control performance A novel control model is established for the SCP and IT2 T–S fuzzy nonlinearities in a unified representation by using a fuzzy periodic switching related to the transmission token and the membership function Then, the system state, the SCP-based control perturbation, and the previous input under the SCP are fully taken into consideration for constructing the objective function By virtue of the “min–max” strategy, a few optimizations are formulated, and the corresponding EMPC algorithm is provided, where the feedback gain is designed offline, while the control perturbation is obtained online Furthermore, by means of the matrix partition technique, sufficient conditions are presented to rigidly guarantee the feasibility of the proposed EMPC algorithm and the mean-square stability of the underlying IT2 T–S fuzzy system Finally, two illustrative examples are utilized to demonstrate the validity of the proposed EMPC strategy
TL;DR: This article presents a new concept called R-sets, in which different risk cases of a membership function due to both future events and unreliable information sources are investigated, and the governing mathematical relations are presented.
Abstract: Fuzzy sets were initially proposed to address ambiguities and uncertainties. However, in certain cases, the fuzzy sets show some degree of uncertainty and risk, when the available data are either obtained from unreliable sources or related to future events. To solve this problem, the R -numbers methodology has been recently developed as a powerful approach to model the risk of fuzzy sets and numbers due to risk factors. In R -numbers, only the variability of x values has been taken into account in risk modeling of the fuzzy sets, but not their membership function. Moreover, merely one source of risk factors related to fuzzy sets and numbers has been considered. Therefore, this article presents a new concept called R -sets, in which different risk cases of a membership function due to both future events and unreliable information sources are investigated, and the governing mathematical relations are presented. Subsequently, to overcome previous limitations of R -numbers, the R -sets are applied to develop a decision-making method, and it is tested by using a case study.
TL;DR: Based on a state-feedback closed-loop system, a polynomials fitting method is utilized, and an improved membership function transformation technique is proposed to approximate the membership functions of the fuzzy system, and conservatism reduction effects are shown.
Abstract: For the stability analysis of a polynomial fuzzy system, a new polynomial membership function approach is proposed to reduce conservatism. In this article, based on a state-feedback closed-loop system, a polynomials fitting method is utilized, and an improved membership function transformation technique is proposed to approximate the membership functions of the fuzzy system. Then, the membership-function-dependent polynomial-based stability conditions are derived. The obtained polynomial membership functions and approximation errors will be involved in the stability analysis process. Based on the sum-of-squares optimization technique, polynomial conditions can be directly solved. Finally, by several numerical and practical examples, conservatism reduction effects are shown by comparisons with existing methods.
TL;DR: In this paper, the novelty of complex multi-fuzzy hypersoft set (CMFHSS) is discussed, which can deal with uncertainties, vagueness, and unclearness of data that lie in the information by taking into account the amplitude and phase terms of the complex numbers (C-numbers) at the same time.
Abstract: Hypersoft set (HSS) was proposed in 2018 as a generalization of the soft set (SS). In this paper, the novelty of complex multi-fuzzy hypersoft set (CMFHSS) is discussed, which can deal with uncertainties, vagueness, and unclearness of data that lie in the information by taking into account the amplitude and phase terms (P-terms) of the complex numbers (C-numbers) at the same time. This CMFHSS establishes a hybrid framework of the multi-fuzzy set (MFS) and HSS characterized in a complex system. This framework is more flexible in two ways; firstly, it permits a wide range of values for membership function by expanding them to the unit circle in a complex frame of reference through characterization of the multi-fuzzy hypersoft set (MFHSS) involves an additional term called the P-terms to consider the periodic nature of the information. Secondly, in CMFHSS, the attributes can be further sub-partitioned into attribute values for a better understanding. We characterize its fundamental operations as a complement, union, and intersection and support them with examples. We develop the proverbial meaning of similarity measures (SM) and entropy (ENT) of CMFHSS and present the fundamental relationship. These tools can be utilized to figure out the best alternative out of a bunch that has various applications in the field of optimization. Additionally, mathematical models are given to analyze the reliability and predominance of the established methodologies. Moreover, the advantages and comparative analysis of the proposed measures with existing measures are also depicted in detail. Lastly, the mathematical models are given to represent the validity and applicability of the presented measures.
TL;DR: By using the measurable premise variables, a novel output feedback controller scheme is proposed and via restricting the reachable set into an ellipsoid set, the system state can be contained into a prespecified area so that the purpose of local stabilization can be fulfilled.
Abstract: This paper investigates the local stabilization problem for T–S fuzzy systems with partly measurable premise variables and time-varying delay. First, by using the measurable premise variables, a novel output feedback controller scheme is proposed. Second, via restricting the reachable set into an ellipsoid set, which is bounded by the objective region, the system state can be contained into a prespecified area so that the purpose of local stabilization can be fulfilled. Furthermore, because of network delay, there is a deviation between the membership function of the system and those of the controller. By exploring the information of the deviation, the stabilization condition can be further relaxed. Compared with the existing results, the new asynchronous controller strategy can simultaneously make full use of the information of the measurable premise variables and the aforementioned deviation for a less conservative result. Finally, an illustrative example is given to show the applicability of the presented approach.
TL;DR: A three-stages clustering strategy is presented in a fuzzy framework for automating this selection process in the context of Input/Output and Output-Only identification and it is shown how the membership function obtained for the cluster of physical modes can be interpreted as a new synthetic modal indicator and helps with pole-splitting detection, outlier rejection and generally improves the final modal parameters estimation.
TL;DR: The results showed that the ANFIS model can provide fast computational calculation, and adding more nodes for the prediction cannot change the overall time of calculation due to the meshless behavior of the model.
Abstract: Modeling suspended sediment load is a critical element of water resources engineering. In this work, using the ANFIS method, everyday suspended sediment particles were estimated in different categories of the river in US Sediment big data, and various flow rates were utilized for testing and training. The artificial intelligent (AI) method called ANFIS is used to train actual data from the river and provide an AI model with artificial data points. This artificial data point can show the occurrence of disaster for a critical day with different flow rates. The changing parameter in the AI model enables us to make a correct decision about critical time for rivers. This study also concentrates on the sensitivity investigation of ANFIS setting parameters on the accurateness of numerical results in order to find the best ANFIS model for rapid oscillation in the data set. The best performance of the ANFIS method is achieved with the trimf membership function, the number of input membership function = 16, and the number of iteration = 1000. The results also showed that the ANFIS model can provide fast computational calculation, and adding more nodes for the prediction cannot change the overall time of calculation due to the meshless behavior of the model. In addition to this model, we used the ant colony method for training of data set, and we found that the ANFIS method is better in learning and prediction of the dataset.
TL;DR: The results demonstrate that the proposed approach, called grey earned value management (EVM-G), has a unique performance in highly uncertain environments when experts have become unavailable and a potential approach for overcoming this issue lies in Grey theory.
Abstract: Project stakeholders always investigate possible approaches to monitor project progress closely and further, taking necessary actions during the whole phases of the project in order to manage delays. Earned value management (EVM) is one of the methods, which can forecast the required costs for accomplishment of the project. The data collected from projects undertaken in order to update the master schedule often suffer from a level of uncertainty. Ignoring these uncertainties may even lead to project failure. Fuzzy theory has been previously used in the EVM for taking uncertainties into account. A major disadvantage of using fuzzy approaches is the need for incorporating expert judgments to construct a suitable membership function for all activities in the project undertaken. A potential approach for overcoming this issue lies in Grey theory. In this article, the current study deals with the EVM method in grey systems paradigm. Also, the performance of the proposed method, called grey earned value management (EVM-G), is evaluated through some numerical examples and a case study. The results demonstrate that the proposed approach has a unique performance in highly uncertain environments when experts have become unavailable. Comparisons between EVM-G and the fuzzy earned value management approaches reveal the superior performance of EVM-G.
TL;DR: A novel concept of dependency is proposed: inner product dependency to describe the classification error, and a criterion function to evaluate the importance of candidate features is proposed to overcome this weakness.
Abstract: Classical fuzzy rough set often uses fuzzy rough dependency as an evaluation function of feature selection. However, this function only retains the maximum member- ship degree of a sample to one decision class, it can not describe the classification error. Therefore, in this work, a novel criterion function for feature selection is proposed to overcome this weakness. To characterize the classification error rate, we first introduce a class of irreflexive and symmetric fuzzy binary relations to redefine the concepts of fuzzy rough approximations. Then, we propose a novel concept of dependency: inner product dependency to describe the classification error, and construct a criterion function to evaluate the importance of candidate features. The proposed criterion function not only can maintain a maximum dependency function, but also guarantees the minimum classification error. The experimental analysis shows that the proposed criterion function is effective for data sets with a large overlap between different categories.
TL;DR: A novel membership-function-dependent finite frequency fault detection filtering design approach is proposed by using the information of the lower and upper membership functions together with the footprint of uncertainties to design an admissible filter such that the fault detection system is asymptotically stable with prescribed finite frequency filters.
Abstract: This article studies the problem of finite frequency fault detection filtering design for uncertain nonlinear systems based on interval type-2 Takagi–Sugeno fuzzy models. It is assumed that the frequencies of disturbances and faults are in finite frequency sets, respectively. The objective is to design an admissible filter such that the fault detection system is asymptotically stable with prescribed finite frequency $\mathscr H_{\infty }$ and $\mathscr H_{-}$ performances. Based on Fourier transform and Projection lemma, finite frequency filtering synthesis results are obtained. Then, a novel membership-function-dependent finite frequency fault detection filtering design approach is proposed by using the information of the lower and upper membership functions together with the footprint of uncertainties. Two algorithms with linear matrix inequality constraints are developed to optimize the finite frequency $\mathscr H_{\infty }$ performance and the finite frequency $\mathscr H_{-}$ performance, respectively. Finally, simulation studies are provided to show the effectiveness of the proposed method.
TL;DR: This article is about explainable artificial intelligence (XAI) for rule-based fuzzy systems, and provides a novel multi-step approach to obtain such a small subset of rules for three kinds of fuzzy systems.
Abstract: This paper is about explainable AI (XAI) for rule-based fuzzy systems [that can be expressed generically, as y(x) = f(x)]. It explains why it is not valid to explain the output of Mamdani or TSK rule-based fuzzy systems using IF-THEN rules, and why it is valid to explain the output of such rule-based fuzzy systems as an association of the compound antecedents of a small subset of the original larger set of rules, using a phrase such as These linguistic antecedents are symptomatic of this output. Importantly, it provides a novel multi-step approach to obtain such a small subset of rules for three kinds of fuzzy systems, and illustrates it by means of a very comprehensive example. It also explains why the choice for antecedent membership function shapes may be more critical for XAI than before XAI, why Linguistic Approximation and similarity are essential for XAI, and, it provides a way to estimate the quality of the explanations.
TL;DR: A new learning methodology is defined that avoids building the initial fuzzy classifier but directly learns interval-valued fuzzy rules and allows one to represent each membership function using the most proper type of fuzzy set for the sake of modeling the uncertainty in the best possible manner.
TL;DR: An algorithm that is developed for handling multi-attribute decision-making problems based on the proposed q-rung orthopair uncertain linguistic interaction power partitioned Maclaurin Symmetric mean operators is reported.
Abstract: The q-rung orthopair uncertain linguistic set, which combines the q-rung orthopair fuzzy set and uncertain linguistic variable, can simultaneously represent the quantitative and qualitative information given by experts. In the procedure of addressing q-rung orthopair uncertain linguistic information, to eliminate extreme evaluation values for arguments and capture the multilayer heterogeneous relationship among the membership function and attributes, q-rung orthopair uncertain linguistic interaction power partitioned Maclaurin Symmetric mean operators are presented in this paper. Firstly, we introduce the interaction operational rules between q-rung orthopair uncertain linguistic sets. Then, we integrate the power average operator and partitioned Maclaurin Symmetric mean (PMSM) operator into a framework and present the power PMSM (PPMSM) operator. Furthermore, we embed the PPMSM operator into the q-rung orthopair uncertain linguistic sets based on the interaction operational laws and propose the q-rung orthopair uncertain linguistic interaction power partitioned Maclaurin Symmetric mean operator and its weighted form. Meanwhile, we analyze some properties and special cases of the proposed operators. Afterward, we report an algorithm that we developed for handling multi-attribute decision-making problems based on the proposed operator. Finally, we conduct case studies and comparison analysis over existing methods to demonstrate the effectiveness and superiority of the proposed algorithm.
TL;DR: In this paper, a general fuzzy logic-based approach is proposed for the analysis of experimental and numerical data in which the calibration of Chaboche-Lemaitre model hardening parameters of PA6 aluminum is considered.
Abstract: A very good knowledge of material properties is required in the analysis of severe plastic deformation problems in which the classical material processing methods are accelerated by the application of the additional cyclic load. A general fuzzy logic-based approach is proposed for the analysis of experimental and numerical data in this paper. As an application of the fuzzy analysis, the calibration of Chaboche–Lemaitre model hardening parameters of PA6 aluminum is considered here. The experimental data obtained in a symmetrical strain-controlled cyclic tension–compression test were used to estimate the material’s hardening parameters. The numerically generated curves were compared to the experimental ones. For better fitting of numerical and experimental results, the optimization approach using the least-square method was applied. Unfortunately, commonly accepted calibration methods can provide various sets of hardening parameters. In order to choose the most reliable set, the fuzzy analysis was used. Primarily selected values of hardening parameters were assumed to be fuzzy input parameters. The error of the hysteresis loop approximation for each set was used to compute its membership function. The discrete value of this error was obtained in the defuzzification step. The correct selections of hardening parameters were verified in ratcheting and mean stress relaxation tests. The application of the fuzzy analysis has improved the convergence between experimental and numerical stress–strain curves. The fuzzy logic allows analyzing the variation of elastic–plastic material response when some imprecisions or uncertainties of input parameters are taken into consideration.