Set Membership Research Articles

A Fuzzy Radial Basis Adaptive Inference Network and Its Application to Time-Varying Signal Classification.

A fuzzy radial basis adaptive inference network (FRBAIN) is proposed for multichannel time-varying signal fusion analysis and feature knowledge embedding. The model which combines the prior signal feature embedding mechanism of the radial basis kernel function with the rule-based logic inference ability of fuzzy system is composed of a multichannel time-varying signal input layer, a radial basis fuzzification layer, a rule layer, a regularization layer, and a T-S fuzzy classifier layer. The dynamic fuzzy clustering algorithm was used to divide the sample set pattern class into several subclasses with similar features. The fuzzy radial basis neurons (FRBNs) were defined and used as parameterized membership functions, and typical feature samples of each pattern subclass were used as kernel centers of the FRBN to realize the embedding of the diverse prior feature knowledge and the fuzzification of the input signals. According to the signal categories of FRBN kernel centers, nodes in the rule layer were selectively connected with nodes in the FRBN layer. A fuzzy multiplication operation was used to achieve synthesis of pattern class membership information and establishment of fuzzy inference rules. The excitation intensity of each rule was used as the input of T-S fuzzy classifier to classify the input signals. The FRBAIN can adaptively establish fuzzy set membership functions, fuzzy inference, and classification rules based on the learning of sample set, realize structural and data constraints of the model, and improve the modeling properties of imbalanced datasets. In this paper, the properties of FRBAIN were analyzed and a comprehensive learning algorithm was established. Experimental validation was performed with classification diagnoses from four complex cardiovascular diseases based on 12-lead ECG signals. Results demonstrated that, in the case of small-scale imbalanced datasets, the proposed method significantly improved both classification accuracy and generalizability comparing with other methods in the experiment.

Operator Splitting for a Homogeneous Embedding of the Linear Complementarity Problem

We present a first-order quadratic cone programming algorithm that can scale to very large problem sizes and produce modest accuracy solutions quickly. Our algorithm returns primal-dual optimal solutions when available or certificates of infeasibility otherwise. It is derived by applying Douglas--Rachford splitting to a homogeneous embedding of the linear complementarity problem, which is a general set membership problem that includes quadratic cone programs (QCPs) as a special case. Each iteration of our procedure requires projecting onto a convex cone and solving a linear system with a fixed coefficient matrix. If a sequence of related problems are solved, then the procedure can easily be warm-started and make use of factorization caching of the linear system. We demonstrate on a range of public and synthetic datasets that for feasible problems our approach tends to be somewhat faster than applying operator splitting directly to the QCP, and in cases of infeasibility our approach can be significantly faster than alternative approaches based on diverging iterates. The algorithm we describe has been implemented in C and is available open-source in the solver SCS v3.0.

Interior Design Scheme Recommendation Method Based on Improved Collaborative Filtering Algorithm

The recommendation engine is similar to the function of the product recommender in our real life, which provides great convenience for people to choose the appropriate decoration scheme in the process of interior design and decoration. A home improvement website or company can design a suitable recommendation algorithm to provide home improvement program recommendation services for users with decoration needs. After understanding the user behavior of the home decoration website, this paper proposes an interior design scheme recommendation method based on an improved collaborative filtering algorithm. The method designs a collaborative filtering algorithm that combines multilayer hybrid similarity and trust mechanisms. Fuzzy set membership function is introduced to correct users’ rating similarity, and users’ interest vector is extracted to calculate users’ preference for different types of items. The algorithm dynamically fuses those two aspects to obtain the mixed similarity of users; meanwhile, the user’s hybrid similarity and trust are fused in an adaptive model. Then, the user neighbor data set generated based on the overall similarity of users is used as a training set, taking the item scores and features into consideration. On the one hand, the users and the projects are taken into account as well. The final prediction score is more accurate, and the recommendation effect is better. The experimental results show that this method can recommend interior design schemes with high performance, and its performance is better than other methods.

Privacy-Enhancing Decentralized Anonymous Credential in Smart Grids

Decentralized Anonymous Credential (DAC) has posed enormous potential in smart grids for protecting user privacy (e.g. preventing user’s daily life from being sketched out). However, the existing DAC protocols still compromise user privacy for a full list of attributes are disclosed during showing credentials. In this paper, to construct a privacy-enhancing decentralized anonymous credential (PEDAC) protocol, we first design a more efficient range proof to hide user’s attributes. Specifically, we are inspired by Camenisch et al. (ASIACRYPT 2008), but replace their adopted Boneh-Boyen signature scheme with the Chinese standard SM2 signature scheme (incorporated in the ISO/IEC 14888-3) to propose pairing-free set membership and range proof protocols. These protocols can be executed non-interactively upon the Fiat-Shamir heuristic (INDOCRYPT 2012), and then be used to construct our PEDAC protocol. By compared with the protocols of Camenisch et al. (ASIACRYPT 2008) and Poelstra et al. (FC 2018), our proposed range proofs are with less communication and computation costs and hence more practical for constructing PEDAC protocols in smart grids.

Sparsity aware affine-projection-like filtering integrated with robust set membership and M-estimate approach for acoustic feedback cancellation in hearing aids

This paper introduces a new adaptive feedback cancellation technique for hearing aid employing robust upper error bound of set membership filtering in the M-estimate function and applied for affine-projection-like algorithm. Additionally a l1 norm based sparsity term is appended in the cost function which takes care of the convergence while estimating feedback path of the hearing aid exhibiting sparse characteristics. The proposed method of sparsity aware affine-projection-like robust set membership M-estimate (SAPL-RSM) filtering has been utilized for alleviating the impact of impulsive noise on the adaptation of feedback canceler’s weights. The SAPL-RSM technique is derived by minimizing a modified cost function involving M-estimate function constrained by a robust error bound and sparsity dependent penalty term with the motive of enhancing the convergence and lowering the computational expenses involved in the weight update process. The validation of the proposed method is carried out in the context of adaptive feedback cancellation in hearing aids. Simulations assess the efficacy of the proposed technique as an adaptive feedback canceler in terms of misalignment, added stable gain and sound quality deliverable at the user end.

Power‐control and speed‐control modes of a DFIG using adaptive sliding mode type‐2 neuro‐fuzzy for wind energy conversion system

This study proposes an adaptive sliding mode type-2 neuro-fuzzy control scheme for power-control and speed-control modes of doubly fed induction generator (DFIG). DFIG-based wind turbine system operates as variable-speed wind energy conversion system (WECS) with constant frequency. In the proposed controller design, a sliding mode control (SMC) strategy is used for online training of the parameters of type-2 fuzzy set (T2FS) membership functions. Due to the uncertainty of the wind speed and variation in parameters in the WECS, an interval T2FS is used in the proposed control scheme. Based on the controller inputs, the SMC adaptive strategy is used to tune the parameters of antecedent and consequent parts of T2FS. These inputs are active and reactive power and rotor speed errors and their time derivative. These inputs fed to the type-2 neuro-fuzzy system. The results of simulation for a 1.5 MW DFIG-based WECS are compared with the classical proportional–integral (PI) controller and type-1 neuro-fuzzy controller to validate the effectiveness of the proposed controller in power-control and speed-control regions. The results of simulation indicate that, in comparison to the PI and type-1 neuro-fuzzy controller, the proposed control scheme has better performance in both power-control and speed-control modes.

A new scoring system for the Rapid Entire Body Assessment (REBA) based on fuzzy sets and Bayesian networks

Traditional methods for assessing the risk of work-related musculoskeletal disorders (WMSDs) have a low sensitivity to changes in input variables. Using them, it is possible to obtain the same risk score for totally different postures, and in some cases, the effectiveness of ergonomic interventions cannot be demonstrated. This study aimed to develop a new scoring system for REBA, FBnREBA, using fuzzy sets and the Bayesian network (BN) approach to cover the drawbacks of the traditional REBA. First, the risk factors of WMSDs were defined in terms of fuzzy membership sets. Next, a BN model was developed based on REBA. Fourteen different postures were assessed using FBnREBA, and the results were compared with those of the original REBA. Lastly, a case study was performed to demonstrate how the new scoring system can be used to rank various interventions based on their effectiveness. FBnREBA is a BN model with 26 nodes and is based completely on REBA, but its results differ from those of REBA for identical postures. A comparison of the results of FBnREBA with those of REBA indicated that FBnREBA is more sensitive to changes in WMSDs risk factors than REBA. A case study was conducted using FBnREBA, and the effectiveness of modifying each body segment was determined and ranked. FBnREBA is more sensitive to changes in input variables so that it is unlikely to obtain the same risk score for different body postures. The introduced methodology can be used to modify the scoring systems of other similar methods.

Adaptive interpolating control for constrained systems with parametric uncertainty and disturbances

SummaryAn adaptive interpolating control (AIC) algorithm is proposed for constrained linear systems with parametric uncertainty and additive disturbance. This adaptive algorithm consists of an iterative set membership identification algorithm, which updates the uncertain parameter set at each time step, and an interpolating controller, which robustly stabilizes the uncertain system with state and input constraints. We prove that the AIC algorithm is recursively feasible and guarantees robust constraint satisfaction and robust asymptotic stability of the closed‐loop system in the presence of uncertainties. Moreover, we detail two possible extensions of the AIC algorithm: (a) persistent excitation conditions can be embedded into the AIC algorithm to accelerate the convergence of system parameters and (b) the combination of the AIC algorithm and aggressive learning is able to enlarge the size of the feasible region with every iteration by exploiting information from previous iterations. We illustrate the effectiveness of the proposed algorithms through comparisons with adaptive model predictive control and one example of mobile carrier robot.

Lazily Adapted Constant Kinky Inference for nonparametric regression and model-reference adaptive control

Techniques known as Nonlinear Set Membership prediction or Lipschitz Interpolation are approaches to supervised machine learning that utilise presupposed Lipschitz properties to perform inference over unobserved function values. Provided a bound on the true best Lipschitz constant of the target function is known a priori, they offer convergence guarantees, as well as bounds around the predictions. Considering a more general setting that builds on Lipschitz continuity, we propose an online method for estimating the Lipschitz constant online from function value observations that are possibly corrupted by bounded noise. Utilising this as a data-dependent hyper-parameter gives rise to a nonparametric machine learning method, for which we establish strong universal approximation guarantees. That is, we show that our prediction rule can learn any continuous function on compact support in the limit of increasingly dense data, up to a worst-case error that can be bounded by the level of observational error. We also consider applications of our nonparametric regression method to learning-based control. For a class of discrete-time settings, we establish convergence guarantees on the closed-loop tracking error of our online learning-based controllers. To provide evidence that our method can be beneficial not only in theory but also in practice, we apply it in the context of nonparametric model-reference adaptive control (MRAC). Across a range of simulated aircraft roll-dynamics and performance metrics our approach outperforms recently proposed alternatives that were based on Gaussian processes and RBF-neural networks.

Stable learned bloom filters for data streams

Bloom filter and its variants are elegant space-efficient probabilistic data structures for approximate set membership queries. It has been recently shown that the space cost of Bloom filters can be significantly reduced via a combination with pre-trained machine learning models, named Learned Bloom filters (LBF). LBF eases the space requirement of a Bloom filter by undertaking part of the queries using a classifier. However, current LBF structures generally target a static member set. Their performances would inevitably decay when there is a member update on the set, while this update requirement is not uncommon for real-world data streaming applications such as duplicate item detection, malicious URL checking, and web caching. To adapt LBF to data streams, we propose the Stable Learned Bloom Filters (SLBF) which addresses the performance decay issue on intensive insertion workloads by combining classifier with updatable backup filters. Specifically, we propose two SLBF structures, Single SLBF (s-SLBF) and Grouping SLBF (g-SLBF). The theoretical analysis on these two structures shows that the expected false positive rate (FPR) of SLBF is asymptotically a constant over the insertion of new members. Extensive experiments on real-world datasets show that SLBF introduces a similar level of false negative rate (FNR) but yields a better FPR/storage trade-off compared with the state-of-the-art (non-learned) Bloom filters optimized on data streams.

A Novel Intelligent System for Brain Tumor Diagnosis Based on a Composite Neutrosophic-Slantlet Transform Domain for Statistical Texture Feature Extraction.

Discrete wavelet transform (DWT) is often implemented by an iterative filter bank; hence, a lake of optimization of a discrete time basis is observed with respect to time localization for a constant number of zero moments. This paper discusses and presents an improved form of DWT for feature extraction, called Slantlet transform (SLT) along with neutrosophy, a generalization of fuzzy logic, which is a relatively new logic. Thus, a novel composite NS-SLT model has been suggested as a source to derive statistical texture features that used to identify the malignancy of brain tumor. The MR images in the neutrosophic domain are defined using three membership sets, true (T), false (F), and indeterminate (I); then, SLT was applied to each membership set. Three statistical measurement-based methods are used to extract texture features from images of brain MRI. One-way ANOVA has been applied as a method of reducing the number of extracted features for the classifiers; then, the extracted features are subsequently provided to the four neural network classification techniques, Support Vector Machine Neural Network (SVM-NN), Decision Tree Neural Network (DT-NN), K-Nearest Neighbor Neural Network (KNN-NN), and Naive Bayes Neural Networks (NB-NN), to predict the type of the brain tumor. Meanwhile, the performance of the proposed model is assessed by calculating average accuracy, precision, sensitivity, specificity, and Area Under the Curve (AUC) of the Receiver Operating Characteristic (ROC) curve. The experimental results demonstrate that the proposed approach is quite accurate and efficient for diagnosing brain tumors when the Gray Level Run Length Matrix (GLRLM) features derived from the composite NS-SLT technique is used.

Limited-complexity controller tuning: A set membership data-driven approach

Data-driven tuning is an alternative to model-based controller design where controllers are directly identified from data, avoiding a plant identification step. In this paper, an approach to tune limited-complexity controllers from data for linear systems is proposed. The controller is parametrized as a linear combination of a large set of basis functions and the proposed algorithm allows to select a sparse subset of bases, guaranteeing a bounded approximation error. A feasibility condition allows to adjust the trade-off between accuracy and sparsity. The controller design is performed by solving a set of linear programming problems, allowing to handle large data-sets. The proposed strategy is evaluated by means of a Monte-Carlo simulation experiment on a flexible transmission benchmark model. Results show that the proposed solution offers similar results than previous approaches for large data-sets, requiring less adjustable parameters. However, for reduced data-sets, the presented algorithm shows better performance than the compared approaches.

A Fuzzy Based Approach for Empirical Analysis of Unstructured Data

Computational intelligence and soft computing has many promising technologies such as Text Mining. Document Classification using soft computing techniques like fuzzy logic helps to find a more practical solution due to ambiguity and uncertainty present in the text data. Uncertainty and information may be reflected as the part and parcel of any industrial or engineering problem to be solved. Information refers to the facts required to solve it and uncertainty refers to the non-random lack of certainty (‘non-random uncertainty’), ambiguity, haziness in the system. It is very important to ponder on the nature of uncertainty involved in a problem. Father of fuzzy logic, Lofti Zadeh (1965) suggested that decision-making using set membership is the key when it is required to deal with uncertainty. Fuzzy clustering helps to identify patterns which are difficult to be discovered using crisp clustering. Natural languages contain non-random uncertainty. To deal with non-random uncertainty or different degrees of truth or partial truth Fuzzy logic may be used. This work focuses on fuzzy logic based approaches being utilized for identification of coherent patterns. Empirical Analysis are conducted to realize and evaluate the effect of the methodology proposed.

Air in industrial premises

The article considers a method for increasing the stability of air parameters in a limited space of the general production process using simulation methods in the environments of SolidWorks Flow Simulation HVAC Module Add-In and Matlab Simulink and Fuzzy Logic Toolbox. To select the simulation method, the models of Boussinesq, Spalart - Almaras, k - ω and k - ε; models, Reynolds, and the equations describing these models are considered. It is established that the most effective for the problem is the Navier-Stokes equation averaged by Reynolds. For the calculated ventilation system, as a result of simulation, we obtained the distribution of temperatures, air velocities, and temperatures of enclosing surfaces, floors, and objects. The results obtained were used to create a fuzzy controller. We obtained the set term and membership functions for input and output variables for four zones. The hierarchical structure consisting of three levels was used to implement the control process. Setting the FC parameters to the desired parameters is achieved by changing the dimension of the terms of the sets, the number and type of the membership function. An analytical description of the control method based on fuzzy logic is obtained. The control process is being carried out continuously in tracking mode. The results of experiments are submitted. The simulation showed that it is possible to stabilize the parameters in a given temperature range with a specified error.

Fuzzy Logic Approach to Determine the Optimum Nugget Production Capacity

This research aimed to present the Fuzzy approach in determining the optimal production capacity of the Nugget Production. The Fuzzy Model was developed by using two membership sets; i.e. the Overall Equipment Effectiveness (OEE) variable membership set of the production machine and Nugget Demand Forecasting. Nugget demand forecasting uses an exponential smoothing method due to its time-series type of query history data. OEE values were calculated using Availability, Performance and Quality Yield. In the Fuzzy approach, the Forecasting Membership Set uses the Triangular Membership Function type, and the OEE Membership Set uses the Trapezoidal Membership Function type. The fuzzy set model produced can be used as a tool for the company in determining the value of the Optimal Capacity production so that demands can be fulfilled and the product stocks decrease.

Uncovering hidden semantics of set information in knowledge bases

Knowledge Bases (KBs) contain a wealth of structured information about entities and predicates. This paper focuses on set-valued predicates, i.e., the relationship between an entity and a set of entities. In KBs, this information is often represented in two formats: (i) via counting predicates such as numberOfChildren and staffSize, that store aggregated integers, and (ii) via enumerating predicates such as parentOf and worksFor, that store individual set memberships. Both formats are typically complementary: unlike enumerating predicates, counting predicates do not give away individuals, but are more likely informative towards the true set size, thus this coexistence could enable interesting applications in question answering and KB curation.In this paper we aim at uncovering this hidden knowledge. We proceed in two steps. (i) We identify set-valued predicates from a given KB predicates via statistical and embedding-based features. (ii) We link counting predicates and enumerating predicates by a combination of co-occurrence, correlation and textual relatedness metrics. We analyse the prevalence of count information in four prominent knowledge bases, and show that our linking method achieves up to 0.55 F1 score in set predicate identification versus 0.40 F1 score of a random selection, and normalized discounted gains of up to 0.84 at position 1 and 0.75 at position 3 in relevant predicate alignments. Our predicate alignments are showcased in a demonstration system available at https://counqer.mpi-inf.mpg.de/spo.

Set Streams: Visual Exploration of Dynamic Overlapping Sets

AbstractIn many applications, membership of set elements changes over time. Since each element can be present in multiple sets, the sets also overlap. As a result, it becomes challenging to visualize the temporal change in set membership of elements across several timesteps while showing individual set intersections. We propose Set Streams, a visualization technique that represents changing set structures on a timeline as branching and merging streams. The streams encode the changing membership of elements with set intersections. A query‐based selection mechanism supports a flexible comparison of selected groups of elements across the temporal evolution. The main timeline view is complemented with additional panels to provide details about the elements. While the proposed visualization is an application‐independent visualization technique for dynamic sets, we demonstrate its effectiveness and applicability through three diverse application examples and expert feedback.

Design of experiments for nonlinear system identification: A set membership approach

Design of Experiments (DoE) is an important step in system identification. Regardless of the chosen model structure and identification method, the DoE quality determines an upper bound on the accuracy of the identified models. One of the greatest challenges in this context is to design an experiment which gives the maximum information about the dynamics of the system of interest. In this paper, a novel DoE algorithm for input-constrained MISO nonlinear systems, based on set membership identification, is proposed. The DoE algorithm is aimed to minimize the so-called radius of information, a quantity giving the worst-case model error. Two numerical examples are presented, showing the effectiveness of the approach and its potential in view of real-world applications.

Top-down resolution of lexico-semantic competition in speech production and the role of the left inferior frontal gyrus: an fMRI study

ABSTRACT Recent neurobiological speech production accounts propose the left inferior frontal gyrus (LIFG) resolves lexical competition using top-down control. The current fMRI experiment investigates whether response set membership influences LIFG involvement. In the picture-word interference paradigm target pictures were presented with distractor words that were, or were not, targets on other trials. Production models predict greater LIFG involvement in the high-coactivation trials with response set target-distractor pairs. Surprisingly, we found no effect of response set. Semantic interference elicited activation in the left posterior temporal cortex, similar to previous reports. Pooling data across response set conditions revealed additional significant activation in pars orbitalis of the LIFG, indicating detection benefited from the additional statistical power. Our findings challenge the co-activation assumption and indicate inconsistent LIFG results reported in the literature might reflect a combination of small effect size and low signal-to-noise, thus questioning the prominent role afforded to the LIFG.

The detection of multiple faults in a Bayesian setting using dynamic programming approaches

Inspired by the need for improving the reliability and safety of complex dynamic systems, this paper tackles the multiple faults detection problem using Dynamic Programming (DP) based methods under the Bayesian framework. These methods include (i) Maximum-A-Posteriori (MAP) estimator approach, (ii) Monte Carlo Markov Chain (MCMC) posteriors, (iii) Set Membership (SM) approach, (iv) probability of fault and (v) alternative methods. Using Bernoulli and Poisson priors, the Bayesian DP-type MAP estimate of all unknown parameters is presented. To derive the posterior distributions of Bayesian point estimations, the MCMC method is applied. For the SM approach, the Bayesian feasible parameter space is derived, as Bayesian confidence interval. The SM criteria are proposed to detect multiple faults which also reduces the Bayesian complexity of MAP estimator. For online fault detection, using the Bayesian model selection technique and the MAP estimator, the DP-based probability of faults is given, serving as a Bayesian early warning system. Since running DP algorithms is a time-consuming, alternative methods are also proposed using the modified MAP estimator. These methods use iterative approximations of MAP estimates, via the application of an iterative Expectation–Maximization algorithm technique. Numerical simulations are conducted and analysed to evaluate the performance of the proposed methods.