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This paper is concerned with the problem of event-triggered optimized control for uncertain nonlinear Itô-type stochastic systems with time-delay and unknown dynamic. By using fuzzy logic systems to approximate two unknown nonlinear functions with the delayed state and current state, respectively. The adaptive identifier is constructed to determine the stochastic system, and the optimized control is designed by using the identifier and adaptive dynamic programming (ADP) of actor-critic architecture. Almost all of the works are concentrated on ADP-based optimal control and it will inevitably cause the complexity of computation and requirements of persistence excitation (PE) assumption. In this paper, the ADP algorithm is obtained based on the negative gradient of a simple positive function (equivalent to the HJB equation), and so the proposed optimal control is simple and can release the PE assumption. Moreover, the event-triggered control approach is proposed to reduce computing burden and communication resources. Furthermore, we prove that the states of system and FLSs parameter errors are semi-globally uniformly ultimately bounded (SGUUB) in mean square via the adaptive identifier and the Lyapunov direct method as well as identifier-actor-critic architecture-based ADP algorithm. Finally, the effectiveness of the proposed method is illustrated through two numerical examples. [ABSTRACT FROM AUTHOR]

• A novel approach is discussed to incorporate fuzzy algorithm into a single board microcomputer based processor for intelligent relaying operation. • A fastest intelligent relaying algorithm reported by validating the same under IEEE 13 Bus test system with respect to performed simulation result analysis. • A proper validation of an idea authenticated based on distinguished result obtained from both the Fuzzy based as well as Non Fuzzy based systems. Protection and reliability enactment of electrical systems are important and emerging in power system research. Nowadays, it is very evident that the implementation of an intelligent algorithm is found in the field of substation equipment protection and relaying purposes. Majority of the researches are based on single load connected to a single feeder line and validated using simulation. A hardware based implementation and validation system will be an additional aspects. In this paper, we have discussed an expert system based intelligent relaying scheme by incorporating fuzzy algorithm in microcontroller. Purpose is to control the moving contacts of the breaker part for controlling multiple loads connected to a single feeder line. This paper reports the entire performance of intelligent relaying mechanism only considering stage - I with respect to non-fuzzy based relaying scheme and successfully achieved fastest coordination time after validating it under IEEE 13 Bus system. We have also validated the cascaded fuzzy based system and a non-fuzzy based system using ATMEL microcontroller. [ABSTRACT FROM AUTHOR]

In a type-2 fuzzy logic system, one of the important operations is to calculate the centroid of an interval type-2 fuzzy set (IT2 FS). In this paper, two novel algorithms called binary algorithms are proposed to calculate the centroid of IT2 FSs. Then, the outputs of the proposed binary algorithms are proven to be the optimal values. After analyzing the computational complexities of Karnik-Mendel (KM) algorithms, enhanced Karnik-Mendel (EKM) algorithms, enhanced iterative algorithms based on stopping condition (EIASC) algorithms and the proposed binary algorithms, it is found that the proposed binary algorithms are superior to the KM algorithms, EKM algorithms and EIASC algorithms. Finally, two extended binary algorithms are proposed to compute the centroid of an IT2 FS. The efficiencies of the proposed binary algorithms and extended binary algorithms are demonstrated by extensive simulations. [ABSTRACT FROM AUTHOR]

In this paper, optimization of a linear objective function subject to a generalized fuzzy relational inequalities is investigated in which an arbitrary continuous t-norm is considered as fuzzy composition, and fuzzy inequality replaces ordinary inequality in the constraints. Unlike most optimization algorithms, in fuzzy relational inequalities with fuzzy constraints (FRI-FC) we find a near-feasible solution having a better objective value than those resulting from the resolution of the similar problems with crisp (ordinary) inequality constraints. Such solutions are called super-optima in this paper. Subsequently, an algorithm is proposed to find a super-optimum with pre-specified desirable infeasibility. For this purpose, we firstly study some structural properties of the FRI-FC problem and present a new formulization that is independent of t-norms used in the constraints of the problem. This new formulation converts the primary problem into an equivalent problem with simple constraints without considering any penalty parameters. However, it is proved that the transformed equivalent problem enables our algorithm to distinguish unfavorable points and generate a sequence of solutions converging to a super-optimum under a certain sufficient condition. Finally, a modified PSO is presented in which the ability of PSO to solve unconstrained problems with continuous domain, the structure of the transformed problem and some fuzzy structural modifications are combined and form an efficient algorithm to solve the generalized FRI-FC problems. The modified PSO algorithm has been applied to the generalized FRI-FC problem defined with ten well-known continuous t-norms. Additionally, an idea of the FRI-FC problems as outer approximators for FRI problems with ordinary inequalities is also investigated. [ABSTRACT FROM AUTHOR]

Rule learning is a special type of machine learning approaches, and its key advantage is the generation of interpretable models, which provides a transparent process of showing how an input is mapped to an output. Traditional rule learning algorithms are typically based on Boolean logic for inducing rule antecedents, which are very effective for training models on data sets that involve discrete attributes only. When continuous attributes are present in a data set, traditional rule learning approaches need to employ crisp intervals. However, in reality, problems usually show shades of grey, which motivated the development of fuzzy rule learning approaches by employing fuzzy intervals for handling continuous attributes. While a data set contains a large portion of discrete attributes or even no continuous attributes, fuzzy approaches cannot be used to learn rules effectively, leading to a drop in the performance. In this paper, a multi-stage approach of mixed rule learning is proposed, which involves strategic combination of both traditional and fuzzy approaches to handle effectively various types of attributes. We compare our proposed approach with existing algorithms of rule learning. Our experimental results show that our proposed approach leads to significant advances in the performance compared with the existing algorithms. [ABSTRACT FROM AUTHOR]

In this paper we introduce a classifier named TEDAClass (Typicality and Eccentricity based Data Analytics Classifier) which is based on the recently proposed AnYa type fuzzy rule based system. Specifically, the rules of the proposed classifier are defined according to the recently proposed TEDA framework. This novel and efficient systematic methodology for data analysis is a promising addition to the traditional probability as well as to the fuzzy logic. It is centred at non-parametric density estimation derived from the data sample. In addition, the proposed framework is computationally cheap and provides fast and exact per-point processing of the data set/stream. The algorithm is demonstrated to be suitable for different classification tasks. Throughout the paper we give evidence of its applicability to a wide range of practical problems. Furthermore, the algorithm can be easily adapted to different classical data analytics problems, such as clustering, regression, prediction, and outlier detection. Finally, it is very important to remark that the proposed algorithm can work “from scratch” and evolve its structure during the learning process. [ABSTRACT FROM AUTHOR]

Abstract Fuzzy objective relation systems are an important class of datasets that are generalizations of many types of decision tables. This paper proposes an approach, based on relation systems and fuzzy sets, to reduce data redundancy in fuzzy objective relation systems. We study lower and upper approximation reductions of a relation system for a given fuzzy set. As a generalization of such reductions, we consider lower and upper approximation reductions of fuzzy objective relation systems and give their corresponding reduction algorithms using methods based on the discernibility matrix. We note that the usual positive region reduction for a decision table can be considered a special case of our lower approximation reduction. Finally, we provide two examples from the UCI datasets to verify our theoretical results. These results can help in the decision making analysis of fuzzy objective relation systems. [ABSTRACT FROM AUTHOR]

It is well known that one of the basic advantages of evolutionary programming is in deciding the most suitable place for breeding offspring and finding the route toward the global minimum. To reach this goal, the algorithm needs to estimate the coordinates of the global minimum and then steer the new point toward it. In this paper, the estimation of the global minimum is calculated by weighted mean coordination of individuals (WMP), and then a road is mapped between the coordinates of the parents and the WMP. In the proposed method, fuzzy logic is used for deciding on the road and the best coordination to breed offspring. The proposed algorithm is tested on 65 well-known cost functions and is compared with five algorithms inside the EP family. In the next section of the paper, the algorithm is tested on the high-dimensional problem of modeling ozone layer data, which includes almost 26,000 unknown parameters. The results demonstrate the capability of the proposed method in having acceptable speed and accuracy. [ABSTRACT FROM AUTHOR]

“ Fuzzy Theoretic Approach to Signals and Systems ” assumes all system variables and parameters as uncertain (i.e. being characterized by membership functions), develops a mathematical theory for analytically determining the membership functions on system variables and parameters, derives algorithms for estimating the parameters of membership functions, and establishes robustness and convergence properties of the estimation algorithms. The membership functions are analytically determined via solving a variational optimization problem that maximizes the “ over-uncertainties-averaged-log-membership ” of the observed data around an initial guess. This paper develops the analytical fuzzy theory for the particular case of a multi-input single-output static system affected by noises. The theory facilitates designing an adaptive filtering algorithm. The robustness of the adaptive filtering algorithm is proved theoretically via a mathematical analysis. Numerical experiments further demonstrate the robustness of the filtering algorithm. A comparison of the algorithm with the state-of-art methods is made using the practical biomedical applications related to the modeling and analysis of heart rate signals for assessing the physiological state of an individual. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to extend a methodology for solving multi-objective linear programming (MOLP) problems, when the objective functions and constraints coefficients are stated as interval numbers. Design/methodology/approach – The approach proposed in this paper for the considered problem is based on the maximization of the sum of membership degrees which are defined for each objective of multi objective problem. These membership degrees are constructed based on the deviation from optimal solutions of individual objectives. Then, the final model based on membership degrees is itself an interval linear programming which can be solved by current methods. Findings – The efficiency of the solutions obtained by the proposed method is proved. It is shown that the obtained solution by the proposed method for an interval multi objective problem is Pareto optimal. Research limitations/implications – The proposed method can be used in modeling and analyzing of uncertain systems which are modeled in the context of multi objective problems and in which required information is ill defined. Originality/value – The paper proposed a novel and well-defined algorithm to solve the considered problem. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to present a new methodology for identification of the parameters of the local linear Takagi-Sugeno fuzzy models using weighted recursive least squares. The weighted recursive least squares (WRLS) is sensitive to initialization which leads to no converge. In order to overcome this problem, Euclidean particle swarm optimization (EPSO) is employed to optimize the initial states of WRLS. Finally, validation results are given to demonstrate the effectiveness and accuracy of the proposed algorithm. A comparative study is presented. Validation results involving simulations of numerical examples and the liquid level process have demonstrated the practicality of the algorithm. Design/methodology/approach – A new method for nonlinear system modelling. The proposed algorithm is employed to optimize the initial states of WRLS algorithm in two phases of learning algorithm. Findings – The results obtained using this novel approach were comparable with other modeling approaches reported in the literature. The proposed algorithm is able to handle various types of modeling problems with high accuracy. Originality/value – In this paper, a new method is employed to optimize the initial states of WRLS algorithm in two phases of the learning algorithm. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to present an implementation of a soft-computing (SC) based navigation approach on a bi-steerable mobile robot, Robucar. This approach must provide Robucar with capability to acquire the obstacle avoidance, target localization, decision-making and action behaviors after learning and adaptation. This approach uses three neural networks (NN) and fuzzy logic (FL) controller to achieve the desired task. The NNs corresponding to the obstacle avoidance and target localization are trained using the back-propagation algorithm and the last one is based on the reinforcement learning paradigm while the FL controller uses the Mamdani search and match algorithm. Simulation and experimental results are presented, showing the effectiveness of the overall navigation control system. Design/methodology/approach – In this paper, an interesting navigation approach is applied to a car-like robot, Robucar, with addition of an action behavior to deal with the generation of smooth motions. Indeed, this approach is based on four basic behaviors; three of them are fused under a neural paradigm using Gradient Back-Propagation (GBP) and reinforcement learning (RL) algorithms and the last behavior uses a FL controller. It uses a set of suggested rules to describe the control policy to achieve the action behavior. Findings – In the implemented SC-based navigation, the intelligent behaviors necessary to the navigation are acquired by learning using GBP algorithm and adaptation using FL. The proposed approach provides Robucar with more autonomy, intelligence and real-time processing capabilities. Indeed, the proposed NNs and FLC are able to remedy problems of analytical approaches, missing or incorrect environment knowledge and uncertainties which can lead to undesirable effects as the rough velocity changes. The simulation and experimental results display the ability of the proposed SC-based navigation approach to provide Robucar with capability to intelligently navigate in a priori unknown environment, illustrating the robustness and adaptation capabilities of the approach. Research limitations/implications – This work can be extended to consider mobile obstacles with a velocity higher than the velocity of the robot. Originality/value – This paper presents a learning approach to navigating a bi-steerable mobile robot in an unknown environment using GBP and RL paradigms. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to present a more objective evaluation method for a mining area ecological environment. It proposes the weight of indices with respect to the total goal, and provides a new evaluation method which generalizes the weighted-average method. Design/methodology/approach – First, the authors describe the evaluation grades by fuzzy variables in credibility space, and the degree of an index belonging to a grade is transformed to be the credibility measure of a fuzzy event by the credibility inversion theorem. Second, a new algorithm which generalizes the weighted-average method is proposed to realize the transformation from the credibility degree of the underlying indices to the credibility degree of the total target. Findings – The method proposed in this paper can obtain the correct results illustrated with a numerical evaluation example. The comparison with two other methods shows that the proposed method has stronger classification ability. Originality/value – The new method presented in this paper generalizes the weighted-average method, and provides methods for other evaluation systems with a hierarchical structure. [ABSTRACT FROM AUTHOR]

This paper investigates the group decision making (GDM) problems with interval-valued Atanassov intuitionistic fuzzy preference relations (IV-AIFPRs) and develops a novel method for solving such problems. A new consistency index of an Atanassov intuitionistic fuzzy preference relation (AIFPR) is introduced to judge the consistency of an AIFPR and then a convergent iterative Algorithm I is designed to repair the consistency of an AIFPR with unacceptable consistency. Subsequently, the consistency and acceptable consistency of an IV-AIFPR are defined through separating an IV-AIFPR into two AIFPRs. Based on Algorithm I, a new iterative Algorithm II is devised to repair the consistency of an IV-AIFPR with unacceptable consistency. Afterwards, to determine decision makers’ (DMs’) weights objectively, an optimization model is established by minimizing the deviations between each individual IV-AIFPR and the collective one. This model is skillfully transformed into a linear goal program to resolve sufficiently considering different principles of decision making. A linear program is built to derive interval-valued Atanassov intuitionistic fuzzy (IVAIF) priority weights of alternatives. Then, a TOPSIS (technique for order performance by similarity to an ideal solution) based approach is proposed to rank such IVAIF priority weights. Thereby, a method for GDM with IV-AIFPRs is put forward. At length, a practical example of a virtual enterprise partner selection is provided to illustrate the feasibility and validity of the proposed method. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to attempt to propose a method based on evidential reasoning for hybrid grey attribute decision-making problems where the attribute weights are partially known, in which the attribute values are interval grey numbers and linguistic grades. Design/methodology/approach – The method is that the decision-maker gives whitenization of each interval grey number based on their preference and belief structure of the form of qualitative attribute values, whitenization of quantitative attributes can be equivalently expressed in the form of belief structure with the principle of utility value equivalence, and then the grade belief structure decision matrix can be determined. By using the analytical evidential reasoning algorithm, belief degrees of each alternative belonging to each linguistic grade are obtained. Two pairs of nonlinear optimization models which are solved by genetic algorithms (GA) are constructed to compute the maximum and the minimum expected utilities of each alternative, respectively. Findings – The results show that decision-maker based on his/her risk preference gives whitenization of each interval grey number and selects corresponding alternative policy. Practical implications – The method exposed in the paper can be used to deal with problems of grey multiple attribute decision making and hybrid grey multiple attribute decision making. Originality/value – The paper succeeds in constructing two pairs of nonlinear optimization models based on the analytical evidential reasoning algorithm which are solved by genetic algorithms and the hybrid grey multiple attribute decision-making approach with partial weight information. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to attempt to realize a distribution network optimization in supply chain using grey systems theory for uncertain information. Design/methodology/approach – There is much uncertain information in the distribution network optimization of supply chain, including fuzzy information, stochastic information and grey information, etc. Fuzzy information and stochastic information have been studied in supply chain, however grey information of the supply chain has not been covered. In the distribution problem of supply chain, grey demands are taken into account. Then, a mathematics model with grey demands has been constructed, and it can be transformed into a grey chance-constrained programming model, grey simulation and a proposed hybrid particle swarm optimization are combined to resolve it. An example is also computed in the last part of the paper. Findings – The results are convincing: not only that grey system theory can be used to deal with grey uncertain information about distribution of supply chain, but grey chance-constrained programming, grey simulation and particle swarm optimization can be combined to resolve the grey model. Practical implications – The method exposed in the paper can be used to deal with distribution problems with grey information in the supply chain, and network optimization results with a grey uncertain factor could be helpful for supply chain efficiency and practicability. Originality/value – The paper succeeds in realising both a constructed model of the distribution of supply chain with grey demands and a solution algorithm of the grey mathematics model by using one of the newest developed theories: grey systems theory. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a fuzzy wavelet network is proposed to approximate arbitrary nonlinear functions based on the theory of multiresolution analysis (MRA) of wavelet transform and fuzzy concepts. The presented network combines TSK fuzzy models with wavelet transform and ROLS learning algorithm while still preserve the property of linearity in parameters. In order to reduce the number of fuzzy rules, fuzzy clustering is invoked. In the clustering algorithm, those wavelets that are closer to each other in the sense of the Euclidean norm are placed in a group and are used in the consequent part of a fuzzy rule. Antecedent parts of the rules are Gaussian membership functions. Determination of the deviation parameter is performed with the help of gold partition method. Here, mean of each function is derived by averaging center of all wavelets that are related to that particular rule. The overall developed fuzzy wavelet network is called fuzzy wave-net and simulation results show superior performance over previous networks. The present work is complemented by a second part which focuses on the control aspects and to be published in this journal(). This paper proposes an observer based self-structuring robust adaptive fuzzy wave-net (FWN) controller for a class of nonlinear uncertain multi-input multi-output systems. [Copyright &y& Elsevier]

Purpose - The purpose of this paper is to consider the process of design and implementation of an enhanced fuzzy H8 (EFH8) estimation algorithm to determine the attitude and heading angles of ground vehicles, which are frequently affected by considerable exogenous disturbances. To detect the changes of disturbances, a fuzzy system is designed based on expert knowledge and experiences of a navigation engineer. In the EFH8 estimator, the intensity bounds of disturbances affecting the measurements are updated using a heuristic combination of three change-detection indices. Performance of the proposed estimator is evaluated by Monte-Carlo simulations and field tests of three kinds of vehicles using a manufactured attitude-heading reference system (AHRS). In both simulations and real tests, the proposed estimator results in a superior performance compared to those of the recently developed and standard H8 estimators. Design/methodology/approach - Design, implementation and real tests of the EFH8 estimator are considered for an AHRS specialized for vehicular applications. In the AHRS, three-axis accelerometers (TAA) and three-axis magnetometers (TAM) may be affected by large disturbances due to non-gravitational accelerations and local magnetic fields. Therefore, the design parameters of EFH8 estimator including the theoretic bound of disturbance intensity and the attenuation level are adaptively tuned using a fuzzy combination of three change-detection indices. Once a sensor is affected by an exogenous disturbance, the fuzzy system will increase the scale factor of the corresponding measurement disturbance to place more confidence on the data of the AHRS dynamics including measurements of gyros with respect to the data coming from the TAA and TAM. Findings - An intelligent fault detector is proposed for considering changes of disturbances to adjust the upper bounds of the estimator''s disturbances and the length of data to update the fuzzy system inputs. The EFH8 estimator is suitable to attenuate the effects of disturbances changes on accurate estimation of the attitude and heading angles, intelligently. Originality/value - The paper provides a fuzzy state estimator for adaptively adjusting the theoretic disturbance matrices according to the actual intensity of the disturbances affecting the AHRS dynamics and the measurement sensors. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to show that exploiting fundamental ideas of granular computing can lead to further conceptual developments of granular metastructures, which are inherently associated with computing involving a large number of individual datasets; and to show that such processing leads to the representatives of information granules and granular models in the form of metastructures and metamodels. Design/methodology/approach – The formulation of the concept of granular metastructures is provided and presented along with some essential algorithmic developments and associated optimization strategies. The overall methodological framework is the one of granular computing, especially fuzzy sets and fuzzy sets of higher type. Given the structural facet of optimization, the paper stresses the relevance of the use of evolutionary optimization. Findings – This paper focused on the underlying concepts and while it elaborated on some development aspects and optimization tools, it should be stressed that further refinement and a thorough exploitation of optimization techniques in application to the inherently combinatorial facet of the problem are to be pursued in detail. Practical implications – The introduced approach and algorithms could be of interest when solving problems of granular metastructures, in particular those encountered in knowledge-based systems. Originality/value – The main aspects of originality concern a formulation of the concept of granular metastructures and their design, based on granular evidence (experimental data) of lower type. A constructive way of forming type-2 fuzzy sets via the principle of justifiable granularity exhibits a significant level of originality and offers a general way of designing information granules. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a hybrid method for identification of Pareto-optimal fuzzy classifiers (FCs). In contrast to many existing methods, the initial population for multiobjective evolutionary algorithms (MOEAs) is neither created randomly nor a priori knowledge is required. Instead, it is created by the proposed two-step initialization method. First, a decision tree (DT) created by C4.5 algorithm is transformed into an FC. Therefore, relevant variables are selected and initial partition of input space is performed. Then, the rest of the population is created by randomly replacing some parameters of the initial FC, such that, the initial population is widely spread. That improves the convergence of MOEAs into the correct Pareto front. The initial population is optimized by NSGA-II algorithm and a set of Pareto-optimal FCs representing the trade-off between accuracy and interpretability is obtained. The method does not require any a priori knowledge of the number of fuzzy sets, distribution of fuzzy sets or the number of relevant variables. They are all determined by it. Performance of the obtained FCs is validated by six benchmark data sets from the literature. The obtained results are compared to a recently published paper [H. Ishibuchi, Y. Nojima, Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning, International Journal of Approximate Reasoning 44 (1) (2007) 4–31] and the benefits of our method are clearly shown. [Copyright &y& Elsevier]

Purpose - The paper seeks to provide an adaptive fuzzy logic controller for permanent magnet synchronous motor (PMSM) under direct torque control (DTC) algorithm to minimize the torque ripple. Design/methodology/approach - The design methodology is based on vector control analysis. MATLAB simulations supported with experimental study under C++ are used to execute the proposed work. Findings - The results show that considerable torque ripple reduction as well as considerable current ripple reduction can be achieved by utilizing adaptive fuzzy switching algorithm to fire the inverter supplying the PMSM. Research limitations/implications - This research is limited to PMSM, however the research can be extended to include other AC motors as well. In addition, the following points can be studied, the effects of harmonics in control signals on the torque ripple. Digital and active filters as solution to these harmonics can be also addressed. The actual mathematical relation between the torque ripple and flux ripple can be studied to set the flux and torque bands width in reasonable value. Practical implications - Based on existence DTC control system, it is only required to change the software-switching algorithm, to provide smooth torque, given that the switching frequency of the inverter module is more than or equal to 15?kHz and the system is supplied with timers. In addition, a relatively higher DC voltage may be required to achieve higher speed compared with the traditional DTC. Originality/value - In this paper, the stator flux position, and errors due to deviations from reference values of the torque and stator flux are used to select two active vectors while at the same time the absolute value of the torque error and the stator flux position are fuzzified to adapt the switching of the inverter in order to control the applied average voltage level in such a way as to minimize the torque ripple, so instead of fixed time table structure, a fuzzy logic is used to calculate the switching time for the selected vectors and no PI controller is used as the case in the traditional-space vector modulation. This work is directed to motor drive system designers who seek highly smooth torque performance with fast response. [ABSTRACT FROM AUTHOR]

Abstract: This paper discusses the full implication inference of fuzzy reasoning. For all residuated implications induced by left continuous t-norms, unified α-triple I algorithms are constructed to generalize the known results. As the corollaries of the main results of this paper, some special algorithms can be easily derived based on four important residuated implications. These algorithms would be beneficial to applications of fuzzy reasoning. Based on properties of residuated implications, the proofs of the many conclusions are greatly simplified. [Copyright &y& Elsevier]

Abstract: The major contribution of fuzzy set theory lies in its capability of representing vague data. Fuzzy logic offers a systematic base to deal with situations, which are ambiguous or not well defined. In the literature, there exist few papers on fuzzy control charts, which use defuzziffication methods in the early steps of their algorithms. The use of defuzziffication methods in the early steps of the algorithm makes it too similar to the classical analysis. Linguistic data in those works are transformed into numeric values before control limits are calculated. Thus both control limits as well as sample values become numeric. In this paper, some contributions to fuzzy control charts based on fuzzy transformation methods are made by the use of α-cut to provide the ability of determining the tightness of the inspection: the higher the value of α the tighter inspection. A new alternative approach “Direct Fuzzy Approach (DFA)” is also developed in this paper. In contrast to the existing fuzzy control charts, the proposed approach is quite different in the sense it does not require the use of the defuzziffication. This prevents the loss of information included by the samples. It directly compares the linguistic data in fuzzy space without making any transformation. We use some numeric examples to illustrate the performance of the method and interpret its results. [Copyright &y& Elsevier]

In this paper we extend our previous results on sets of graded attribute implications with witnessed non-redundancy. We assume finite residuated lattices as structures of truth degrees and use arbitrary idempotent truth-stressing linguistic hedges as parameters which influence the semantics of graded attribute implications. In this setting, we introduce algorithm which transforms any set of graded attribute implications into an equivalent non-redundant set of graded attribute implications with saturated consequents whose non-redundancy is witnessed by antecedents of the formulas. As a consequence, we solve the open problem regarding the existence of general systems of pseudo-intents which appear in formal concept analysis of object-attribute data with graded attributes and linguistic hedges. Furthermore, we show a polynomial-time procedure for determining bases given by general systems of pseudo-intents from sets of graded attribute implications which are complete in data. [ABSTRACT FROM AUTHOR]

In this paper, a novel fuzzy sliding mode control (FSMC) guidance law with terminal constraints of miss distance, impact angle and acceleration is presented for a constant speed missile against the stationary or slowly moving target. The proposed guidance law combines the sliding mode control algorithm with a fuzzy logic control scheme for the lag-free system and the first-order lag system. Through using Lyapunov stability theory, we prove the sliding surface converges to zero in finite time. Furthermore, considering the uncertain information and system disturbances, the guidance gains are on-line optimized by fuzzy logic technique. Numerical simulations are performed to demonstrate the performance of the FSMC guidance law and the results illustrate the validity and effectiveness of the proposed guidance law. [ABSTRACT FROM AUTHOR]

This paper attempts to provide a new solution to the model approximation problem for dynamic systems with time-varying delays under the fuzzy framework. For a given high-order system, our focus is on the construction of a reduced-order model, which approximates the original one in a prescribed error performance level and guarantees the asymptotic stability of the corresponding error system. Based on the reciprocally convex technique, a less conservative stability condition is established for the dynamic error system with a given error performance index. Furthermore, the reduced-order model is eventually obtained by applying the projection approach, which converts the model approximation into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Traditional c-means clustering partitions a group of objects into a number of non-overlapping sets. Rough sets provide more flexible and objective representation than classical sets with hard partition and fuzzy sets with subjective membership function for a given dataset. Rough c-means clustering and its extensions were introduced and successfully applied in many real life applications in recent years. Each cluster is represented by a reasonable pair of lower and upper approximations. However, the most available algorithms pay no attention to the influence of the imbalanced spatial distribution within a cluster. The limitation of the mean iterative calculation function, with the same weight for all the data objects in a lower or upper approximation, is analyzed. A hybrid imbalanced measure of distance and density for the rough c-means clustering is defined, and a modified rough c-means clustering algorithm is presented in this paper. To evaluate the proposed algorithm, it has been applied to several real world data sets from UCI. The validity of this algorithm is demonstrated by the results of comparative experiments. [ABSTRACT FROM AUTHOR]

This paper presents a complex-valued interval type-2 neuro-fuzzy inference system (CIT2FIS) and derive its metacognitive projection-based learning (PBL) algorithm. Metacognitive CIT2FIS (Mc-CIT2FIS) consists of a CIT2FIS, which realizes Takagi-Sugeno-Kang type inference mechanism, as its cognitive component. A PBL with self-regulation is its metacognitive component. The rules of CIT2FIS employ interval type- \(2~q\) -Gaussian membership functions that can represent different radial basis functions for different values of \(q\) . As each sample is presented to the network, the metacognitive component monitors the hinge-loss error and class-specific knowledge potential of the current sample to efficiently decide on what-to-learn, when-to-learn, and how-to-learn it. When a new rule is added or existing rules are updated, the optimal parameters of CIT2FIS corresponding to the minimum of the hinge-loss error function are computed using a PBL algorithm derived using the Wirtinger calculus. The performance of Mc-CIT2FIS is evaluated on a set of benchmark real-valued classification problems from the UCI machine learning repository. A circular transformation is used to convert the real-valued features to the complex-valued features in these problems. The performance comparison and statistical study clearly show the superior classification ability of Mc-CIT2FIS. Finally, the proposed complex-valued network is used to solve a practical human action recognition problem that is represented by complex-valued optical flow-based feature set, and a human emotion recognition problem represented using complex-valued Gabor filter-based features. The performance results on these problems substantiate the superior classification ability of Mc-CIT2FIS. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we have proposed two extensions to pixon-based image modeling. The first one is using bicubic interpolation instead of bilinear interpolation and the second one is using fuzzy filtering method, aiming to improve the quality of the pixonal image. Finally, partial differential equations (PDEs) are applied on the pixonal image for noise removing. The proposed algorithm has been examined on variety of standard images and their performance compared with the existing algorithms. Experimental results show that in comparison with the other existing methods, the proposed algorithm has a better performance in denoising and preserving image edges. [Copyright &y& Elsevier]

Abstract: In this paper, a hybrid of algorithms for electromagnetism-like mechanisms (EM) and particle swarm optimisation (PSO), called HEMPSO, is proposed for use in designing a functional-link-based Petri recurrent fuzzy neural system (FLPRFNS) for nonlinear system control. The FLPRFNS has a functional link-based orthogonal basis function fuzzy consequent and a Petri layer to eliminate the redundant fuzzy rule for each input calculation. In addition, the FLPRFNS is trained by the proposed hybrid algorithm. The main innovation is that the random-neighbourhood local search is replaced by a PSO algorithm with an instant-update strategy for particle information. Each particle updates its information instantaneously and in this way receives the best current information. Thus, HEMPSO combines the advantages of multiple-agent-based searching, global optimisation, and rapid convergence. Simulation results confirm that HEMPSO can be used to perform global optimisation and offers the advantage of rapid convergence; they also indicate that the FLPRFNS exhibits high accuracy. [Copyright &y& Elsevier]

Abstract: A considerable amount of twig pattern matching algorithms have been proposed to holistically process a twig query. Those algorithms mainly focus on twig pattern query with the AND-logic. However, there is often a need to process a twig query with the OR-predicates. Furthermore, the existing algorithms fall short in their ability to support twig query with OR-logic in fuzzy XML. To overcome this limitation, in this paper, we first introduce a novel encoding scheme to represent node information in fuzzy XML. Based on the encoding scheme, we then propose an effective algorithm for matching a twig pattern query with the AND/OR-logic in fuzzy XML. Our approach adopts a compact stack technique to process the complicated twig query consisting of both AND-logic and OR-logic. More importantly, our method eliminates re-scanning unnecessary portions of XML documents and redundant intermediate results. Finally, the experimental results demonstrate the performance advantages of our approach. [Copyright &y& Elsevier]

Abstract: This paper presents a real-time segmentation algorithm to obtain moving objects from the H.264 compressed domain. The proposed segmentation works with very little information and is based on two features of the H.264 compressed video: motion vectors associated to the macroblocks and decision modes. The algorithm uses fuzzy logic and allows to describe position, velocity and size of the detected regions in a comprehensive way, so the proposed approach works with low level information but manages highly comprehensive linguistic concepts. The performance of the algorithm is improved using dynamic design of fuzzy sets that avoids merge and split problems. Experimental results for several traffic scenes demonstrate the real-time performance and the encouraging results in diverse situations. [Copyright &y& Elsevier]

Abstract: This paper is directed towards an infrastructure for handling both uncertainty and vagueness in the Rules, Logic, and Proof layers of the Semantic Web. More concretely, we present probabilistic fuzzy description logic programs, which combine fuzzy description logics, fuzzy logic programs (with stratified default-negation), and probabilistic uncertainty in a uniform framework for the Semantic Web. We define important concepts dealing with both probabilistic uncertainty and fuzzy vagueness, such as the expected truth value of a crisp sentence and the probability of a vague sentence. Furthermore, we describe a shopping agent example, which gives evidence of the usefulness of probabilistic fuzzy description logic programs in realistic Web applications. We also provide algorithms for query processing in probabilistic fuzzy description logic programs, and we delineate a special case where query processing can be done in polynomial time in the data complexity. [Copyright &y& Elsevier]

Abstract: This paper concerns a class of maximum covering location problems in networks in uncertain environments. It is assumed that (a) relative weights of demand nodes are either deterministic or imprecise, described by linguistic expressions and (b) potential facility site locations are limited to network nodes. The concept of coverage is extended to include a degree of node coverage which means that the borders between the subset of covered demand nodes and the subset of uncovered demand nodes are inexact. The acceptable service distance/travelling times from a facility site to demand nodes are modelled by fuzzy sets. Three new algorithms for choosing the best facility locations are developed which assume that (1) demands at all nodes are equally important, (2) relative weights of demand at nodes are deterministic and (3) weights of demand at nodes are imprecise and described by linguistic terms, respectively. The algorithms are based on searching among potential facility nodes by applying comparison operations on discrete fuzzy sets. It is shown how to extend the proposed algorithms from one-site to multi-site covering problems. Illustrative examples of selecting locations for logistics centres in a distribution company are given. [Copyright &y& Elsevier]

Abstract: Algorithms for preprocessing databases with incomplete and imprecise data are seldom studied. For the most part, we lack numerical tools to quantify the mutual information between fuzzy random variables. Therefore, these algorithms (discretization, instance selection, feature selection, etc.) have to use crisp estimations of the interdependency between continuous variables, whose application to vague datasets is arguable. In particular, when we select features for being used in fuzzy rule-based classifiers, we often use a mutual information-based ranking of the relevance of inputs. But, either with crisp or fuzzy data, fuzzy rule-based systems route the input through a fuzzification interface. The fuzzification process may alter this ranking, as the partition of the input data does not need to be optimal. In our opinion, to discover the most important variables for a fuzzy rule-based system, we want to compute the mutual information between the fuzzified variables, and we should not assume that the ranking between the crisp variables is the best one. In this paper we address these problems, and propose an extended definition of the mutual information between two fuzzified continuous variables. We also introduce a numerical algorithm for estimating the mutual information from a sample of vague data. We will show that this estimation can be included in a feature selection algorithm, and also that, in combination with a genetic optimization, the same definition can be used to obtain the most informative fuzzy partition for the data. Both applications will be exemplified with the help of some benchmark problems. [Copyright &y& Elsevier]

Abstract: This paper proposed an algorithm to design a fuzzy classification system based on immune principles. The proposed algorithm evolves a population of antibodies based on the clonal selection and hypermutation principles. The membership function parameters and the fuzzy rule set including the number of rules inside it are evolved at the same time. Each antibody (candidate solution) corresponds to a fuzzy classification rule set. We compared our algorithm with other classification schemes on some benchmark datasets. The results demonstrated the effectiveness of the proposed immune algorithm. [Copyright &y& Elsevier]

Abstract: Evolutionary structural design has been the topic of much recent research; however, such designs are usually hampered by the time-consuming stage of prototype evaluations using standard finite element analysis (FEA). Replacing the time-consuming FEA by neural network approximations may be a computationally efficient alternative, but the error in such approximation may misguide the optimization procedure. In this paper, a multi-objective meta-level (MOML) soft computing-based evolutionary scheme is proposed that aims to strike a balance between accuracy vs. computational efficiency and exploration vs. exploitation. The neural network (NN) is used here as a pre-filter when fitness is estimated to be of lesser significance while the standard FEA is used for solutions that may be optimal in their current population. Furthermore, a fuzzy controller updates parameters of the genetic algorithm (GA) in order to balance exploitation vs. exploration in the search process, and the multi-objective GA optimizes parameters of the membership functions in the fuzzy controller. The algorithm is first optimized on two benchmark problems, i.e. a 2-D Truss frame and an airplane wing. General applicability of the resulting optimization algorithm is then tested on two other benchmark problems, i.e. a 3-layer composite beam and a piezoelectric bimorph beam. Performance of the proposed algorithm is compared with several other competing algorithms, i.e. a fuzzy-GA–NN, a GA–NN, as well as a simple GA that only uses only FEA, in terms of both computational efficiency and accuracy. Statistical analysis indicates the superiority as well as robustness of the above approach as compared with the other optimization algorithms. Specifically, the proposed approach finds better structural designs more consistently while being computationally more efficient. [Copyright &y& Elsevier]

Purpose - This paper sets out to design hyperbox classifiers of high interpretation capabilities. They are based on a collection of hyperboxes - generic and highly interpretable geometric descriptors of data belonging to a certain class. Such hyperboxes directly translate into conditional statements (rules) taking on the well-known format "if feature1 assumes values in [a,b] and feature2 assumes values in [d,f] and ? and featuren assumes values in [w,z] then class ?" where the intervals ([a,b],?[w,z]) are the respective edges (features) of the corresponding hyperbox. Design/methodology/approach - The proposed design process of hyperboxes consists of two main phases. In the first phase, a collection of "seeds" of the hyperboxes is constructed through data clustering being realized by means of the fuzzy C-means algorithm. During the second phase, the hyperboxes are "grown" (expanded) by applying mechanisms of genetic optimization (and genetic algorithm, in particular). Findings - It is demonstrated how the underlying geometry of the hyperboxes supports an immediate interpretation of arrhythmia data by linking the ranges of the features (parameters of the ECG signal) forming the edges of the hyperboxes with the two classes of the signals (normal - abnormal). A collection of comprehensive experiments offers an interesting insight into the geometry of the individual categories of the ECG signals and discusses how the resulting hyperbox classifiers link their geometric properties with the obtained classification rates. Research limitations/implications - The structure of the classifier is essential to enhance interpretation capabilities of the architecture and generate a collection of "if-then" classification rules. Originality/value - The study addresses an issue of design of highly interpretable, granular classifiers with the use of the technology of computational intelligence and evolutionary optimization, in particular. [ABSTRACT FROM AUTHOR]

Purpose - This paper aims to study modeling of the nonlinear behavior of the Torus machine back EMF using an adaptive networks fuzzy inference system (ANFIS). The model can be used to study the steady-state as well as the dynamic performances of the machine operating as a motor or as a generator. Design/methodology/approach - Using the universal approximation capability of fuzzy systems the authors designed an ANFIS network to model the nonlinear behavior of the back EMF of the Torus motor. The ANFIS is trained using an actual set machine measurements data to generate the motor back EMF for different operating conditions. Findings - Simulation results of the ANFIS model of the Torus motor at different loads proved the ability of the algorithm to effectively model the complex electromagnetic behavior of the machine. Such efficient modeling can directly help in improving and optimizing the Torus motor drive system design. Originality/value - It demonstrates that ANFIS can model the nonlinear behavior of the back EMF of the Torus motor with excellent accuracy. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a genetic fuzzy feature transformation method for support vector machines (SVMs) to do more accurate data classification. Given data are first transformed into a high feature space by a fuzzy system, and then SVMs are used to map data into a higher feature space and then construct the hyperplane to make a final decision. Genetic algorithms are used to optimize the fuzzy feature transformation so as to use the newly generated features to help SVMs do more accurate biomedical data classification under uncertainty. The experimental results show that the new genetic fuzzy SVMs have better generalization abilities than the traditional SVMs in terms of prediction accuracy. [Copyright &y& Elsevier]

Abstract: In this paper, we describe a granular algorithm for translating information between two granular worlds, represented as fuzzy rulebases. These granular worlds are defined on the same universe of discourse, but employ different granulations of this universe. In order to translate information from one granular world to the other, we must regranulate the information so that it matches the information granularity of the target world. This is accomplished through the use of a first-order interpolation algorithm, implemented using linguistic arithmetic, a set of elementary granular computing operations. We first demonstrate this algorithm by studying the common “fuzzy-PD” rulebase at several different granularities, and conclude that the “3×3” granulation may be too coarse for this objective. We then examine the question of what the “natural” granularity of a system might be; this is studied through a 10-fold cross-validation experiment involving three different granulations of the same underlying mapping. For the problem under consideration, we find that a 7×7 granulation appears to be the minimum necessary precision. [Copyright &y& Elsevier]

Abstract: This paper examines the interpretability-accuracy tradeoff in fuzzy rule-based classifiers using a multiobjective fuzzy genetics-based machine learning (GBML) algorithm. Our GBML algorithm is a hybrid version of Michigan and Pittsburgh approaches, which is implemented in the framework of evolutionary multiobjective optimization (EMO). Each fuzzy rule is represented by its antecedent fuzzy sets as an integer string of fixed length. Each fuzzy rule-based classifier, which is a set of fuzzy rules, is represented as a concatenated integer string of variable length. Our GBML algorithm simultaneously maximizes the accuracy of rule sets and minimizes their complexity. The accuracy is measured by the number of correctly classified training patterns while the complexity is measured by the number of fuzzy rules and/or the total number of antecedent conditions of fuzzy rules. We examine the interpretability-accuracy tradeoff for training patterns through computational experiments on some benchmark data sets. A clear tradeoff structure is visualized for each data set. We also examine the interpretability-accuracy tradeoff for test patterns. Due to the overfitting to training patterns, a clear tradeoff structure is not always obtained in computational experiments for test patterns. [Copyright &y& Elsevier]

Fuzzy C-Means (FCM) and hard clustering are the most common tools for data partitioning. However, the presence of noisy observations in the data being partitioned may render these clustering algorithms unreliable. In this paper, we introduce a robust noise-rejection clustering algorithm based on a combination of techniques that treat the FCM pitfalls with an outliers exclusion criterion. Unlike the traditional FCM, the proposed clustering tool provides much efficient data partitioning capabilities in the presence of noise and outliers. At the conclusion of the theoretical development, we validate the effectiveness of the proposed noise-rejection data partitioning tool through various comparison studies with existing noise-rejection clustering approaches in the literature. [Copyright &y& Elsevier]

In this paper, the problem of traditional validity indices when applied to the Gustafson—Kessel (GK) clustering are reviewed. A new cluster validity index for the GK algorithm is proposed. This validity index is defined as the average value of the relative degrees of sharing of all possible pairs of fuzzy clusters in the system. It computes the overlap of each pair of fuzzy clusters by considering the degree of sharing of each data point in the overlap. The optimal number of clusters is obtained by minimizing the validity index. Experiments in which the proposed validity index and several traditional validity indices were applied to 6 data sets highlight the superior qualities of the proposed index. The results indicate that the proposed validity index is very reliable. [ABSTRACT FROM AUTHOR]

Fuzzy cognitive map is a soft computing technique for modeling systems, which combines synergistically the theories of neural networks and fuzzy logic. Developing of fuzzy cognitive map (FCM) relies on human experience and knowledge, but still exhibits weaknesses in utilization of learning methods. The critical dependence on experts and the potential uncontrollable convergence to undesired steady-states are important deficiencies to manage FCMs. Overcoming these deficiencies will improve the efficiency and robustness of the FCM methodology. Learning and convergence algorithms constitute the mean to improve these characteristics of FCMs, by modifying the values of cause–effect weights among concepts. In this paper a new learning algorithm that alleviates the problem of the potential convergence to a steady-state, named Active Hebbian Learning (AHL) is presented, validated and implemented. This proposed learning procedure is a promising approach for exploiting experts'' involvement with their subjective reasoning and at the same time improving the effectiveness of the FCM operation mode and thus it broadens the applicability of FCMs modeling for complex systems. [Copyright &y& Elsevier]

There is a challenging man machine-interface issue in existing association analysis algorithms because they are Apriori-like and the Apriori Algorithm is based on the assumption that users can specify the threshold: minimum-support. It is impossible that users give a suitable minimum-support for a database to be mined if the users are without knowledge concerning the database. In this paper, we propose a fuzzy mining strategy with database-independent minimum-support, which provides a good man machine interface that allows users to specify the minimum-support threshold without any knowledge concerning their databases to be mined. We have evaluated the proposed approach and the experimental results have demonstrated that our algorithm is promising and efficient. [ABSTRACT FROM AUTHOR]