Fuzzy Stochastic Research Articles

Stability Analysis of Stochastic Fuzzy Neural Networks with Time-Varying Delays and Reaction–Diffusion Terms

This paper investigates the problem of the global exponential stability for a class of stochastic Takagi–Sugeno fuzzy neural networks (STSFNNs) with time-varying delays and reaction–diffusion terms. Based on the piecewise Lyapunov–Krasovskii functional, Poincare integral inequality, and Ito differential formula, we obtain some sufficient conditions ensuring the global exponential stability of an equilibrium point for STSFNNs with time-varying delays and reaction–diffusion terms. These sufficient conditions depend on the reaction–diffusion terms and time delays. Finally, some examples are given to show the effectiveness and superiority of the proposed approach.

Prediction of Output Response Probability of Sound Environment System Using Simplified Model with Stochastic Regression and Fuzzy Inference

The traditional standard stochastic system models, such as the autoregressive (AR), moving average (MA) and autoregressive moving average (ARMA) models, usually assume the Gaussian property for the fluctuation distribution, and the well-known least squares method is applied on the basis of only the linear correlation data. In the actual sound environment system, the stochastic process exhibits various non-Gaussian distributions, and there exist potentially various nonlinear correlations in addition to the linear correlation between input and output time series. Consequently, the system input and output relationship in the actual phenomenon cannot be represented by a simple model. In this study, a prediction method of output response probability for sound environment systems is derived by introducing a correction method based on the stochastic regression and fuzzy inference for simplified standard system models. The proposed method is applied to the actual data in a sound environment system, and the practical usefulness is verified.

An interval-parameter two-stage stochastic fuzzy program with type-2 membership functions: an application to water resources management

This paper presents an interval-parameter two-stage stochastic fuzzy programming with type-2 membership functions (ITSFP–T2MF) approach for supporting water resources management under uncertainty. ITSFP–T2MF is capable not only of dealing with a variety of uncertainties expressed as probability distributions, intervals, and type-2 fuzzy sets, but also of reflecting the complexity of uncertainty presented as the concept of a flexible fuzzy decision. A scenario-based solution method is proposed for solving ITSFP–T2MF, which takes into account different attitudes of decision makers (DMs) towards the objective-function value and constraints. Moreover, the solution method can ensure that no infeasible solutions are included in the results by means of a feasibility test and a constricting algorithm, leading to an enhanced system safety. ITSFP–T2MF is applied to a case study of water resources allocation under uncertainty. The results indicate that interval solutions can be obtained under different scenarios, which enhances the diversity of solutions for supporting the decisions of water resources allocation. Furthermore, a variety of decision alternatives can be generated under different policies for water resources management, which permits an in-depth policy analysis associated with different levels of economic penalties when the promised water-allocation targets are violated, and thus helps DMs identify desired water-allocation plans according to practical situations.

Filtering for Discrete Fuzzy Stochastic Time-Delay Systems with Sensor Saturation

This paper addresses the filtering problem for discrete fuzzy stochastic systems with time-varying delay and sensor saturation. Random noise depending on state and external disturbance is also taken into account. A decomposition approach is employed to solve the characteristic of sensor saturation. The scaled small gain (SSG) theorem is extended to the stochastic systems, which is employed to handle with the time-varying delay by transforming the original system into the form of an interconnected system consisting of two subsystems. By the proposed Lyapunov-Krasovskii function, the scaled small gains of the subsystems are analyzed, respectively. Sufficient conditions for the stochastic stability of the filtering error system with a prescribed level are established such that the gains of the filter can be obtained explicitly. Finally, simulation results are presented to demonstrate the effectiveness of the proposed approach.

Actuator Saturation Constrained Fuzzy Control for Discrete Stochastic Fuzzy Systems with Multiplicative Noises

This paper deals with the fuzzy controller design problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with multiplicative noises. Using the Lyapunov stability theory and Itô formula, the sufficient conditions are derived to guarantee the stability of the closed-loop nonlinear stochastic systems subject to actuator saturation. Based on the Parallel Distributed Compensation (PDC) concept, the fuzzy controller can be obtained to stabilize the T-S fuzzy models with multiplicative noises by combining the same membership functions of plants and desired state feedback gains. In order to illustrate the availability and practicability of proposed fuzzy controller design approach, the numerical simulations for the nonlinear truck-trailer system are given to demonstrate the applications of this paper.

${\cal H}_{\infty}$ Model Reduction of Takagi–Sugeno Fuzzy Stochastic Systems

This paper is concerned with the problem of H(∞) model reduction for Takagi-Sugeno (T-S) fuzzy stochastic systems. For a given mean-square stable T-S fuzzy stochastic system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with an H(∞) performance but also translates it into a linear lower dimensional system. Then, the model reduction is converted into a convex optimization problem by using a linearization procedure, and a projection approach is also presented, which casts the model reduction 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 methods.

Compuational Algorithm of Fuzzy Stochastic Model for Forecasting

In our daily life, often we use forecasting techniques to predict weather, economy, population growth, stock, etc. In recent years, many fuzzy time series methods are developed for forecasting of enrollments of Universities. Song and Chissom (1993) were the pioneers in studying such type of problems. Shiva Raj Sing (2007) presented a simple time variant method for forecasting the enrollment of the University of Alabama using fuzzy time series. Forecasts are needed only if there is uncertainty about the future. In this paper develop the modified algorithm to forecast enrollment for the same data set and compared with existing methods. The proposed method shows the better forecasting accuracy rate for enrollments, compared than other methods.

Stress Monitoring Based on Stochastic Fuzzy Analysis of Heartbeat Intervals

Quantifying stress levels of an individual based on a mathematical analysis of real-time physiological data measurements is challenging. This study suggests a stochastic fuzzy analysis method to evaluate the short time series of R-R intervals (time intervals between consecutive heart beats) for a quantification of the stress level. The 5-min-long series of R-R intervals recorded under a given stress level are modeled by a stochastic fuzzy system. The stochastic model of heartbeat intervals is individual specific and corresponds to a particular stress level. Once the different heartbeat interval models are available for an individual, an analysis of the given R-R interval series generated under an unknown stress level is performed by a stochastic interpolation of the models. The stress estimation method has been implemented in a mobile telemedical application employing an e-health system for an efficient and cost-effective monitoring of patients while at home or at work. The experiments involve 50 individuals whose stress scores were assessed at different times of the day. The subjective rating scores showed a high correlation with the values predicted by the proposed analysis method.

The Stationary Fuzzy Stochastic Time Series Prediction Methods based on Fuzzy Stochastic Process

The Stationary Fuzzy Stochastic Time Series Prediction Methods based on Fuzzy Stochastic Process

Continuous Review Inventory Model with Fuzzy Stochastic Demand and Variable Lead Time

The present study considers a continuous review inventory system for the inventory model involving fuzzy random demand, variable lead-time with backorders and lost sales. The authors first use the triangular fuzzy number count upon lead-time to construct a lead-time demand. Using credibility criterion, the expected shortages are calculated. Without loss of generality, the authors have assumed that all the observed values of the fuzzy random variable, representing the demand are triangular fuzzy numbers. Consequently, the value of total expected cost in the fuzzy sense is derived using the expected value criterion or credibility criterion. For the proposed model, the authors provide a solution to find the optimal lead-time and the optimal order quantity along with the reorder point such that the total expected cost in the fuzzy sense has a minimum value. Numerical study is also provided to illustrate the results of proposed model.

Exponential stability of impulsive stochastic fuzzy reaction–diffusion Cohen–Grossberg neural networks with mixed delays

The problem of mean square exponential stability for a class of impulsive stochastic fuzzy Cohen–Grossberg networks with mixed delays and reaction–diffusion terms is investigated in this paper. By using the properties of “M-cone”, eigenspace of the spectral radius of nonnegative matrices, Lyapunov functional, Itô's formula and inequality techniques, several sufficient conditions guaranteeing the mean square exponential stability of its equilibrium solution are obtained. These results extend and improve the earlier publications. Two examples are presented to illustrate the effectiveness and efficiency of the results.

Identifying Optimal Water Resources Allocation Strategies through an Interactive Multi-Stage Stochastic Fuzzy Programming Approach

In this study, an interactive multi-stage stochastic fuzzy programming (IMSFP) approach has been developed through incorporating an interactive fuzzy resolution (IFR) method within an inexact multi-stage stochastic programming framework. IMSFP can deal with dual uncertainties expressed as fuzzy boundary intervals that exist in the objective function and the left- and right-hand sides of constraints. Moreover, IMSFP is capable of reflecting dynamics of uncertainties and the related decision processes through constructing a set of representative scenarios within a multi-stage context. A management problem in terms of water resources allocation has been studied to illustrate applicability of the proposed approach. The results indicate that a set of solutions under different feasibility degrees (i.e., risk of constraint violation) has been generated for planning the water resources allocation. They can not only help quantify the relationship between the objective-function value and the risk of violating the constraints, but also enable decision makers (DMs) to identify, in an interactive way, a desired compromise between two factors in conflict: satisfaction degree of the goal and feasibility degree of constraints. Besides, a number of decision alternatives have been generated under different policies for water resources management, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic penalties when the promised water-allocation targets are violated, and thus help DMs to identify desired water-allocation schemes under uncertainty.

Stationary Fuzzy Fokker–Planck Learning and Stochastic Fuzzy Filtering

The application of nonlinear optimization to the estimation of fuzzy model parameters is well known. To do the reverse of this, the concept of stationary fuzzy Fokker-Planck learning (SFFPL) is introduced, i.e., SFFPL applies the fuzzy modeling technique in nonlinear optimization problems. SFFPL is based on the fuzzy approximation of the stationary cumulative distribution function of a stochastic search process associated with the nonlinear optimization problem. A carefully designed algorithm is suggested for SFFPL to locate the optimum point. This paper also considers the variational Bayes (VB)-based inference of a stochastic fuzzy filter whose consequents, as well as antecedents, are random variables. The problem of VB inference of stochastic antecedents, because of the nonlinearity of the likelihood function, is analytically intractable. The SFFPL algorithm for high-dimensional nonlinear optimization that does not require the derivative of the objective function can be used to numerically solve the stochastic fuzzy filtering problem.

Robust Exponential Stability Criteria for T–S Fuzzy Stochastic Delayed Neural Networks of Neutral Type

This paper is concerned with the problem of robust exponential stability for T–S fuzzy stochastic neural networks of neutral type. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, new delay-dependent stability criteria are established in terms of linear matrix inequalities (LMIs) which can be checked easily by the LMI Control Toolbox in MATLAB. Finally, numerical examples are given to illustrate the feasibility and effectiveness of the proposed method.

Passive fuzzy controller design for stochastic Takagi—Sugeno fuzzy systems with time-varying delay

This paper discusses the issue of stability and stabilization for the non-linear stochastic systems with time-varying delay subject to passivity performance. Based on the fuzzy modelling approach, the non-linear systems can be represented by a stochastic T—S fuzzy model whose consequent part is described by linear differential equations with a multiplicative noise term. For analysing the stability of the stochastic T—S fuzzy model, the less conservative stability criterion derived by Itô's formula and the Lyapunov—Krasovskii function is proposed as a linear matrix inequality (LMI) problem. Furthermore, the passivity theory is employed to discuss the external disturbance effect on the considered system. Through applying the above techniques, the sufficiency conditions are derived to design fuzzy controllers such that the stochastic T—S fuzzy model with time delay is asymptotically stable and passive in the mean square. Finally, two numerical examples are proposed to show the application and effectiveness of the proposed fuzzy controller design method.

ファジィ確率環境下における多目的最適化

ファジィ確率環境下における多目的最適化

Global Asymptotic Stability of Stochastic Fuzzy Cellular Neural Networks with Time-Varying Delays

In this paper, the problem of global asymptotic stability in the mean square for stochastic fuzzy cellular neural networks (SFCNN) with time-varying delays is investigated. By constructing a newly proposed Lyapunov-Krasovskii function (LKF) and using Ito’s stochastic stability theory, a novel delay-dependent stability criterion is derived. The obtained stability result is helpful to design the stability of fuzzy cellular neural networks (FCNN) with time-varying delays when stochastic noise is taken into consideration. Since it is presented in terms of a linear matrix inequality (LMI), the sufficient condition is easy to be checked efficiently by utilizing some standard numerical packages such as the LMI Control Toolbox in Matlab. Finally, an illustrate example is given to verify the feasibility and usefulness of the proposed result.

Stability Analysis of Stochastic Fuzzy Cellular Neural Networks With Time-Varying Delays and Reaction-Diffusion Terms

In this paper, a class of stochastic fuzzy cellular neural networks with time-varying delays and reaction-diffusion terms is investigated. By using Lyapunov---Krasovskii functional and stochastic analysis approaches, new and less conservative delay-derivative-dependent stability criteria are presented to guarantee the neural networks to be globally exponentially stable in the mean square for all admissible stochastic perturbations. Numerical simulations are carried out to illustrate the main results.

On the Noise-Enhancing Ability of Stochastic Hodgkin-Huxley Neuron Systems

Recently noise has been shown to be useful in enhancing neuron sensitivity by stochastic resonance. In this study, in order to measure the noise-enhancing factor (NEF), a nonlinear stochastic model is introduced for the Hodgkin-Huxley (HH) neuron system with synaptic noise input stimulation and channel noises in the sodium and potassium channels. The enhancing factor of the HH neuron system is measured from the point of view of the noise-exploiting level of nonlinear stochastic H(infinity) signal processing. Since the nonlinear stochastic-enhancing measure problem of HH neuron systems requires a solution for the difficulty presented by the Hamilton Jacobi inequality (HJI), a fuzzy interpolation of locally linearized systems is employed to simplify the nonlinear noise-enhancing problems by solving only a set of linear matrix inequalities. The NEF of the HH neuron system is found to be related to the locations of eigenvalues of linearized HH neuron systems and can be estimated through the H(infinity) signal processing method. Based on a stochastic fuzzy linearized HH neuron system, we found that channel noises are enhanced by the active eigenvalues of ionic channels while synaptic noises are attenuated by the passive eigenvalues of synaptic process.

On Passivity and Passification of Stochastic Fuzzy Systems With Delays: The Discrete-Time Case

Takagi-Sugeno (T-S) fuzzy models, which are usually represented by a set of linear submodels, can be used to describe or approximate any complex nonlinear systems by fuzzily blending these subsystems, and so, significant research efforts have been devoted to the analysis of such models. This paper is concerned with the passivity and passification problems of the stochastic discrete-time T-S fuzzy systems with delay. We first propose the definition of passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the stochastic analysis combined with the matrix inequality techniques, a sufficient condition in terms of linear matrix inequalities is presented, ensuring the passivity performance of the T-S fuzzy models. Finally, based on this criterion, state feedback controller is designed, and several criteria are obtained to make the closed-loop system passive in the sense of expectation. The results acquired in this paper are delay dependent in the sense that they depend on not only the lower bound but also the upper bound of the time-varying delay. Numerical examples are also provided to demonstrate the effectiveness and feasibility of our criteria.