Fuzzy polynomial regression with fuzzy neural networks

Recently, fuzzy linear regression is considered by Mosleh et al. [1]. In this paper, a novel hybrid method based on fuzzy neural network for approximate fuzzy coefficients (parameters) of fuzzy polynomial regression models with fuzzy output and crisp inputs, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate parameters, a simple algorithm from the cost function of the fuzzy neural network is proposed. Finally, we illustrate our approach by some numerical examples.     

Bivalent and other solutions of fuzzy relational equations via linguistic hedges

We show that the well-known results regarding solutions of fuzzy relational equations and their systems can easily be generalized to obtain criteria regarding constrained solutions such as solutions which are crisp relations. When the constraint is empty, constrained solutions are ordinary solutions. The generalization is obtained by employing intensifying and relaxing linguistic hedges, conceived in this paper as certain unary functions on the scale of truth degrees. One aim of the paper is to highlight the problem of constrained solutions and to demonstrate that this problem naturally appears when identifying unknown relations. The other is to emphasize the role of linguistic hedges as constraints.     

Tracking a near-field moving target using fuzzy neural networks

In this paper we explore the problem of tracking a near-field moving target using fuzzy neural networks (FNNs). The moving target radiates narrow band waves that impinge on an array of passive sensors. At a particular time instance, the location of the target is estimated by several judiciously constructed FNN-based angle and distance estimators. When the target is moving, its trajectory can be on-line estimated due to the parallel and real-time computational capability of the FNNs. Computer simulation results illustrate the performance of the FNN-based angle estimator, distance estimator, and the near-field moving target tracker.     

A self-organizing adaptive fuzzy controller

There are two main parts in this paper. The first part presents a knowledge representation and reasoning scheme, called tree-searched neural networks (TNN). The TNN is based on a well-known intuitive knowledge representation (IKR) and can reduce the number of the processing nodes in the neural networks. The second part proposes a self-organizing adaptive fuzzy controller (SOAFC) based on the TNN model. It can help acquire control knowledge and thus can reduce the dependence on experts. Furthermore, designers do not need to predefine all membership functions to cover whole input space domain. For improving its performance further, we design a D-controller which is included within the SOAFC. Whether the fuzzy controller is incorporated with the D-controller or not, it is also guaranteed to be globally stable. Simulation results show that this approach has faster convergence speed, results in better transient response, and in addition requires less total control energy.     

Synchronization for delayed non-autonomous reaction-diffusion fuzzy cellular neural networks

In this letter, the synchronization schemes for delayed non-autonomous reaction-diffusion fuzzy cellular neural networks is considered. Based on the simple adaptive controller, a set of sufficient conditions to guarantee the synchronization are obtained. Moreover, the asymptotic behavior of the unknown parameters can be derived in the meanwhile. At last, some examples are given to show the effectiveness of the main results.     

An application of Liapunov''s method for the analysis of neural networks

The stability is studied of a class of nonlinear dynamical systems which possess many nonlinearities and many equilibrium states. As a special case, the analyzed class of systems includes analog neural networks. Sufficient conditions for the nonoscillatory behaviour of these systems, in the form of frequency domain criteria, are presented. The main result is proved relying on a suitable Liapunov function which is subsequently used for the simultaneous computation of regions of attraction for each stable equilibrium.     

A parametric representation of linguistic hedges in Zadeh’s fuzzy logic

This paper proposes a model for the parametric representation of linguistic hedges in Zadeh’s fuzzy logic. In this model each linguistic truth-value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth-values is introduced.     

Nonmonotone BFGS-trained recurrent neural networks for temporal sequence processing

In this paper we propose a nonmonotone approach to recurrent neural networks training for temporal sequence processing applications. This approach allows learning performance to deteriorate in some iterations, nevertheless the network’s performance is improved over time. A self-scaling BFGS is equipped with an adaptive nonmonotone technique that employs approximations of the Lipschitz constant and is tested on a set of sequence processing problems. Simulation results show that the proposed algorithm outperforms the BFGS as well as other methods previously applied to these sequences, providing an effective modification that is capable of training recurrent networks of various architectures.     

Agent based e-commerce systems that react to buyers’ feedbacks - A fuzzy approach

In this paper, we have introduced an agent based e-commerce system which recommends products to buyers as per their preferences. Initially, the agent collects the buyers’ preferences in fuzzy or linguistically defined terms and based on this, presents them an ordered set of products. After obtaining the buyers’ feedbacks when they actually come across the products, the seller’s agent interacts with the buyer (buyer’s agent), revises the products preferential order and recommends either the same set of products or a new set of similar products with the revised preferential order. The buyer’s revised preferences are taken here as his/her feedback after he/she comes across with the actual products (presented products). Concepts of fuzzy logic and Fuzzy Linear Programming are used here to identify the buyer’s feedbacks on the initial presentation of the products. Our methodology also measures the degree of customers’ focus on the products which are finally recommended by the e-commerce agent. The product ranking obtained through buyers’ initial preferences is considered here as his/her subjective information and the available information from the agents’ presented products are taken as the objective information.     

A neural fuzzy control system with structure and parameter learning

A general connectionist model, called neural fuzzy control network (NFCN), is proposed for the realization of a fuzzy logic control system. The proposed NFCN is a feedforward multilayered network which integrates the basic elements and functions of a traditional fuzzy logic controller into a connectionist structure which has distributed learning abilities. The NFCN can be constructed from supervised training examples by machine learning techniques, and the connectionist structure can be trained to develop fuzzy logic rules and find membership functions. Associated with the NFCN is a two-phase hybrid learning algorithm which utilizes unsupervised learning schemes for structure learning and the backpropagation learning scheme for parameter learning. By combining both unsupervised and supervised learning schemes, the learning speed converges much faster than the original backpropagation algorithm. The two-phase hybrid learning algorithm requires exact supervised training data for learning. In some real-time applications, exact training data may be expensive or even impossible to obtain. To solve this problem, a reinforcement neural fuzzy control network (RNFCN) is further proposed. The RNFCN is constructed by integrating two NFCNs, one functioning as a fuzzy predictor and the other as a fuzzy controller. By combining a proposed on-line supervised structure-parameter learning technique, the temporal difference prediction method, and the stochastic exploratory algorithm, a reinforcement learning algorithm is proposed, which can construct a RNFCN automatically and dynamically through a reward-penalty signal (i.e., “good” or “bad” signal). Two examples are presented to illustrate the performance and applicability of the proposed models and learning algorithms.     

Evaluation of fuzzy regression models by fuzzy neural network

In this paper, a novel hybrid method based on fuzzy neural network for approximate fuzzy coefficients (parameters) of fuzzy linear and nonlinear regression models with fuzzy output and crisp inputs, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate parameters, a simple algorithm from the cost function of the fuzzy neural network is proposed. Finally, we illustrate our approach by some numerical examples.     

Techniques for the mathematical analysis of neural networks

This expository paper covers the following topics: (1) a very brief introduction to neural networks for those unfamiliar with the basic concepts; (2) an equality brief survey of various mathematical approaches to neural systems with an emphasis on approximation theory; (3) an algorithmic approach to the analysis of networks developed by this author using the tools of numerical linear algebra. This approach is novel and was first proposed by the author in (1990).

A detailed analysis of one popular algorithm (the delta rule) will be given, indicating why one implementation leads to a stable numerical process, whereas an initially attractive variant (essentially a form of steepest descent) does not. Similar considerations apply to the backpropagation algorithm. The effect of filtering and other preprocessing of the input data will also be discussed systematically, with a new result on the effect of linear filtering on the rate of convergence of the delta rule.     

Robust passivity analysis of fuzzy Cohen-Grossberg BAM neural networks with time-varying delays

This paper is concerned with the problem of passivity analysis for a class of Cohen-Grossberg fuzzy bidirectional associative memory (BAM) neural networks with time varying delay. By employing the delay fractioning technique and linear matrix inequality optimization approach, delay dependent passivity criteria are established that guarantees the passivity of fuzzy Cohen-Grossberg BAM neural networks with uncertainties. The passivity condition is expressed in terms of LMIs, which can be easily solved by various convex optimization algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed result.     

Design of fuzzy radial basis function-based polynomial neural networks

In this study, we introduce a new design methodology of fuzzy radial basis function-based polynomial neural networks. In many cases, these models do not come with capabilities to deal with granular information. With this regard, fuzzy sets offer several interesting and useful opportunities. This study presents the development of fuzzy radial basis function-based neural networks augmented with virtual input variables. The performance of the proposed category of models is quantified through a series of experiments, in which we use two machine learning data sets and two publicly available software development effort data.     

Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control

-In this paper, we investigate the synchronization problems of chaotic fuzzy cellular neural networks with time-varying delays. To overcome the difficulty that complete synchronization between non-identical chaotic neural networks cannot be achieved only by utilizing output feedback control, we use a sliding mode control approach to study the synchronization of non-identical chaotic fuzzy cellular neural networks with time-varying delays, where the parameters and activation functions are mismatched. This research demonstrates the effectiveness of application in secure communication. Numerical simulations are carried out to illustrate the main results.     

Logistic evolutionary product-unit neural networks: Innovation capacity of poor Guatemalan households

A new logistic regression algorithm based on evolutionary product-unit (PU) neural networks is used in this paper to determine the assets that influence the decision of poor households with respect to the cultivation of non-traditional crops (NTC) in the Guatemalan Highlands. In order to evaluate high-order covariate interactions, PUs were considered to be independent variables in product-unit neural networks (PUNN) analysing two different models either including the initial covariates (logistic regression by the product-unit and initial covariate model) or not (logistic regression by the product-unit model). Our results were compared with those obtained using a standard logistic regression model and allow us to interpret the most relevant household assets and their complex interactions when adopting NTC, in order to aid in the design of rural policies.     

Analysis of stability for impulsive fuzzy Cohen–Grossberg BAM neural networks with delays

In this paper, based on the topological degree theory, Lyapunov functional method and inequality analysis technique, the existence and global exponential stability of equilibrium of impulsive fuzzy Cohen–Grossberg bi‐directional associative memory neural networks with delays, are investigated. Moreover, an illustrative example is given to demonstrate the effectiveness of the results obtained. Copyright © 2012 John Wiley & Sons, Ltd.     

Exponential synchronization of fuzzy cellular neural networks with mixed delays and general boundary conditions

In this paper, we study exponential synchronization of delayed reaction-diffusion fuzzy cellular neural networks with general boundary conditions. By using Sobolev inequality techniques and constructing suitable Lyapunov functional, some sufficient conditions are given to ensure the exponential synchronization of the drive-response delayed fuzzy cellular neural networks with general boundary conditions. Finally, an example is given to verify the theoretical analysis.     

Coordinated control of distribution supply chains in the presence of fuzzy customer demand

This paper considers a single product inventory control in a Distribution Supply Chain (DSC). The DSC operates in the presence of uncertainty in customer demands. The demands are described by imprecise linguistic expressions that are modelled by discrete fuzzy sets. Inventories at each facility within the DSC are replenished by applying periodic review policies with optimal order up-to-quantities. Fuzzy customer demands imply fuzziness in inventory positions at the end of review intervals and in incurred relevant costs per unit time interval. The determination of the minimum of defuzzified total cost of the DSC is a complex problem which is solved by applying decomposition; the original problem is decomposed into a number of simpler independent optimisation subproblems, where each retailer and the warehouse determine their optimum periodic reviews and order up-to-quantities. An iterative coordination mechanism is proposed for changing the review periods and order up-to-quantities for each retailer and the warehouse in such a way that all parties within the DSC are satisfied with respect to total incurred costs per unit time interval. Coordination is performed by introducing fuzzy constraints on review periods and fuzzy tolerances on retailers and warehouse costs in local optimisation subproblems.