Sliding mode-like learning control for SISO complex systems with T-S fuzzy models

In this paper, a sliding mode-like learning control scheme is developed for a class of single input single output (SISO) complex systems. First, the Takagi-Sugeno (T-S) fuzzy modelling technique is employed to model the uncertain complex dynamical systems. Second, a sliding mode-like learning control is designed to drive the sliding variable to converge to the sliding surface, and the system states can then asymptotically converge to zero on the sliding surface. The advantages of this scheme are that: 1) the information about the uncertain system dynamics and the system model structure is not required for the design of the learning controller; 2) the closed-loop system behaves with a strong robustness with respect to uncertainties; 3) the control input is chattering-free. The sufficient conditions for the sliding mode-like learning control to stabilise the global fuzzy model are discussed in detail. A simulation example for the control of an inverted pendulum cart is presented to demonstrate the effectiveness of the proposed control scheme.

Australian forex market anaylsis using connectionist models

The need for intelligent monitoring systems has become a necessity to keep track of the complex forex market. The forex market is difficult to understand by an average individual. However, once the market is broken down into simple terms, the average individual can begin to understand the foreign exchange market and use it as a financial instrument for future investing. This paper is an attempt to compare the performance of a Takagi-Sugeno type neuro-fuzzy system and a feed forward neural network trained using the scaled conjugate gradient algorithm to predict the average monthly forex rates. The exchange values of Australian dollar are considered with respect to US dollar, Singapore dollar, New Zealand dollar, Japanese yen and United Kingdom pound. The connectionist models were trained using 70% of the data and remaining was used for testing and validation purposes. It is observed that the proposed connectionist models were able to predict the average forex rates one month ahead accurately. Experiment results also reveal that neuro-fuzzy technique performed better than the neural network.

Interval type-2 fuzzy logic systems for load forecasting : a comparative study

Accurate short term load forecasting (STLF) is essential for a variety of decision-making processes. However, forecasting accuracy can drop due to the presence of uncertainty in the operation of energy systems or unexpected behavior of exogenous variables. This paper proposes the application of Interval Type-2 Fuzzy Logic Systems (IT2 FLSs) for the problem of STLF. IT2 FLSs, with additional degrees of freedom, are an excellent tool for handling uncertainties and improving the prediction accuracy. Experiments conducted with real datasets show that IT2 FLS models precisely approximate future load demands with an acceptable accuracy. Furthermore, they demonstrate an encouraging degree of accuracy superior to feedforward neural networks and traditional type-1 Takagi-Sugeno-Kang (TSK) FLSs.

Hydrological modelling with a dynamic neural fuzzy inference system

Dynamic Evolving Neural-Fuzzy Inference System (DENFIS) is a Takagi-Sugeno-type fuzzy inference system for online learning which can be applied for dynamic time series prediction. Data from Heshui catchment (2,275 km2) which is rural catchment in China, comprising daily time series of rainfall and discharge from January 1, 1990 to January 21, 2006 were analyzed. Rainfall and discharge antecedents were the inputs used for the DENFIS and ANFIS models and the output was discharge at the present time. DENFIS model results were compared with the results obtained from the physically-based University Regina Hydrologic Model (URHM) and an Adaptive Network-based Fuzzy Inference System (ANFIS) which employs offline learning. Our analysis shows that DENFIS results are better or at least comparable to URHM, but almost identical to ANFIS.

Dynamic evolving neural-fuzzy inference system for rainfall-runoff (R-R) modelling

Dynamic Evolving Neural-Fuzzy Inference System (DENFIS) is a Takagi-Sugeno-type fuzzy inference system for online learning which can be applied for dynamic time series prediction. To the best of our knowledge, this is the first time that DENFIS has been used for rainfall-runoff (R-R) modeling. DENFIS model results were compared to the results obtained from the physically-based Storm Water Management Model (SWMM) and an Adaptive Network-based Fuzzy Inference System (ANFIS) which employs offline learning. Data from a small (5.6 km2) catchment in Singapore, comprising 11 separated storm events were analyzed. Rainfall was the only input used for the DENFIS and ANFIS models and the output was discharge at the present time. It is concluded that DENFIS results are better or at least comparable to SWMM, but similar to ANFIS. These results indicate a strong potential for DENFIS to be used in R-R modeling.

An intelligent forex monitoring system

The need for intelligent monitoring systems has become a necessity to keep track of the complex forex market. The vast currency market is a foreign concept to the average individual. However, once it is broken down into simple terms, the average individual can begin to understand the foreign exchange market and use it as a financial instrument for future investing. We attempt to compare the performance of a Takagi-Sugeno, type neuro-fuzzy system and a feedforward neural network trained using the scaled conjugate gradient algorithm to predict the average monthly forex rates. We considered the exchange values of Australian dollar with respect to US dollar, Singapore dollar, New Zealand dollar, Japanese yen and United Kingdom pounds. The connectionist models were trained using 70% of the data and remaining was used for testing and validation purposes. It is observed that the proposed connectionist models were able to predict the average forex rates one month ahead accurately. Experiment results also reveal that the neuro-fuzzy technique performed better than the neural network

Prediction interval construction using interval type-2 fuzzy logic systems

This study proposes a novel non-parametric method for construction of prediction intervals (PIs) using interval type-2 Takagi-Sugeno-Kang fuzzy logic systems (IT2 TSK FLSs). The key idea in the proposed method is to treat the left and right end points of the type-reduced set as the lower and upper bounds of a PI. This allows us to construct PIs without making any special assumption about the data distribution. A new training algorithm is developed to satisfy conditions imposed by the associated confidence level on PIs. Proper adjustment of premise and consequent parameters of IT2 TSK FLSs is performed through the minimization of a PI-based objective function, rather than traditional error-based cost functions. This new cost function covers both validity and informativeness aspects of PIs. A metaheuristic method is applied for minimization of the non-linear non-differentiable cost function. Quantitative measures are applied for assessing the quality of PIs constructed using IT2 TSK FLSs. The demonstrated results for four benchmark case studies with homogenous and heterogeneous noise clearly show the proposed method is capable of generating high quality PIs useful for decision-making.

An incremental meta-cognitive-based scaffolding fuzzy neural network

The idea of meta-cognitive learning has enriched the landscape of evolving systems, because it emulates three fundamental aspects of human learning: what-to-learn; how-to-learn; and when-to-learn. However, existing meta-cognitive algorithms still exclude Scaffolding theory, which can realize a plug-and-play classifier. Consequently, these algorithms require laborious pre- and/or post-training processes to be carried out in addition to the main training process. This paper introduces a novel meta-cognitive algorithm termed GENERIC-Classifier (gClass), where the how-to-learn part constitutes a synergy of Scaffolding Theory - a tutoring theory that fosters the ability to sort out complex learning tasks, and Schema Theory - a learning theory of knowledge acquisition by humans. The what-to-learn aspect adopts an online active learning concept by virtue of an extended conflict and ignorance method, making gClass an incremental semi-supervised classifier, whereas the when-to-learn component makes use of the standard sample reserved strategy. A generalized version of the Takagi-Sugeno Kang (TSK) fuzzy system is devised to serve as the cognitive constituent. That is, the rule premise is underpinned by multivariate Gaussian functions, while the rule consequent employs a subset of the non-linear Chebyshev polynomial. Thorough empirical studies, confirmed by their corresponding statistical tests, have numerically validated the efficacy of gClass, which delivers better classification rates than state-of-the-art classifiers while having less complexity.

A non-linear programming-based similarity reasoning scheme for modelling of monotonicity-preserving multi-input fuzzy inference systems

In this paper, the zero-order Sugeno Fuzzy Inference System (FIS) that preserves the monotonicity property is studied. The sufficient conditions for the zero-order Sugeno FIS model to satisfy the monotonicity property are exploited as a set of useful governing equations to facilitate the FIS modelling process. The sufficient conditions suggest a fuzzy partition (at the rule antecedent part) and a monotonically-ordered rule base (at the rule consequent part) that can preserve the monotonicity property. The investigation focuses on the use of two Similarity Reasoning (SR)-based methods, i.e., Analogical Reasoning (AR) and Fuzzy Rule Interpolation (FRI), to deduce each conclusion separately. It is shown that AR and FRI may not be a direct solution to modelling of a multi-input FIS model that fulfils the monotonicity property, owing to the difficulty in getting a set of monotonically-ordered conclusions. As such, a Non-Linear Programming (NLP)-based SR scheme for constructing a monotonicity-preserving multi-input FIS model is proposed. In the proposed scheme, AR or FRI is first used to predict the rule conclusion of each observation. Then, a search algorithm is adopted to look for a set of consequents with minimized root means square errors as compared with the predicted conclusions. A constraint imposed by the sufficient conditions is also included in the search process. Applicability of the proposed scheme to undertaking fuzzy Failure Mode and Effect Analysis (FMEA) tasks is demonstrated. The results indicate that the proposed NLP-based SR scheme is useful for preserving the monotonicity property for building a multi-input FIS model with an incomplete rule base.

Special issue : Computational intelligence models for image processing and information reasoning

Computational Intelligence (CI) models comprise robust computing methodologies with a high level of machine learning quotient. CI models, in general, are useful for designing computerized intelligent systems/machines that possess useful characteristics mimicking human behaviors and capabilities in solving complex tasks, e.g., learning, adaptation, and evolution. Examples of some popular CI models include fuzzy systems, artificial neural networks, evolutionary algorithms, multi-agent systems, decision trees, rough set theory, knowledge-based systems, and hybrid of these models. This special issue highlights how different computational intelligence models, coupled with other complementary techniques, can be used to handle problems encountered in image processing and information reasoning.

Modeling the flow behavior, recrystallization, and crystallographic texture in hot-deformed Fe-30 Wt Pct Ni Austenite

The present work describes a hybrid modeling approach developed for predicting the flow behavior, recrystallization characteristics, and crystallographic texture evolution in a Fe-30 wt pct Ni austenitic model alloy subjected to hot plane strain compression. A series of compression tests were performed at temperatures between 850 °C and 1050 °C and strain rates between 0.1 and 10 s⁻¹. The evolution of grain structure, crystallographic texture, and dislocation substructure was characterized in detail for a deformation temperature of 950 °C and strain rates of 0.1 and 10 s⁻¹, using electron backscatter diffraction and transmission electron microscopy. The hybrid modeling method utilizes a combination of empirical, physically-based, and neuro-fuzzy models. The flow stress is described as a function of the applied variables of strain rate and temperature using an empirical model. The recrystallization behavior is predicted from the measured microstructural state variables of internal dislocation density, subgrain size, and misorientation between subgrains using a physically-based model. The texture evolution is modeled using artificial neural networks.

Building monotonicity-preserving fuzzy inference models with optimization-based similarity reasoning and a monotonicity index

In this paper, a novel approach to building a Fuzzy Inference System (FIS) that preserves the monotonicity property is proposed. A new fuzzy re-labeling technique to re-label the consequents of fuzzy rules in the database (before the Similarity Reasoning process) and a monotonicity index for use in FIS modeling are introduced. The proposed approach is able to overcome several restrictions in our previous work that uses mathematical conditions in building monotonicity-preserving FIS models. Here, we show that the proposed approach is applicable to different FIS models, which include the zero-order Sugeno FIS and Mamdani models. Besides, the proposed approach can be extended to undertake problems related to the local monotonicity property of FIS models. A number of examples to demonstrate the usefulness of the proposed approach are presented. The results indicate the usefulness of the proposed approach in constructing monotonicity-preserving FIS models.

On the use of fuzzy rule interpolation techniques for monotonic multi-input fuzzy rule base models

Constructing a monotonicity relating function is important, as many engineering problems revolve around a monotonicity relationship between input(s) and output(s). In this paper, we investigate the use of fuzzy rule interpolation techniques for monotonicity relating fuzzy inference system (FIS). A mathematical derivation on the conditions of an FIS to be monotone is provided. From the derivation, two conditions are necessary. The derivation suggests that the mapped consequence fuzzy set of an FIS to be of a monotonicity order. We further evaluate the use of fuzzy rule interpolation techniques in predicting a consequent associated with an observation according to the monotonicity order. There are several findings in this article. We point out the importance of an ordering criterion in rule selection for a multi-input FIS before the interpolation process; and hence, the practice of choosing the nearest rules may not be true in this case. To fulfill the monotonicity order, we argue with an example that conventional fuzzy rule interpolation techniques that predict each consequence separately is not suitable in this case. We further suggest another class of interpolation techniques that predicts the consequence of a set of observations simultaneously, instead of separately. This can be accomplished with the use of a search algorithm, such as the brute force, genetic algorithm or etc.

Fuzzy rule base assessment models : theoretical analyses and a case study

An assessment model is usually a mathematical model that produces a measuring index, in the form of a numerical score to a situation/object, with respect to the subject of measure. To allow a valid and useful comparison among various situations/objects according to their associated numerical scores to be made, two important properties, i.e., the monotone output property and output resolution properties, are essential in fuzzy inference-based assessment problems. In this paper, the conditions for a fuzzy assessment model to fulfill the monotone output property is investigated using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to the input, whereby the derivative should be greater than a minimum resolution. Based on the derivative, improvements to the output resolution property by refining the fuzzy production rules are suggested. A case study on the Bowles fuzzy RPN model to demonstrate the effectiveness of the properties is also included.