Combining multiple prioritized knowledge bases by negotiation.

Recently, several belief negotiation models have been introduced to deal with the problem of belief merging. A negotiation model usually consists of two functions: a negotiation function and a weakening function. A negotiation function is defined to choose the weakest sources and these sources will weaken their point of view using a weakening function. However, the currently available belief negotiation models are based on classical logic, which makes them difficult to define weakening functions. In this paper, we define a prioritized belief negotiation model in the framework of possibilistic logic. The priority between formulae provides us with important information to decide which beliefs should be discarded. The problem of merging uncertain information from different sources is then solved by two steps. First, beliefs in the original knowledge bases will be weakened to resolve inconsistencies among them. This step is based on a prioritized belief negotiation model. Second, the knowledge bases obtained by the first step are combined using a conjunctive operator which may have a reinforcement effect in possibilistic logic.

Robust fuzzy Gustafson-Kessel clustering for nonlinear system identification

This paper deals with Takagi-Sugeno (TS) fuzzy model identification of nonlinear systems using fuzzy clustering. In particular, an extended fuzzy Gustafson-Kessel (EGK) clustering algorithm, using robust competitive agglomeration (RCA), is developed for automatically constructing a TS fuzzy model from system input-output data. The EGK algorithm can automatically determine the 'optimal' number of clusters from the training data set. It is shown that the EGK approach is relatively insensitive to initialization and is less susceptible to local minima, a benefit derived from its agglomerate property. This issue is often overlooked in the current literature on nonlinear identification using conventional fuzzy clustering. Furthermore, the robust statistical concepts underlying the EGK algorithm help to alleviate the difficulty of cluster identification in the construction of a TS fuzzy model from noisy training data. A new hybrid identification strategy is then formulated, which combines the EGK algorithm with a locally weighted, least-squares method for the estimation of local sub-model parameters. The efficacy of this new approach is demonstrated through function approximation examples and also by application to the identification of an automatic voltage regulation (AVR) loop for a simulated 3 kVA laboratory micro-machine system.

A fast method for fuzzy neural modeling and refinement

In the identification of complex dynamic systems using fuzzy neural networks, one of the main issues is the curse of dimensionality, which makes it difficult to retain a large number of system inputs or to consider a large number of fuzzy sets. Moreover, due to the correlations, not all possible network inputs or regression vectors in the network are necessary and adding them simply increases the model complexity and deteriorates the network generalisation performance. In this paper, the problem is solved by first proposing a fast algorithm for selection of network terms, and then introducing a refinement procedure to tackle the correlation issue. Simulation results show the efficacy of the method.

Dynamic evolution of the genetic search region through fuzzy coding

A technique for automatic exploration of the genetic search region through fuzzy coding (Sharma and Irwin, 2003) has been proposed. Fuzzy coding (FC) provides the value of a variable on the basis of the optimum number of selected fuzzy sets and their effectiveness in terms of degree-of-membership. It is an indirect encoding method and has been shown to perform better than other conventional binary, Gray and floating-point encoding methods. However, the static range of the membership functions is a major problem in fuzzy coding, resulting in longer times to arrive at an optimum solution in large or complicated search spaces. This paper proposes a new algorithm, called fuzzy coding with a dynamic range (FCDR), which dynamically allocates the range of the variables to evolve an effective search region, thereby achieving faster convergence. Results are presented for two benchmark optimisation problems, and also for a case study involving neural identification of a highly non-linear pH neutralisation process from experimental data. It is shown that dynamic exploration of the genetic search region is effective for parameter optimisation in problems where the search space is complicated.

Molecular Logic Gate Arrays

Chemists are now able to emulate the ideas and instruments of mathematics and computer science with molecules. The integration of molecular logic gates into small arrays has been a growth area during the last few years. The design principles underlying a collection of these cases are examined. Some of these computing molecules are applicable in medical- and biotechnologies. Cases of blood diagnostics, 'lab-on-a-molecule' systems, and molecular computational identification of small objects are included.

Improved structure optimization for fuzzy-neural networks

Fuzzy-neural-network-based inference systems are well-known universal approximators which can produce linguistically interpretable results. Unfortunately, their dimensionality can be extremely high due to an excessive number of inputs and rules, which raises the need for overall structure optimization. In the literature, various input selection methods are available, but they are applied separately from rule selection, often without considering the fuzzy structure. This paper proposes an integrated framework to optimize the number of inputs and the number of rules simultaneously. First, a method is developed to select the most significant rules, along with a refinement stage to remove unnecessary correlations. An improved information criterion is then proposed to find an appropriate number of inputs and rules to include in the model, leading to a balanced tradeoff between interpretability and accuracy. Simulation results confirm the efficacy of the proposed method.

A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.

Feedforward Control of Shape Memory Alloy Actuators Using Fuzzy-Based Inverse Preisach Model

This brief investigates a possible application of the inverse Preisach model in combination with the feedforward and feedback control strategies to control shape memory alloy actuators. In the feedforward control design, a fuzzy-based inverse Preisach model is used to compensate for the hysteresis nonlinearity effect. An extrema input history and a fuzzy inference is utilized to replace the inverse classical Preisach model. This work allows for a reduction in the number of experimental parameters and computation time for the inversion of the classical Preisach model. A proportional-integral-derivative (PID) controller is used as a feedback controller to regulate the error between the desired output and the system output. To demonstrate the effectiveness of the proposed controller, real-time control experiment results are presented.