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.

An Investigation of Fuzzy Multiple Heuristic Orderings in the Construction of University Examination Timetables

In this paper, we present an investigation into using fuzzy methodologies to guide the construction of high quality feasible examination timetabling solutions. The provision of automated solutions to the examination timetabling problem is achieved through a combination of construction and improvement. The enhancement of solutions through the use of techniques such as metaheuristics is, in some cases, dependent on the quality of the solution obtained during the construction process. With a few notable exceptions, recent research has concentrated on the improvement of solutions as opposed to focusing on investigating the ‘best’ approaches to the construction phase. Addressing this issue, our approach is based on combining multiple criteria in deciding on how the construction phase should proceed. Fuzzy methods were used to combine three single construction heuristics into three different pair wise combinations of heuristics in order to guide the order in which exams were selected to be inserted into the timetable solution. In order to investigate the approach, we compared the performance of the various heuristic approaches with respect to a number of important criteria (overall cost penalty, number of skipped exams, number of iterations of a rescheduling procedure required and computational time) on twelve well-known benchmark problems. We demonstrate that the fuzzy combination of heuristics allows high quality solutions to be constructed. On one of the twelve problems we obtained lower penalty than any previously published constructive method and for all twelve we obtained lower penalty than when any of the single heuristics were used alone. Furthermore, we demonstrate that the fuzzy approach used less backtracking when constructing solutions than any of the single heuristics. We conclude that this novel fuzzy approach is a highly effective method for heuristically constructing solutions and, as such, has particular relevance to real-world situations in which the construction of feasible solutions is often a difficult task in its own right.

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.

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.

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.

Distinguished algebraic semantics for t-norm based fuzzy logics:Methods and algebraic equivalencies

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and ?-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics-namely the class of algebras defined over the real unit interval, the rational unit interval, the hyperreals (all ultrapowers of the real unit interval), the strict hyperreals (only ultrapowers giving a proper extension of the real unit interval) and finite chains, respectively-and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and (strict) hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. © 2009 Elsevier B.V. All rights reserved.

Parental leave regulations and the persistence of the male breadwinner model: Using fuzzy-set ideal type analysis to assess gender equality in an enlarged Europe

his paper uses fuzzy-set ideal type analysis to assess the conformity of European leave regulations to four theoretical ideal typical divisions of labour: male breadwinner, caregiver parity, universal breadwinner and universal caregiver. In contrast to the majority of previous studies, the focus of this analysis is on the extent to which leave regulations promote gender equality in the family and the transformation of traditional gender roles. The results of this analysis demonstrate that European countries cluster into five models that only partly coincide with countries’ geographical proximity. Second, none of the countries considered constitutes a universal caregiver model, while the male breadwinner ideal continues to provide the normative reference point for parental leave regulations in a large number of European states. Finally, we witness a growing emphasis at the national and EU levels concerning the universal breadwinner ideal, which leaves gender inequality in unpaid work unproblematized.