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.

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.

Dynamic pricing model and algorithm for perishable products with fuzzy demand (ABS 2* Journal)

This paper studies the dynamic pricing problem of selling fixed stock of perishable items over a finite horizon, where the decision maker does not have the necessary historic data to estimate the distribution of uncertain demand, but has imprecise information about the quantity demand. We model this uncertainty using fuzzy variables. The dynamic pricing problem based on credibility theory is formulated using three fuzzy programming models, viz.: the fuzzy expected revenue maximization model, a-optimistic revenue maximization model, and credibility maximization model. Fuzzy simulations for functions with fuzzy parameters are given and embedded into a genetic algorithm to design a hybrid intelligent algorithm to solve these three models. Finally, a real-world example is presented to highlight the effectiveness of the developed model and algorithm.

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.

Towards Possibilistic Fuzzy Answer Set Programming

Fuzzy answer set programming (FASP) is a generalization of answer set programming to continuous domains. As it can not readily take uncertainty into account, however, FASP is not suitable as a basis for approximate reasoning and cannot easily be used to derive conclusions from imprecise information. To cope with this, we propose an extension of FASP based on possibility theory. The resulting framework allows us to reason about uncertain information in continuous domains, and thus also about information that is imprecise or vague. We propose a syntactic procedure, based on an immediate consequence operator, and provide a characterization in terms of minimal models, which allows us to straightforwardly implement our framework using existing FASP solvers.

A Generalized Fuzzy Linguistic Model for Predicting Component Concentrations in an Optical Gas Sensing System

Motivated by environmental protection concerns, monitoring the flue gas of thermal power plant is now often mandatory due to the need to ensure that emission levels stay within safe limits. Optical based gas sensing systems are increasingly employed for this purpose, with regression techniques used to relate gas optical absorption spectra to the concentrations of specific gas components of interest (NOx, SO2 etc.). Accurately predicting gas concentrations from absorption spectra remains a challenging problem due to the presence of nonlinearities in the relationships and the high-dimensional and correlated nature of the spectral data. This article proposes a generalized fuzzy linguistic model (GFLM) to address this challenge. The GFLM is made up of a series of “If-Then” fuzzy rules. The absorption spectra are input variables in the rule antecedent. The rule consequent is a general nonlinear polynomial function of the absorption spectra. Model parameters are estimated using least squares and gradient descent optimization algorithms. The performance of GFLM is compared with other traditional prediction models, such as partial least squares, support vector machines, multilayer perceptron neural networks and radial basis function networks, for two real flue gas spectral datasets: one from a coal-fired power plant and one from a gas-fired power plant. The experimental results show that the generalized fuzzy linguistic model has good predictive ability, and is competitive with alternative approaches, while having the added advantage of providing an interpretable model.

A generalized fuzzy linguistic model for predicting component concentrations in an optical gas sensing system

Motivated by environmental protection concerns, monitoring the flue gas of thermal power plant is now often mandatory due to the need to ensure that emission levels stay within safe limits. Optical based gas sensing systems are increasingly employed for this purpose, with regression techniques used to relate gas optical absorption spectra to the concentrations of specific gas components of interest (NO_x, SO₂ etc.). Accurately predicting gas concentrations from absorption spectra remains a challenging problem due to the presence of nonlinearities in the relationships and the high-dimensional and correlated nature of the spectral data. This article proposes a generalized fuzzy linguistic model (GFLM) to address this challenge. The GFLM is made up of a series of “If-Then” fuzzy rules. The absorption spectra are input variables in the rule antecedent. The rule consequent is a general nonlinear polynomial function of the absorption spectra. Model parameters are estimated using least squares and gradient descent optimization algorithms. The performance of GFLM is compared with other traditional prediction models, such as partial least squares, support vector machines, multilayer perceptron neural networks and radial basis function networks, for two real flue gas spectral datasets: one from a coal-fired power plant and one from a gas-fired power plant. The experimental results show that the generalized fuzzy linguistic model has good predictive ability, and is competitive with alternative approaches, while having the added advantage of providing an interpretable model.