Paulo Serra

Transformation of a Mamdani FIS to First Order Sugeno FIS

In many decision support applications, it is important to guarantee the expressive power, easy formalization and interpretability of Mamdani-type fuzzy inference systems (FIS), while ensuring the computational efficiency and accuracy of Sugeno-type FIS. Hence, in this paper we present an approach to transform a Mamdani-type FIS into a Sugeno-type FIS. We consider the problem of mapping Mamdani FIS to Sugeno FIS as an optimization problem and by determining the first order Sugeno parameters, the transformation is achieved. To solve this optimization problem we compare three methods: least squares, genetic algorithms and an adaptive neuro-fuzzy inference system. An illustrative example is presented to discuss the approaches.

Defining Fuzzy Measures: A Comparative Study with Genetic and Gradient Descent Algorithms

Due to limitations of classical weighted average aggregation operators, there is an increase usage of fuzzy integrals, like the Sugeno and Choquet integrals, as alternative aggregation operators. However, their applicability has been threatened by the crux of determining the fuzzy measures in real problems. One way to determine these measures is by using learning data and optimizing the parameters. In this paper we made a comparative study of two well known optimization algorithms, Genetic Algorithm and Gradient Descent to determine fuzzy measures. Two illustrative cases are used to compare the algorithms and assess their performance.

RULE CORRELATION AND CHOQUET INTEGRATION IN FUZZY INFERENCE SYSTEMS

We propose an extension of the Takagi-Sugeno-Kang (TSK) fuzzy inference system, using Choquet integration for aggregating the single rule outputs. In the new Choquet-TSK fuzzy inference system, the pairwise synergies between rules are encoded in a rule correlation matrix computed from the activation pattern of the rule base. The rule correlation matrix is then used to modulate the parameters of the Choquet integration scheme in order to compensate for the effect of rule synergies, which are present in most rule bases to a higher or lesser extent. The standard TSK fuzzy inference system remains a particular instance of the proposed Choquet-TSK extension and corresponds to the ideal case of rule independence. However, when rule correlation is present, the Choquet-TSK fuzzy inference system takes it into account when computing the final output of the system. On the basis of the rule correlation matrix, the new aggregation scheme of the Choquet-TSK fuzzy inference system attenuates the effective weight of positively correlated rules and emphasizes that of negatively correlated rules. Some case studies are discussed in order to illustrate the proposed methodology.

Adaptive Empirical Bayesian Smoothing Splines

In this paper we develop and study adaptive empirical Bayesian smoothing splines. These are smoothing splines with both smoothing parameter and penalty order determined via the empirical Bayes method from the marginal likelihood of the model. The selected order and smoothing parameter are used to construct adaptive credible sets with good frequentist coverage for the underlying regression function. We use these credible sets as a proxy to show the superior performance of adaptive empirical Bayesian smoothing splines compared to frequentist smoothing splines.

Choquet Integration and Correlation Matrices in Fuzzy Inference Systems

where we consider the individual weights of the fuzzy rules, wi > 0, to be the normalized activation levels αi for i = 1, . . . , n. In this paper we propose an extension to the TSK fuzzy inference system based on Choquet interation [5, 6], called Choquet–TSK. In our model, a matrix of pairwise correlations among the activation levels of the FIS rules is explicitly used in the aggregation process, leading to attenuation effects when correlations are positive and emphasizing effects when correlations are negative. Consider a finite set of interacting criteria N = {1, 2, . . . , n}. A Choquet measure [1] on the set N is a set function μ : P(N) −→ [0, 1] satisfying

On properties of the algorithm for pursuing a drifting quantile

The recurrent algorithm for pursuing a time-varying (“drifting”) quantile is suggested. The common nonasymptotic upper bound of the algorithm quality is established, which is then used in a few examples of the conditions for the quantile drift function. Estimates of the degree (rate) of convergence of the algorithm for the considered examples are obtained.

Comparison of Genetic and Gradient Descent Algorithms for Determining Fuzzy Measures

The increasing usage of fuzzy integrals as aggregation operators, such as Sugeno and Choquet integrals, is threatened by the crux of determining the fuzzy measures in real problems. One way to determine these measures is by using historical data and tuning the parameters. During the past decade many algorithms have been introduced for this purpose and in this paper we make a comparison between two well known, genetic algorithm and gradient descent. Our objective is to assess which algorithm performs better for usage in real applications; hence we use two illustrative cases to compare the algorithms. The results show that gradient descent performs better in recognizing the pattern in less time and with less deviation

Recursive Estimation of Conditional Spatial Medians and Conditional Quantiles

Abstract We consider the problem of constructing an on-line (recursive) algorithm for tracking a conditional spatial median, a center of a multivariate distribution. In the one-dimensional case we also track conditional quantiles of arbitrary level. We establish a nonasymptotic upper bound for the L p -risk of the algorithm, which is then minimized under different assumptions on the magnitude of the variation of the spatial median or quantile. We derive convergence rates for the examples we consider.

Fuzzy Alarm System For Laser Gyroscopes Degradation

Abstract ROSETTA is a European Space Agency (ESA) unrnanned space probe launched in 2004 to study the comet 67P/Churyumov-Gerasimenko. This paper discusses the design of a fuzzy alarm system regarding the intensity degradation of ROSETTA’s laser gyroscopes. The fuzzy alarm system proposed makes use of a novel fuzzy inference scheme, incorporating the technique of Choquet integration. This research work was done in the scope of an ESA project, as aproof-of-concept for a new fuzzy inference scheme.