Fuzzy modelling using a simplified rule base

Transparency and complexity are two major concerns of fuzzy rule-based systems. To improve accuracy and precision of the outputs, we need to increase the partitioning of the input space. However, this increases the number of rules exponentially, thereby increasing the complexity of the system and decreasing its transparency. The main factor behind these two issues is the conjunctive canonical form of the fuzzy rules. We present a novel method for replacing these rules with their singleton forms, and using aggregation operators to provide the mechanism for combining the crisp outputs

Macrostate Data Clustering

We develop an effective nonhierarchical data clustering method using an analogy to the dynamic coarse graining of a stochastic system. Analyzing the eigensystem of an interitem transition matrix identifies fuzzy clusters corresponding to the metastable macroscopic states (macrostates) of a diffusive system. A "minimum uncertainty criterion" determines the linear transformation from eigenvectors to cluster-defining window functions. Eigenspectrum gap and cluster certainty conditions identify the proper number of clusters. The physically motivated fuzzy representation and associated uncertainty analysis distinguishes macrostate clustering from spectral partitioning methods. Macrostate data clustering solves a variety of test cases that challenge other methods.Comment: keywords: cluster analysis, clustering, pattern recognition, spectral graph theory, dynamic eigenvectors, machine learning, macrostates, classificatio

Clustering of TS-fuzzy system

This paper presents a fuzzy c-means clustering method for partitioning symbolic interval data, namely the T-S fuzzy rules. The proposed method furnish a fuzzy partition and prototype for each cluster by optimizing an adequacy criterion based on suitable squared Euclidean distances between vectors of intervals. This methodology leads to a fuzzy partition of the TS-fuzzy rules, one for each cluster, which corresponds to a new set of fuzzy sub-systems. When applied to the clustering of TS-fuzzy system the result is a set of additive decomposed TS-fuzzy sub-systems. In this work a generalized Probabilistic Fuzzy C-Means algorithm is proposed and applied to TS-Fuzzy System clustering

Learning fuzzy systems: an ojective function-approach

One of the most important aspects of fuzzy systems is that they are easily understandable and interpretable. This property, however, does not come for free but poses some essential constraints on the parameters of a fuzzy system (like the linguistic terms), which are sometimes overlooked when learning fuzzy system automatically from data. In this paper, an objective function-based approach to learn fuzzy systems is developed, taking these constraints explicitly into account. Starting from fuzzy c-means clustering, several modifications of the basic algorithm are proposed, affecting the shape of the membership functions, the partition of individual variables and the coupling of input space partitioning and local function approximation

Software implementation of automatic Fuzzy system generation and optimization

Automatic fuzzy system generation from sample data is a common task in fuzzy modeling. Here usually first an initial system is created using clustering, grid partitioning or other approaches and next, the parameters of the system are optimized based on the difference between the sample output and the output of the fuzzy system. The software being presented in this paper supports the whole process providing a wide range of parameterization opportunities. It also includes an optimization toolbox that offers five optimization algorithms, from which one represents a novel approach. The proposed new algoríthm was compared with four well-known methods using several benchmark functions and it ensured better results in case of many functions

On the usage of the probability integral transform to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems

We present a new distributed fuzzy partitioning method to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems. The proposed algorithm builds a fixed number of fuzzy sets for all variables and adjusts their shape and position to the real distribution of training data. A two-step process is applied : 1) transformation of the original distribution into a standard uniform distribution by means of the probability integral transform. Since the original distribution is generally unknown, the cumulative distribution function is approximated by computing the q-quantiles of the training set; 2) construction of a Ruspini strong fuzzy partition in the transformed attribute space using a fixed number of equally distributed triangular membership functions. Despite the aforementioned transformation, the definition of every fuzzy set in the original space can be recovered by applying the inverse cumulative distribution function (also known as quantile function). The experimental results reveal that the proposed methodology allows the state-of-the-art multi-way fuzzy decision tree (FMDT) induction algorithm to maintain classification accuracy with up to 6 million fewer leaves.Comment: Appeared in 2018 IEEE International Congress on Big Data (BigData Congress). arXiv admin note: text overlap with arXiv:1902.0935

A robust structure identification method for evolving fuzzy system

This paper proposes a robust structure identification method (RSIM) based on incremental partitioning learning. RSIM starts with an open region (initial domain) that covers all input samples. The initial region starts with one fuzzy rule without fuzzy terms and then evolves through incremental partitioning learning, which creates many subregions for system error minimization. The three major contributions of the proposed RSIM are as follows: It locates sufficient splitting points provided through a robust partitioning technique, determines the optimum trade-off between accuracy and complexity through a novel partition-selection technique, minimizes global error through global least square optimization. These contributions offer many remarkable advantages. First, RSIM provides a solution for the curse of dimensionality. Second, RSIM can also be applied to low-dimensional problems. Third, RSIM seeks to produce few rules with low number of conditions to improve system readability. Fourth, RSIM minimizes the number of fired rules. Therefore, RSIM can achieve low-level complexity systems. Three low-dimension and six high-dimension and real-life benchmarks are used to evaluate the performance of RSIM with state-of-the art methods. Although RSIM has high interpretability, the results prove that RSIM exhibits greater accuracy than other existing methods

Hardware/software codesign methodology for fuzzy controller implementation

This paper describes a HW/SW codesign methodology for the implementation of fuzzy controllers on a platform composed by a general-purpose microcontroller and specific processing elements implemented on FPGAs or ASICs. The different phases of the methodology, as well as the CAD tools used in each design stage, are presented, with emphasis on the fuzzy system development environment Xfuzzy. Also included is a practical application of the described methodology for the development of a fuzzy controller for a dosage system