Asli Celikyilmaz

Enhanced Fuzzy System Models With Improved Fuzzy Clustering Algorithm

Although traditional fuzzy models have proven to have high capacity of approximating the real-world systems, they have some challenges, such as computational complexity, optimization problems, subjectivity, etc. In order to solve some of these problems, this paper proposes a new fuzzy system modeling approach based on improved fuzzy functions to model systems with continuous output variable. The new modeling approach introduces three features: i) an improved fuzzy clustering (IFC) algorithm, ii) a new structure identification algorithm, and iii) a nonparametric inference engine. The IFC algorithm yields simultaneous estimates of parameters of c-regression models, together with fuzzy c-partitioning of the data, to calculate improved membership values with a new membership function. The structure identification of the new approach utilizes IFC, instead of standard fuzzy c-means clustering algorithm, to fuzzy partition the data, and it uses improved membership values as additional input variables along with the original scalar input variables for two different choices of regression methods: least squares estimation or support vector regression, to determine ldquofuzzy functionsrdquo for each cluster. With novel IFC, one could learn the system behavior more accurately compared to other FSM models. The nonparametric inference engine is a new approach, which uses the alike -nearest neighbor method for reasoning. Empirical comparisons indicate that the proposed approach yields comparable or better accuracy than fuzzy or neuro-fuzzy models based on fuzzy rules bases, as well as other soft computing methods.

Fuzzy functions with support vector machines

A new fuzzy system modeling (FSM) approach that identifies the fuzzy functions using support vector machines (SVM) is proposed. This new approach is structurally different from the fuzzy rule base approaches and fuzzy regression methods. It is a new alternate version of the earlier FSM with fuzzy functions approaches. SVM is applied to determine the support vectors for each fuzzy cluster obtained by fuzzy c-means (FCM) clustering algorithm. Original input variables, the membership values obtained from the FCM together with their transformations form a new augmented set of input variables. The performance of the proposed system modeling approach is compared to previous fuzzy functions approaches, standard SVM, LSE methods using an artificial sparse dataset and a real-life non-sparse dataset. The results indicate that the proposed fuzzy functions with support vector machines approach is a feasible and stable method for regression problems and results in higher performances than the classical statistical methods.

Validation criteria for enhanced fuzzy clustering

We introduce two new criterions for validation of results obtained from recent novel-clustering algorithm, improved fuzzy clustering (IFC) to be used to find patterns in regression and classification type datasets, separately. IFC algorithm calculates membership values that are used as additional predictors to form fuzzy decision functions for each cluster. Proposed validity criterions are based on the ratio of compactness to separability of clusters. The optimum compactness of a cluster is represented with average distances between every object and cluster centers, and total estimation error from their fuzzy decision functions. The separability is based on a conditional ratio between the similarities between cluster representatives and similarities between fuzzy decision surfaces of each cluster. The performance of the proposed validity criterions are compared to other structurally similar cluster validity indexes using datasets from different domains. The results indicate that the new cluster validity functions are useful criterions when selecting parameters of IFC models.

Increasing accuracy of two-class pattern recognition with enhanced fuzzy functions

In building an approximate fuzzy classifier system, significant effort is laid on estimation and fine-tuning of fuzzy sets. However, in such systems little thought is given to the way in which membership functions are combined within fuzzy rules. In this paper, a robust method, improved fuzzy classifier functions (IFCF) design is proposed for two-class pattern recognition problems. A supervised hybrid improved fuzzy clustering for classification (IFC-C) algorithm is implemented for structure identification. IFC-C algorithm is based on a dual optimization method, which yields simultaneous estimates of the parameters of c-classification functions together with fuzzy c partitioning of dataset based on a distance measure. The merit of novel IFCF is that the information on natural grouping of data samples i.e., the membership values, are utilized as additional predictors of each fuzzy classifier function to improve accuracy of system model. Improved fuzzy classifier functions are approximated using statistical and soft computing approaches. A new semi-non-parametric inference mechanism is implemented for reasoning. The experimental results of the new modeling approach indicate that the new IFCF is a promising method for two-class pattern recognition problems.

A New Classifier Design with Fuzzy Functions

This paper presents a new fuzzy classifier design, which constructs one classifier for each fuzzy partition of a given system. The new approach, namely Fuzzy Classifier Functions (FCF), is an adaptation of our generic design on Fuzzy Functions to classification problems. This approach couples any fuzzy clustering algorithm with any classification method, in a unique way. The presented model derives fuzzy functions (rules) from data to classify patterns into number of classes. Fuzzy c-means clustering is used to capture hidden fuzzy patterns and a linear or a non-linear classifier function is used to build one classifier model for each pattern identified. The performance of each classifier is enhanced by using corresponding membership values of the data vectors as additional input variables. FCF is proposed as an alternate representation and reasoning schema to fuzzy rule base classifiers. The proposed method is evaluated by the comparison of experiments with the standard classifier methods using cross validation on test patterns.

Modeling Uncertainty with Improved Fuzzy Functions

This chapter introduces a new uncertainty modeling architecture for the new improved fuzzy functions systems. The theory is based on a new interval type-2 fuzzy system. The uncertainties are captured by automatic identification of the structure of fuzzy functions, and upper and lower boundaries of key parameters that define fuzzy sets. A new type reduction method is introduced.

Improved Fuzzy Clustering

The new fuzzy system modeling approach based on fuzzy functions implements fuzzy clustering algorithm during structure identification of the given system. This chapter introduces foundations of fuzzy clustering algorithms and compares different types of well-known fuzzy clustering approaches. Then, a new improved fuzzy clustering approach is presented to be used for fuzzy functions approaches to re-shape membership values into powerful predictors. Lastly, two new cluster validity indices are introduced to be used to validate the improved fuzzy clustering algorithm results.

Evolution of Fuzzy System Models: An Overview and New Directions

Fuzzy System Models (FSM), as one of the constituents of soft computing methods, are used for mining implicit or unknown knowledge by approximating systems using fuzzy set theory. The undeniable merit of FSM is its inherent ability of dealing with uncertain, imprecise, and incomplete data and still being able to make powerful inferences. This paper provides an overview of FSM techniques with an emphasis on new approaches on improving the prediction performances of system models. A short introduction to soft computing methods is provided and new improvements in FSMs, namely, Improved Fuzzy Functions (IFF) approaches is reviewed. IFF techniques are an alternate representation and reasoning schema to Fuzzy Rule Base (FRB) approaches. Advantages of the new improvements are discussed.

New Cluster Validity Index with Fuzzy Functions

A new cluster validity index is introduced to validate the results obtained by the recent Improved Fuzzy Clustering (IFC), which combines two different methods, i.e., fuzzy c-means clustering and fuzzy c-regression, in a novel way. Proposed validity measure determines the optimum number of clusters of the IFC based on a ratio of the compactness to separability of the clusters. The compactness is represented with: (i) the sum of the average distances of each object to their cluster centers, and (ii) the error measure of their fuzzy functions, which utilizes membership values as additional input variables. The separability is based on the ratio between: (i) the maximum distance between the cluster representatives, and (ii) the angles between their representative fuzzy functions. The experiments exhibit that the new cluster validity index is a useful function when selecting the parameters of the IFC.

Fuzzy Sets and Systems

This chapter reviews basic principles of the fuzzy sets and fuzzy logic as well as the inference methodology of the approximate reasoning and the extension principle theories that are fundamental parts of structure identification with traditional fuzzy rule base systems. Also presented is the “Fuzzy Functions” as defined in the literature and as presented in this work. Extensions of some well-known fuzzy inference systems including structures of well known hybrid fuzzy systems are also presented at the end of this chapter.