Janusz T. Starczewski

Connectionist Structures of Type 2 Fuzzy Inference Systems

In Fuzzy Inference Systems (FIS) the rule base consists of fuzzy relations between antecedents and consequents represented by classical fuzzy sets. Because their membership grades are exact real numbers in the unit interval [0, 1], there is no uncertainty in this sort of specification. In many applications there is some uncertainty as to the memberships, hence they can be stated as ordinary fuzzy sets of type 1 and can constitute type 2 fuzzy sets.In the world literature exists a global model of type 2 FIS. However it consists of an enormous number of embedded subsystems of type 1 and with regard to this model it has not found any use in connectionist realizations. In this paper we derive connectionist structures of type 2 FIS.

Interval Type 2 Neuro-Fuzzy Systems Based on Interval Consequents

There are several ways to synthesize fuzzy systems and neural networks. The so-called neuro-fuzzy systems exhibit advantages of both techniques, namely learning abilities of neural networks and natural language description of fuzzy systems. Recently the concept of type 2 fuzzy sets, i.e. fuzzy sets with fuzzy membership grades, was introduced to fuzzy inference systems. This paper presents a new neuro-fuzzy system of type 2 derived under the assumption that the rule antecedents are characterized by interval fuzzy membership grades and the consequents are intervals. An application for the checking of the driver’s steering behaviors is given as an example.

Efficient triangular type-2 fuzzy logic systems

In this study, an efficient fuzzy logic system (FLS) based on triangular type-2 fuzzy sets is designed. In detail, this paper provides a new method for computational complexity reduction in t-norm operations extended on triangular type-2 fuzzy sets. It is demonstrated that our approximate extended t-norms for arguments with triangular membership functions (MFs) satisfy axiomatics of the type-2 t-norm. A new efficient approximate iterative procedure based on the K-M type-reduction is proposed in order to develop triangular type-2 FLSs. The utility of triangular type-2 FLSs in approximate reasoning is illustrated by numerical examples.

A Triangular Type-2 Fuzzy Logic System

So far, computational complexity of non-interval type-2 fuzzy logic systems (FLS) has not allowed to make an engineering use of them. This paper provides a new method for complexity reduction to operations on triangular type-2 fuzzy sets. The method for the algebraic product case is validated with the use of an original theorem for calculating extended continuous t-norms for arguments characterized by normal and upper semicontinuous membership functions (MF). A new approximate type-reduction method similar to the Karnik type-2 FLS and its neuro-fuzzy structure is developed. The use of triangular uncertainties in FLS is justified by the example.

Extended triangular norms

The paper is devoted to classical t-norms extended to operations on fuzzy quantities in accordance with the generalized Zadeh extension principle. Such extended t-norms are used for calculating intersection of type-2 fuzzy sets. Analytical expressions for membership functions of some extended t-norms are derived assuming special classes of fuzzy quantities, i.e., fuzzy truth intervals or fuzzy truth numbers. The possibility of applying these results in the construction of type-2 adaptive network fuzzy inference systems is illustrated on several examples.

Modular type-2 neuro-fuzzy systems

In the paper we study a modular system which can be converted into a type-2 neuro-fuzzy system. The rule base of such system consists of triangular type-2 fuzzy sets. The modular structure is trained using the backpropagation method combined with the AdaBoost algorithm. By applying the type-2 neurofuzzy system, the modular structure is converted into a compressed form. This allows to overcome the training problem of type-2 neuro-fuzzy systems. An illustrative example is given to show the efficiency of our approach in the problems of classification.

A new method for dealing with unbalanced linguistic term set

In this paper, a new method for dealing with an unbalanced linguistic term set is introduced. The proposed method is a modification of the 2-tuple linguistic model, in which we use a set of extended linguistic terms. The extended linguistic term is a pair that consists a linguistic label and a value of correction factor which describes the term shift relative to its position in an equidistant term set. This modification allows us to obtain the method that is computationally less expensive and give simpler semantics than method based on linguistic hierarchies.

Fully controllable ant colony system for text data clustering

The paper presents a new Fully Controllable Ant Colony Algorithm (FCACA) for the clustering of the text documents in vector space. The proposed new FCACA is a modified version of the Lumer and Faieta Ant Colony Algorithm (LF-ACA). The algorithm introduced new version of the basic heuristic decision function significantly improves the convergence and greater control over the process of the grouping data. The proposed solution was shown in a text example proving efficiency of the proposed solution in comparison with other grouping algorithms.

Learning methods for type-2 FLS based on FCM

This paper presents a new two-phase learning method for interval type-2 fuzzy logic systems. The method combines traditional learning approaches to type-1 fuzzy systems with fitting of interval memberships using FCM memberships. Two improving modifications of the proposed method are supplied additionally.

Centroid of triangular and Gaussian type-2 fuzzy sets

Abstract In this paper, we present exact computation procedures for the centroid of type-2 fuzzy sets with either triangular or Gaussian secondary membership functions. We assume the standard formulation of the centroid based on the sup-min extension principle. The centroid of a triangular type-2 fuzzy set can be considered as a subsequent analytical extension of the KM type-reduction procedure dedicated to interval type-2 sets. The centroid of a Gaussian type-2 fuzzy set is recursively expressed by an independent procedure.