International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

We propose a new approach to find a fuzzy set which corresponds to a given intuitionistic fuzzy set (Atanassov, 1986) in a certain sense. This will help extend a huge array of fuzzy properties, models, etc. available to the case of intuitionistic fuzzy sets.

We propose a Generalized Nearest Prototype Classifier (GNPC) as a common framework for a number of classification techniques. Specifically we consider clustering-and-relabeling; Parzen's classifier; radial basis functions (RBF) networks; learning vector quantization (LVQ) type classifiers; and nearest neighbor rules. To classify an unlabeled point x the GNPC combines the degrees of similarity of x to a set of prototypes. Five questions are addressed for these GNPC families: (1) How many prototypes do we need? (2) How are the prototypes found? (3) How are their class labels obtained? (4) How are the similarities defined? (5) How are the similarities and label information combined? The classification performance of a set of GNPCs is illustrated on two benchmark data sets: IRIS and the 2-spirals data. We study the resubstitution error of the GNPC as a function of the number of prototypes. Our conclusions are that: (a) unsupervised selection (or extraction) of prototypes followed by relabeling is inferior to the techniques that use labels to guide them towards prototypes; (b) the edited nearest neighbor rule is a viable option for GNPC design which has not received the attention it deserves.

Notions of generalised fuzzy conditional and equivalence rules relative to a combination function are introduced and a framework for reasoning with such rules is described. The applicability of this framework to machine learning and knowledge discovery problems is demonstrated. Methods for the automatic generation of two particular types of generalised rule are proposed. The two rule forms considered are rules with weighted AND/OR combination functions, as suggested by Zimmerman and Zysno, and evidential logic equivalence rules as defined by Baldwin. The process of generating rule bases is divided into the problem of generating fuzzy sets from data and that of finding combination functions to optimise the performance of the system given these fuzzy sets. For the former problem a mass assignment based approach is adopted and for the latter semantic discrimination analysis is used in conjunction with customised optimisation algorithms. The potential of rule bases of both forms is illustrated by their application to a number of model and real world machine learning problems.

Several real-world applications (e.g., scheduling, configuration, …) can be formulated as Constraint Satisfaction Problems (CSP). In these cases, a set of variables have to be settled to a value with the requirement that they satisfy a set of constraints. Classical CSPs are defined only by means of crisp (Boolean) constraints. However, as sometimes Boolean constraints are too strict in relation to human reasoning, fuzzy constraints were introduced.

When fuzzy constraints are considered, human reasoning usually performs some compensation between alternatives. Thus other operators than t-norms are advisable. Besides of that, not all constraints can be considered with equal importance. In this paper we show that the WOWA operator can consider both aspects: compensation between constraints and constraints of different importance.

In this paper, based on the concept of the semantic proximity, a partition method of fuzzy inheritance hierarchies has been given. It is shown that this method is reasonable and effective. Particularly, for a problem with fuzzy concepts, such as systematic botany and zoology, this partition method has especial advantages.

This section is maintained by Vladik Kreinovich. Please send your abstract (or copies of papers that you want to see reviewed here), to vladik@cs.utep.edu, or by regular mail to: Vladik Kreinovich, Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA.