A Geometrical Interpretation to Define Contradiction Degrees between Two Fuzzy Sets

For inference purposes in both classical and fuzzy logic, neither the information itself should be contradictory, nor should any of the items of available information contradict each other. In order to avoid these troubles in fuzzy logic, a study about contradiction was initiated by Trillas et al. in [5] and [6]. They introduced the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Moreover, the need to study not only contradiction but also the degree of such contradiction is pointed out in [1] and [2], suggesting some measures for this purpose. Nevertheless, contradiction could have been measured in some other way. This paper focuses on the study of contradiction between two fuzzy sets dealing with the problem from a geometrical point of view that allow us to find out new ways to measure the contradiction degree. To do this, the two fuzzy sets are interpreted as a subset of the unit square, and the so called contradiction region is determined. Specially we tackle the case in which both sets represent a curve in [0,1]2. This new geometrical approach allows us to obtain different functions to measure contradiction throughout distances. Moreover, some properties of these contradiction measure functions are established and, in some particular case, the relations among these different functions are obtained.

Experiments with two Approaches for Tracking Drifting Concepts

This paper addresses the task of learning classifiers from streams of labelled data. In this case we can face the problem that the underlying concepts can change over time. The paper studies two mechanisms developed for dealing with changing concepts. Both are based on the time window idea. The first one forgets gradually, by assigning to the examples weight that gradually decreases over time. The second one uses a statistical test to detect changes in concept and then optimizes the size of the time window, aiming to maximise the classification accuracy on the new examples. Both methods are general in nature and can be used with any learning algorithm. The objectives of the conducted experiments were to compare the mechanisms and explore whether they can be combined to achieve a synergetic e ect. Results from experiments with three basic learning algorithms (kNN, ID3 and NBC) using four datasets are reported and discussed.

A Geometrical Construction for the Polynomial Invariants of some Reflection Groups

2000 Mathematics Subject Classification: Primary 20F55, 13F20; Secondary 14L30.

On some Concepts of Residuals

2000 Mathematics Subject Classification: 60E10, 62G15, 62M20