International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Media theory is a new branch of discrete applied mathematics originally developed in mid-nineties to deal with stochastic evolution of preference relations in political science and mathematical psychology. The theory focuses on a particular semigroup of ‘messages’ acting as transformations of a set of ‘states’, called a ‘medium’, whose axioms are both strong and natural. The term ‘medium’ stems from a particular application in which the transformations formalize the effects, on an individual, of ‘tokens’ of information delivered by the environment—that is, the ‘medium’. However, many different types of examples can be found, ranging from learning spaces to hypercube computers, suggesting that this concept is ubiquitous. The paper presents very basic concepts and results of media theory and is aimed at a wide body of researchers in discrete applied mathematics.

Dichotomization of the outcome by a single cut-off point is an important part of medical studies. Usually the relationship between the resulted dichotomized dependent variable and explanatory variables is analyzed with linear regression, probit or logistic regression. However, in many real-life situations, a certain cut-off point is unknown and can be specified only approximately, i.e. surrounded by some (small) uncertainty. It means that in order to have any practical meaning the regression model must be robust to this uncertainty. In this paper, we test the robustness of the linear regression model and get that neither the beta in the model, nor its significance level is robust to the small variations in the dichotomization cut-off point.

As an alternative robust approach to the problem of uncertain categories, we propose to make use of the linear regression model with the fuzzy membership function as a dependent variable. In the paper, we test the robustness of the linear regression model of such fuzzy dependent variable and get that this model can be insensitive against the uncertainty in the cut-off point location.

To demonstrate theoretical conclusions, in the paper we present the modelling results from the real study of low haemoglobin levels in infants.

Naive Bayes models have been successfully used in classification problems where the class variable is discrete. These models have also been applied to regression or prediction problems, i.e. classification problems where the class variable is continuous, but usually under the assumption that the joint distribution of the feature variables and the class is multivariate Gaussian. In this paper we are interested in regression problems where some of the feature variables are discrete while the others are continuous. We propose a Naive Bayes predictor based on the approximation of the joint distribution by a Mixture of Truncated Exponentials (MTE). We have followed a filter-wrapper procedure for selecting the variables to be used in the construction of the model. This scheme is based on the mutual information between each of the candidate variables and the class. Since the mutual information can not be computed exactly for the MTE distribution, we introduce an unbiased estimator of it, based on Monte Carlo methods. We test the performance of the proposed model in artificial and real-world datasets.

The time or space complexity may considerably increase for a single classifier if all features are taken into account. Thus, it is reasonable to train a single classifier by partial features. Then, a set of multiple classifiers can be generated, and an aggregation of outputs from different classifiers is subsequently performed. The aim of this paper is to propose a classification system with a heuristic fusion scheme in which multiple fuzzy association rule-based classifiers with partial features are combined, and show the feasibility and effectiveness of fusing multiple classifiers through the Sugeno integral extended by ordered weighted averaging operators. In comparison with the Sugeno integral by computer simulations on the iris data and the appendicitis data show that the overall classification accuracy rate could be improved by the Sugeno integral with ordered weighted averaging operators. The experimental results further demonstrate that the proposed method performs well in comparison with other fuzzy or non-fuzzy classification methods.

Digital watermark technology has been proposed as an effective method to protect the copyright of multimedia data. An adaptive image watermark scheme based on fuzzy inference system that in discrete wavelet transform domain is proposed. By exploiting the brightness and texture characteristics of human visual system and considering properties of the original image wavelet coefficient, a fuzzy inference system is designed whose inputs are parameters of brightness and texture of the original image and output is the strength of embedded watermarks. It ensures that the watermark embedding strength is determined adaptively. The experimental results show that the watermarks embed by the proposed scheme are robust against attacks commonly used image processing methods such as JPEG compression, Gaussian noise, cropping, mean filtering, median filtering, rotation, and rescaling etc. Proposed scheme are shown to provide very good results in term of image imperceptibility, too.

LCD TV is a rather newly developed product, with limited data available for sales of all panel sizes, and these are collected in a rather vague manner by some research institutes. Therefore, we propose using the fuzzy grey model GM(1,1) with fuzzy-input value to extrapolate the LCD TV demand with fuzzy-output value. By using the fuzzy grey model GM(1,1) we succeeded in forecasting LCD TV demands with limited fuzzy-input data, and carried out a sensitivity analysis to show its robustness for modeling.

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