In the real world, we are confronted not only with complex and high-dimensional data sets, but usually with noisy, incomplete and uncertain data, where the application of traditional methods of knowledge discovery and data mining always entail the danger of modeling artifacts. Originally, information entropy was introduced by Shannon (1949), as a measure of uncertainty in the data. But up to th...

Different generalizations to the case of coverings of the standard approach to entropy applied to partitions of a finite universe X are explored. In the first approach any covering is represented by an identity resolution of fuzzy sets on X and a corresponding probability distribution with associated entropy is defined. A second approach is based on a probability distribution generated by the c...

Entropy is a measurement of the degree of uncertainty. Meanentropy method can be used for modeling the choice among uncertain outcomes. In this paper, we consider the portfolio selection problem under the assumption that security returns are characterized by type-2 fuzzy variables. Since the expectation and entropy of type-2 fuzzy variables haven’t been well defined, type-2 fuzzy variables need...

1. Introduction Cellular Automata have generated much interest [1,2,3] because of their diverse behavior and usefulness as a discrete model for many processes. Wolfram's 1984 paper on universality and complexity in cellular automata [3,4] described four classes of behavior for automata: class 1 for homogeneous stable behavior, class 2 for simple periodic patterns, class 3 for chaotic aperiodic ...

a new cost function based on stochastic fuzzy discrimination information measure is introduced in this paper. focusing on their significant parts, this cost function is used to find the optimal value of threshold for denoising image. it is, in fact, an extension of fuzzy entropy cost function by the present author. multivariable normal distribution is used for creating focus on significant part...

The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...

Here at first we are going to give a brief history of the development of fuzzy entropy. Finally, new measures for entropy of fuzzy sets in continuous cases are introduced. In this article, our main purpose is to show that the entropy of fuzzy number is very much dependent on the selection of intervals. Another important thing which can be observed from the cases discussed is that the entropy of...

An image segmentation technique based on fuzzy entropy is applied for MR brain images to detect a brain tumor is presented in this paper. The proposed method performs image segmentation based on adaptive thresholding of the input MR images. The image is classified into two membership functions, whose member functions of the fuzzy region are Z-function and S-function. The optimal parameters of t...