Image thresholding plays very important role in many computer vision and image processing applications. Segmentation based on gray level histogram thresholding consists of a method that divides an image into two regions of interest; object and background. In image processing, we deal with many ambiguous situations. Fuzzy set theory is a useful mathematical tool for handling the ambiguity or unc...

In the literature of fuzzy measures, there exist many well known parametric and non-parametric measures, each with its own merits and limitations. But our main emphasis is on applications of these measures to a variety of disciplines. To extend the scope of applications of these fuzzy measures to geometry, we need some special fuzzy measures. In this communication, we have introduced two new fu...

In an earlier work, Lee et al. [1] presented a simple and fast fuzzy classifier that employed fuzzy entropy to evaluate pattern distribution information in a pattern space. In this paper, we extend his work to propose a new fuzzy classifier based on hierarchical fuzzy entropy (FC-HFE). We retained the main parts of the original structure and modified some methods (e.g., decision of the number o...

The information-theoretical entropy is an effective measure of uncertainty connected with an information source. Its transfer from the classical probabilistic information theory models to the fuzzy set theoretical environment is desirable and significant attempts were realized in the existing literature. Nevertheless, there are some open topics for analysis in the suggested models of fuzzy entr...

In this paper, new similarity, inclusion measure and entropy between type-2 fuzzy sets corresponding to grades of memberships are proposed. We also create the relationships among these measures between type-2 fuzzy sets. Several examples are used to present the calculation of these similarity, inclusion measure and entropy between type-2 fuzzy sets. The comparison results show that the proposed...

Heart rate variability (HRV) analysis is a non-invasive tool for assessing cardiac health. Entropy measures quantify the chaotic properties of HRV, but they are sensitive to the choice of their required parameters. Previous studies therefore have performed parameter optimization, targeting solely their particular patient cohort. In contrast, this work aimed to challenge entropy measures with re...

There is given a construction of the entropy of a dynamical system on arbitrary MV-algebra M. If M is the MV-algebra of characteristic functions of a σ-algebra (isomorphic to the σ-algebra), then the construction leads to the Kolmogorov Sinaj entropy. If M is the MV-algebra (tribe) of fuzzy sets, then the construction coincides with the Maličký modification of the Kolmogorov Sinaj entropy for f...

With the advent of the Internet of Things, lightweight devices necessitate secure and cost-efficient key storage. Since traditional secure storage is expensive, the valuable entropy could originate from noisy sources, for which fuzzy extractors allow strong key derivation. While providing information-theoretic security, fuzzy extractors require large amount of input entropy to account for entro...

Decision tree induction is one of common approaches for extracting knowledge from a sets of feature-based examples. In real world, many data occurred in a fuzzy and uncertain form. The decision tree must able to deal with such fuzzy data. This paper presents a tree construction procedure to build a fuzzy decision tree from a collection of fuzzy data by integrating fuzzy set theory and entropy. ...

Heart rate variability (HRV) is the variation of the time interval between consecutive heartbeats and depends on the extrinsic regulation of the heart rate. It can be quantified using nonlinear methods such as entropy measures, which determine the irregularity of the time intervals. In this work, approximate entropy (ApEn), sample entropy (SampEn), fuzzy entropy (FuzzyEn) and fuzzy measure entr...