Volume 27, Issue 1 (2016), pp. 141–159
In this paper we establish some properties of fuzzy quasi-pseudo-metric spaces. An important result is that any partial ordering can be defined by a fuzzy quasi-metric, which can be applied both in theoretical computer science and in information theory, where it is usual to work with sequences of objects of increasing information. We also obtain decomposition theorems of a fuzzy quasi-pseudo metric into a right continuous and ascending family of quasi-pseudo metrics. We develop a topological foundation for complexity analysis of algorithms and programs, and based on our results a fuzzy complexity space can be considered. Also, we built a fertile ground to study some types of fuzzy quasi-pseudo-metrics on the domain of words, which play an important role on denotational semantics, and on the poset of all closed formal balls on a metric space.
Volume 25, Issue 4 (2014), pp. 643–662
Wavelet analysis is a powerful tool with modern applications as diverse as: image processing, signal processing, data compression, data mining, speech recognition, computer graphics, etc. The aim of this paper is to introduce the concept of atomic decomposition of fuzzy normed linear spaces, which play a key role in the development of fuzzy wavelet theory. Atomic decompositions appeared in applications to signal processing and sampling theory among other areas.
First we give a general definition of fuzzy normed linear spaces and we obtain decomposition theorems for fuzzy norms into a family of semi-norms, within more general settings. The results are both for Bag–Samanta fuzzy norms and for Katsaras fuzzy norms. As a consequence, we obtain locally convex topologies induced by this types of fuzzy norms.
The results established in this paper, constitute a foundation for the development of fuzzy operator theory and fuzzy wavelet theory within this more general frame.