Affiliations: [1] Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Drăgoi 2, RO-310330 Arad, Romania | [2] Department of Social Sciences, Agora University of Oradea, Piaţa Tineretului 8, RO-485526 Oradea, Romania. E-mails: sorin.nadaban@uav.ro, ioan.dzitac@uav.ro
Correspondence:
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Corresponding author.
Abstract: 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 BX of all closed formal balls on a metric space.
