Algorithmics: theory & practice
Algorithmics: theory & practice
Introduction to algorithms
Quasi-metrics and the semantics of logic programs
Fundamenta Informaticae
The Complexity of Tree Automata and Logics of Programs
SIAM Journal on Computing
Data Structures and Algorithms
Data Structures and Algorithms
Domination of aggregation operators and preservation of transitivity
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
On the aggregation of some classes of fuzzy relations
Technologies for constructing intelligent systems
Theoretical Computer Science - Spatial representation: Discrete vs. continous computational models
Indexing schemes for similarity search in datasets of short protein fragments
Information Systems
Aggregation of infinite sequences
Information Sciences: an International Journal
Aggregation of asymmetric distances in Computer Science
Information Sciences: an International Journal
Fuzzy Sets and Systems
The average running time of an algorithm as a midpoint between fuzzy sets
Mathematical and Computer Modelling: An International Journal
Sequence spaces and asymmetric norms in the theory of computational complexity
Mathematical and Computer Modelling: An International Journal
On quasi-metric aggregation functions and fixed point theorems
Fuzzy Sets and Systems
| Hi-index | 0.98 |
In 1981, Borsik and Dobos studied in depth the problem of how to merge, by means of a function, a collection (not necessarily finite) of distance spaces in order to obtain a single one as a result [J. Borsik, J. Dobos, On a product of metric spaces, Math. Slovaca 31 (1981) 193-205]. Later on, Herburt and Moszynska studied the same problem for the case of normed linear spaces, inspired by the fact that every norm induces in a natural way a distance on a linear space, and analyzed the relationship between the both aforenamed problems [I. Herburt, M. Moszynska, On metric products, Colloq. Math. 62 (1991) 121-133]. More recently, Romaguera and Schellekens introduced a mathematical approach, based on the notions of asymmetric distance and asymmetric normed linear space, which is suitable for the complexity analysis of programs and algorithms in Computer Science [S. Romaguera, M. Schellekens, Quasi-metric properties of complexity spaces, Topology Appl. 98 (1999) 311-322]. In this paper, motivated by the importance of the information fusion techniques in Artificial Intelligence and by the utility of asymmetric distances and asymmetric norms in Computer Science, we study the Herburt and Moszynska problem for asymmetric normed linear spaces. In particular we give a general description of how to combine a collection (not necessarily finite) of asymmetric normed linear spaces in order to obtain a single one as output and, in addition, we clear up the relationship between this problem and its analogous of combining asymmetric distance spaces which has been already explored by Mayor and Valero [G. Mayor, O. Valero, Aggregation of asymmetric distances in computer science, Inform. Sci. 180 (2010) 803-812]. Furthermore, it is shown that the asymmetric norms employed, in the spirit of Romaguera and Schellekens, in complexity analysis can be retrieved as a particular case of the developed theory. The last fact opens the possibility of applying a wide range of properties from the general aggregation theory in Artificial Intelligence to the complexity analysis of programs and algorithms in Computer Science.