Multi-argument distances

• Published in: Fuzzy sets and systems Vol. 167; no. 1; pp. 92 - 100
• Main Authors: Martín, J., Mayor, G.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Kidlington Elsevier B.V 30.03.2011; Elsevier
• Subjects: Applied sciences; Circuit properties; Collection; Computer science; control theory; systems; Digital circuits; Distance; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Exact sciences and technology; Fermat point; Fuzzy set theory; General topology; Information, signal and communications theory; Lists; Mathematical methods; Mathematics; Metric space; Miscellaneous; Multidistance; OWA operator; Sciences and techniques of general use; Sum-based multidistance; Telecommunications and information theory; Theoretical computing; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Multidistance; OWA operator; Distance; Fermat point; Sum-based multidistance; Fuzzy system; Metric space; Information processing; Fuzzy set
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2010.10.018

In this paper, we propose a formal definition of a multi-argument function distance. The conventional definition of a distance is extended to apply to collections of more than two elements. Some general properties of multidistances are investigated and significant examples are exhibited. Finally, we introduce the concept of ball centered at a list in order to extend the one of the usual ball in a metric space.