Affiliations: [a] Federal Research Center “Computer Sciences and Control”, Russian Academy of Sciences, Prospekt 60-let Oktyabrya, Moscow, Russia | [b]
Belgorod State National Research University, Belgorod, Russia
| [c]
V.G. Shukhov Belgorod State Technological University, Belgorod, Russia
| [d]
Volgograd State Technical University, Volgograd, Russia
Correspondence:
[*]
Corresponding author. Alexey B. Petrovsky, E-mail: [email protected].
Abstract: The paper considers new classes of spaces of finite, bounded, measurable multisets with different metrics, pseudometrics, quasimetrics, symmetrics, and some properties of these metrics. We discuss the possibilities to apply new types of metrics for estimating proximity of objects with many numerical and/or verbal attributes. We use the introduced indexes of similarity and dissimilarity of objects represented as multisets in new methods of group multiple criteria decision making.
Keywords: Multiset, space of multisets, metric, pseudometric, quasimetric, symmetric, multi-attribute objects, similarity and dissimilarity of objects, group multiple criteria decision making, group verbal decision analysis
