For citation:
Rozen V. V. An extension of the ordering to the set of probability measures. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2005, vol. 5, iss. 1, pp. 61-70. DOI: 10.18500/1816-9791-2005-5-1-61-70, EDN: ETWWHE
An extension of the ordering to the set of probability measures
A general method for extension of the ordering to the set of the probability measured. It based on the Galois connection between all such extensions and subsets of isotone mappings of the given ordered set in the real numbers. The canonical extension is defined as extension determined by the set of all isotone mappings. For canonical extension, an effective description is given and the maximal measures in convex polyhedra are found. Some applications of considered methods for decision making problems are indicated.
- Розен В. В., “Смешанные расширения игр с упорядоченными исходами”, ЖВМ и МФ, 1976, № 6, 1436–1450
- Розен В. В., “Об упорядочиваемости множества вероятностных мер”, Изв. вузов. Сер. Матем., 1988, № 11, 72–74
- Розен В. В., “О мерах на упорядоченных множествах”, Теория полугрупп и ее приложения, 11, Саратов, 1993, 35–39
- Биркгоф Г., Теория решеток, М., 1984
- Подиновский В. В., Ногин В. Д., Парето-оптимальные решения многокритериальных задач, М., 1982
- Демьянов В. Ф., Малоземов В. Н., Введение в минимакс, М., 1972
- Никайдо Х., Выпуклые структуры и математическая экономика, М., 1972
- 819 reads