Some properties of the variations of non-additive set functions on T-tribes

Authors:
Chunqiao Tan;Qiang Zhang
Affiliations:
School of Management & Economics, Beijing Institute of Technology, Beijing 100081, China and Equipment Support Department, Academy of Military Transportation, Tianjin 300161, China;School of Management & Economics, Beijing Institute of Technology, Beijing 100081, China
Venue:
Fuzzy Sets and Systems
Year:
2007

Citing 7
Cited 0

Values and cores of fuzzy games with infinitely many players

International Journal of Game Theory
Non-monotonic fuzzy measures and the Choquet integral

Fuzzy Sets and Systems
Some properties of the variations of non-additive set functions I

Fuzzy Sets and Systems
Some properties of the variations of non-additive set functions II

Fuzzy Sets and Systems
Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference

Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference
An Introduction to Copulas (Springer Series in Statistics)

An Introduction to Copulas (Springer Series in Statistics)
Non-atomic fuzzy measures and games

Fuzzy Sets and Systems

Quantified Score

Hi-index	0.20

Visualization

Abstract

The inclusion variation and chain variation on T∞-tribes play an important role in T∞-measures and fuzzy games theory, where they were used for additive set functions on T∞-tribe. In this paper classical variation theory is extended to non-additive set functions on Ttribes, after defining the inclusion variation, disjoint and chain variation on T-tribes, we investigate some properties of these three variations in detail, such as, the (null-) null-additivity, exhaustivity, order continuity, continuity from the left and so on. An alternative proof of the Jordan decomposition theorem is given. Thus, some results pertaining to variations in classical measure theory are generalized. In some case, as for T∞-measures on T∞-tribe, its different formal variations can be extended to Ts-measures on Ts-tribes.