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Nonadditive Set Functions on a Finite Set and Linear Inequalities

✍ Scribed by Kenji Kashiwabara

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
256 KB
Volume
210
Category
Article
ISSN
0022-247X

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✦ Synopsis

A set function is a function whose domain is the power set of a set, which is assumed to be finite in this paper. We treat a possibly nonadditive set function, i.e., Ε½ . Ε½ . a set function which does not satisfy necessarily additivity, A q B s Ε½ . AjB for A l B s Π», as an element of the linear space on the power set. Then some of the famous classes of set functions are polyhedral in that linear space, i.e., expressed by a finite number of linear inequalities. We specify the sets of the coefficients of the linear inequalities for some classes of set Ε½ . functions. Then we consider the following three problems: a the domain Ε½ . extension problem for nonadditive set functions, b the sandwich problem for Ε½ . nonadditive set functions, and c the representation problem of a binary relation by a nonadditive set function, i.e., the problem of nonadditive comparative probabilities.

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