Fields of sets, set functions, set function integrals, and finite additivity
نویسندگان
چکیده
منابع مشابه
On the Additivity of Unbounded Set Functions
The set functions associated with Schrr odinger's equation are known to be unbounded on the algebra of cylinder sets. However, there do exist examples of scalar values set functions which are unbounded, yet-additive on the underlying algebra of sets. The purpose of this note is to show that the set functions associated with Schrr odinger's equation and not-additive on cylinder sets. In the cour...
متن کاملMonotone set-valued functions defined by set-valued Choquet integrals
In this paper, some properties of the monotone set-valued function defined by the set-valued Choquet integral are discussed. It is shown that several important structural characteristics of the original set function, such as null-additivity, strong order continuity, property(S) and pseudometric generating property, etc., are preserved by the new set-valued function. It is also shown that integr...
متن کاملInteraction Transform of Set Functions over a Finite Set
The paper introduces a new transform of set functions over a finite set, which is linear and invertible as the well known Möbius transform in combinatorics. This transform leads to the interaction index, a central concept in multicriteria decision making. The interaction index of a singleton happens to be the Shapley value of the set function or, in terms of cooperative game theory, of the valu...
متن کاملInteraction transform for bi-set functions over a finite set
Set functions appear as a useful tool in many areas of decision making and operations research, and several linear invertible transformations have been introduced for set functions, such as the Möbius transform and the interaction transform. The present paper establish similar transforms and their relationships for bi-set functions, i.e. functions of two disjoint subsets. Bi-set functions have ...
متن کاملA Finite Set of Discrete Functions
Wolpert and Macready’s No Free Lunch theorem proves that no search algorithm is better than any other over all possible discrete functions. The meaning of the No Free Lunch theorem has, however, been the subject of intense debate. We prove that for local neighborhood search on problems of bounded complexity, where complexity is measured in terms of number of basins of attraction in the search s...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1984
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171284000235