Admissible and Bayes decisions with fuzzy-valued losses

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2022-04-01 DOI:10.1515/dma-2022-0013

A. S. Shvedov

引用次数: 0

Abstract

Abstract Some results of classical statistical decision theory are generalized by means of the theory of fuzzy sets. The concepts of an admissible decision in the restricted sense, an admissible decision in the broad sense, a Bayes decision in the restricted sense, and a Bayes decision in the broad sense are introduced. It is proved that any Bayes decision in the broad sense with positive prior discrete density is admissible in the restricted sense. The class of Bayes decisions is shown to be complete under certain conditions on the loss function. Problems with a finite set of possible states are considered.

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具有模糊值损失的容许和贝叶斯决策

摘要利用模糊集理论推广了经典统计决策理论的一些结果。介绍了受限制的可容许决策、广义的可容许决策、受限制的贝叶斯决策和广义的贝叶斯决策的概念。证明了广义上具有正先验离散密度的贝叶斯决策在有限意义上是可接受的。在损失函数的一定条件下，贝叶斯决策类是完备的。考虑具有有限可能状态集的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.