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引用次数: 0
摘要
在本文的第一部分,我们考虑了:a) 有限集 X 的幂集上的广义信元集;b) 允许广义信元集非凸的广义信元集的一般定义;c) 广义信元集的基本聚合规则的合理性;d) 更新信息的方法。第二部分专门讨论一般情况下上述问题的解决方案,即广义可信集在任意可测空间上的定义。此外,我们还证明了广义信用集更新后的条件可以选择比率相等。这一结果证实了 R.A. Fisher 的论断,即似然函数的定义是唯一的,直到一个正系数为止。
Updating information based on generalized credal sets. Part 2: General case
In the first part of this paper, we have considered: a) generalized credal sets on the powerset of a finite set X; b) their general definition allowing a generalized credal set to be not convex; c) the justification of basic aggregation rules on generalized credal sets; d) ways of updating information. The second part is devoted to the solutions of the above problems for the general case, when generalized credal sets are defined on arbitrary measurable spaces. In addition, we prove that the conditionals after updating of a generalized credal set could be chosen ratio-equivalent. This result confirms the thesis by R.A. Fisher, which says that the likelihood function is defined uniquely up to a positive coefficient.
期刊介绍:
Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies.
In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.