基于关系和条件聚集算子的Choquet-Sugeno类算子
Choquet-Sugeno-like operator based on relation and conditional aggregation operators
摘要：
我们引入了一个~ \textit{Choquet-Sugeno-like operator}，它推广了文献中关于有界函数和单调测度的许多算子，例如，Sugeno-like算子，Lovász和Owen测度扩张，关于~划分分解系统的$\rF$ -分解积分，以及其他.新算子基于依赖关系和条件聚集算子的概念，但不依赖于$t$ -水平集。我们还提供了Choquet-Sugeno-like算子与最近出现在文献中的定义在有限空间上的Choquet-like积分重合的条件，例如反向Choquet积分，$d$ -Choquet积分，基于$\rF$的离散Choquet-like积分，$C_{\rF_1\rF_2}$ -积分的某些版本，$\mathrm{C}\mathrm{C}$-积分（或Choquet-like Copula-based积分）和离散包含-排除积分.研究了Choquet-Sugeno-like算子的一些基本性质。
英文摘要：
We introduce a~\textit{Choquet-Sugeno-like operator} generalizing many operators for bounded functions and monotone measures from the literature, e.g., Sugeno-like operator, Lovász and Owen measure extensions, $\rF$-decomposition integral with respect to a~partition decomposition system, and others. The new operator is based on the concepts of dependence relation and conditional aggregation operators, but it does not depend on $t$-level sets. We also provide conditions for which the Choquet-Sugeno-like operator coincides with some Choquet-like integrals defined on finite spaces and appeared recently in the literature, e.g. reverse Choquet integral, $d$-Choquet integral, $\rF$-based discrete Choquet-like integral, some version of $C_{\rF_1\rF_2}$-integral, $\mathrm{C}\mathrm{C}$-integrals (or Choquet-like Copula-based integral) and discrete inclusion-exclusion integral. Some basic properties of the Choquet-Sugeno-like operator are studied.
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