保序Galois联络系统参数化的闭包结构
Closure structures parameterized by systems of isotone Galois connections
摘要：
研究了由保序伽罗瓦联络系统参数化的闭包算子和闭包系统的性质。这些参数化表示了对闭包算子的幂等性和单调性条件的更强要求。该方法将以往的方法扩展到模糊闭包算子，该算子出现在具有分级属性的对象-属性数据的分析和分级设置中的“若-则”规则推理中，并且也与线性时态逻辑中的类似结果有关。在本文中，我们提出的运营商的基础，并包括在数据分析中出现这样的运营商的一般问题的例子。
英文摘要：
We study properties of classes of closure operators and closure systems parameterized by systems of isotone Galois connections. The parameterizations express stronger requirements on idempotency and monotony conditions of closure operators. The present approach extends previous approaches to fuzzy closure operators which appeared in analysis of object-attribute data with graded attributes and reasoning with if-then rules in graded setting and is also related to analogous results developed in linear temporal logic. In the paper, we present foundations of the operators and include examples of general problems in data analysis where such operators appear.
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