Non-commutative fuzzy Galois connections
Non-commutative fuzzy Galois connections
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DOI：
10.1007/s00500-003-0280-4
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发表时间：
2003-06
期刊：
影响因子：
4.1
通讯作者：
G. Georgescu;A. Popescu
中科院分区：
文献类型：
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作者：
G. Georgescu;A. Popescu
模糊伽罗瓦连接是由Bhumlohlávek在[4]中引入的。这里考虑的真值集的结构是一个完全剩余格，它将讨论置于“交换模糊世界”中。本文所做的工作是去掉交换性，得到相应的Galois联络的概念，推广了Bohlohlávek在[4]和[7]中的一些结果。在真值结构中缺乏交换律，使得它适合于处理一个句子的连接词，其中连接词项之间的顺序是重要的，从而获得了陈述的时间维度。在这个“非对易世界”中，我们有不是一个，而是两个含义（[15]）。因此，伽罗瓦连接将不是一对，而是四重函数，这实际上是两对函数，每个函数都处于对称的情况下。说明这两对在某种意义上是相容的，我们得到了强L-Galois连接的概念，这是一个更有效和多产的概念，修复了非交换性所造成的“损害”。
Fuzzy Galois connections were introduced by Bělohlávek in [4]. The structure considered there for the set of truth values is a complete residuated lattice, which places the discussion in a “commutative fuzzy world”. What we are doing in this paper is dropping down the commutativity, getting the corresponding notion of Galois connection and generalizing some results obtained by Bělohlávek in [4] and [7]. The lack of the commutative law in the structure of truth values makes it appropriate for dealing with a sentences conjunction where the order between the terms of the conjunction counts, gaining thus a temporal dimension for the statements. In this “non-commutative world”, we have not one, but two implications ([15]). As a consequence, a Galois connection will not be a pair, but a quadruple of functions, which is in fact two pairs of functions, each function being in a symmetric situation to his pair. Stating that these two pairs are compatible in some sense, we get the notion of strongL-Galois connection, a more operative and prolific notion, repairing the “damage” done by non-commutativity.