On order invariant synthesizing functions. (Q1868094)
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scientific article; zbMATH DE number 1901017
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On order invariant synthesizing functions. |
scientific article; zbMATH DE number 1901017 |
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On order invariant synthesizing functions. (English)
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27 April 2003
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The author offers several characterizations of lattice polynomials [see \textit{G. Birkhoff}, Lattice theory, AMS, Providence (1967; Zbl 0153.02501) and \textit{S. Ovchinnikov}, Order 14, 365--371 (1998; Zbl 0910.06001)]. The author calls them Boolean max-min functions -- they are indeed composed of a set function with 0 or 1 as values and of several maximum and minimum functions. Essential characterizing properties are, in addition to continuity, order invariance and, eventually, idempotence \((M(x,\dots ,x)=x)\). Order statistics, medians, and projection functions are considered as particular cases and characterized in corollaries.
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synthesizing functions
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order invariance
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lattice polynomials
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