Associative Polynomial Functions over Bounded Distributive Lattices

被引：0
作者：
Miguel Couceiro
Jean-Luc Marichal
机构：
[1] University of Luxembourg,Mathematics Research Unit, FSTC
来源：
Order | 2011年 / 28卷
关键词：
Bounded distributive lattice; Polynomial function; Associativity; Idempotency; Range-idempotency; Functional equation; Primary—28B15; 39B72; Secondary—06D05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n ⩾ 1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case of polynomial functions over bounded distributive lattices and present explicit descriptions of the corresponding associative functions. We also show that, in this case, both generalizations of associativity are essentially the same.
引用
收藏
页码：1 / 8
页数：7
相关论文
共 20 条
[1]  
Couceiro M(2008)On the lattice of equational classes of Boolean functions and its closed intervals J. Mult.-Valued Log. Soft Comput. 14 81-104
[2]  
Couceiro M(2010)Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices Fuzzy Sets Syst. 161 694-707
[3]  
Marichal J-L(2010)Representations and characterizations of polynomial functions on chains J. Mult.-Valued Log. Soft Comput. 16 65-86
[4]  
Couceiro M(1928)Untersuchengen über einen verallgemeinerten Gruppenbegriff Math. Z. 29 1-19
[5]  
Marichal J-L(1995)Varieties of polyadic groups Filomat 9 657-674
[6]  
Dörnte W(2001)On some old and new problems in Quasigroups Relat. Syst. 8 15-36
[7]  
Dudek WA(1977)-ary groups Colloq. Math. Soc. J. Bolyai [“Universal Algebra”, Esztergom (Hungary)] 29 195-202
[8]  
Dudek WA(1996)A note on the axiom of Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 4 235-243
[9]  
Dudek WA(1967)-groups Colloq. Math. 17 209-219
[10]  
Glazek K(1963)An extension of Fung–Fu’s theorem Publ. Math. Debrecen 10 88-92
12