On generating sets of the clone of aggregation functions on finite lattices

被引：5
|
作者：
Halas, Radomir [1 ]
Mesiar, Radko [1 ,2 ]
Pocs, Jozef [1 ,3 ]
机构：
[1] Palacky Univ Olomouc, Dept Algebra & Geometry, Fac Sci, 17 Listopadu 12, Olomouc 77146, Czech Republic
[2] Slovak Univ Technol Bratislava, Fac Civil Engn, Dept Math & Descript Geometry, Radlinskeho 11, Bratislava 81005 1, Slovakia
[3] Slovak Acad Sci, Math Inst, Gresakova 6, Kosice 04001, Slovakia
来源：
INFORMATION SCIENCES | 2019年 / 476卷
关键词：
(Monotone) clone; Monotone function; Aggregation function; Lattice; Capacity; Generating set;
D O I：
10.1016/j.ins.2018.09.070
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In a recent paper [12] we have shown that aggregation functions on a bounded lattice L form a clone, i.e., the set of functions closed under projections and composition of functions. Moreover, for any finite lattice L we gave a finite set of unary and binary aggregation functions on L from which the aggregation clone is generated. In this paper, a general method for constructing generating sets of the aggregation clone on L is presented. Our approach is based on extending of L-valued capacities leading to so-called full systems of aggregation functions. Several full systems on L are presented (including singleton ones) and their arities are discussed. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：38 / 47
页数：10
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