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

页码：38 / 47

页数：10

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