On the minimality of some generating sets of the aggregation clone on a finite chain

被引：8
|
作者：
Halas, Radomir [1 ]
Kuras, Zbynek [1 ]
Pocs, Jozef [1 ,2 ]
机构：
[1] Palacky Univ Olomouc, Fac Sci, Dept Algebra & Geometry, 17 Listopadu 12, Olomouc 77146, Czech Republic
[2] Slovak Acad Sci, Math Inst, Gresakova 6, Kosice 04001, Slovakia
来源：
INFORMATION SCIENCES | 2021年 / 564卷
关键词：
Aggregation clone; Minimal; (chi; circle plus)-generating set; Chain; Aggregation functions;
D O I：
10.1016/j.ins.2021.02.070
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Clone theory plays an important role in studying aggregation functions on bounded posets or bounded lattices. Several important classes of aggregation functions on a bounded lattice L form a clone, particularly the set of all aggregation functions on L, the so-called full aggregation clone on L. For any finite lattice L, this clone is known to be finitely generated and various generating sets and their constructions have been presented in recent papers. The aim of this paper is to extend previous results concerning generating sets of aggregation clones on finite chains. Namely, the objective is to discuss the minimality of certain generating bases, the so-called (chi,circle plus)-generating sets. (C) 2021 Elsevier Inc. All rights reserved.
引用
收藏
页码：193 / 201
页数：9
相关论文
共 50 条
  • [1] On generating sets of the clone of aggregation functions on finite lattices
    Halas, Radomir
    Mesiar, Radko
    Pocs, Jozef
    INFORMATION SCIENCES, 2019, 476 : 38 - 47
  • [2] Minimality of the system of seven equations for the category of finite sets
    Massol, A
    THEORETICAL COMPUTER SCIENCE, 1997, 176 (1-2) : 347 - 353
  • [3] Minimality of the system of seven equations for the category of finite sets
    Cent Natl de la Recherche, Scientifique, Marseille, France
    Theor Comput Sci, 1-2 (347-353):
  • [4] GENERATING SETS OF FINITE GROUPS
    Cameron, Peter J.
    Lucchini, Andrea
    Roney-Dougal, Colva M.
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 370 (09) : 6751 - 6770
  • [5] ON GENERATING SETS OF FINITE ALGEBRAS
    Krempa, Jan
    Stocka, Agnieszka
    DEMONSTRATIO MATHEMATICA, 2015, 48 (04) : 554 - 561
  • [6] Finite free generating sets
    Monteiro, LF
    Abad, M
    Savini, S
    Sewald, J
    DISCRETE MATHEMATICS, 1998, 189 (1-3) : 177 - 189
  • [7] PSEUDO-FINITE SETS, PSEUDO-O-MINIMALITY
    Meir, Nadav
    JOURNAL OF SYMBOLIC LOGIC, 2021, 86 (02) : 577 - 599
  • [8] Generating Sets in Some Semigroups of Order-Preserving Transformations on a Finite Set
    Ayik, Hayrullah
    Bugay, Leyla
    SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2014, 38 (02) : 163 - 172
  • [9] Flexibility in generating sets of finite groups
    Harper, Scott
    ARCHIV DER MATHEMATIK, 2022, 118 (03) : 231 - 237
  • [10] Flexibility in generating sets of finite groups
    Scott Harper
    Archiv der Mathematik, 2022, 118 : 231 - 237
12345