Convolution lattices

被引：24

作者：

De Miguel, L. ^{[1
,2
]}

Bustince, H. ^{[1
,2
]}

De Baets, B. ^{[3
]}

机构：

[1] Univ Publ Navarra, Dept Automat & Computac, Campus Arrosadia S-N, Pamplona 31006, Spain

[2] Univ Publ Navarra, Inst Smart Cities, Campus Arrosadia S-N, Pamplona 31006, Spain

[3] Univ Ghent, Dept Math Modelling Stat & Bioinformat, KERMIT, Coupure Links 653, Ghent, Belgium

来源：

FUZZY SETS AND SYSTEMS | 2018年 / 335卷

关键词：

Algebra; Convolution operations; Lattice; TYPE-2; FUZZY-SETS; MATHEMATICAL MORPHOLOGY; TRUTH VALUES; FINITE;

D O I：

10.1016/j.fss.2017.04.017

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We propose two convolution operations on the set of functions between two bounded lattices and investigate the algebraic structure they constitute, in particular the lattice laws they satisfy. Each of these laws requires the restriction to a specific subset of functions, such as normal, idempotent or convex functions. Combining all individual results, we identify the maximal subsets of functions resulting in a bounded lattice, and show this result to be equivalent to the distributivity of the lattice acting as domain of the functions. Furthermore, these lattices turn out to be distributive as well. Additionally, we show that for the larger subset of idempotent functions, although not satisfying the absorption laws, the convolution operations satisfy the Birkhoff equation. (c) 2017 Elsevier B.V. All rights reserved.

引用

页码：67 / 93

页数：27

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[2]

[Anonymous], 1988, Possibility Theory

[3]

BIRKHOFF G, 1967, C PUBL AM MATH SOC, V25

[4] FUZZY MATHEMATICAL MORPHOLOGIES - A COMPARATIVE-STUDY [J].