New constructions of uninorms on bounded lattices

被引：34
作者：
Dan, Yexing [1 ,2 ]
Hu, Bao Qing [1 ,2 ]
Qiao, Junsheng [3 ]
机构：
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China
[2] Wuhan Univ, Hubei Key Lab, Computat Sci, Wuhan 430072, Hubei, Peoples R China
[3] Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Gansu, Peoples R China
来源：
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING | 2019年 / 110卷
基金：
中国国家自然科学基金;
关键词：
Uninorms; Idempotent uninorms; t-Norms; t-Conorms; Bounded lattices; MIGRATIVITY PROPERTY; TRIANGULAR NORMS; PSEUDO-UNINORMS; ORDINAL SUMS; COIMPLICATIONS;
D O I：
10.1016/j.ijar.2019.04.009
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
This paper continues to study the construction of uninorms on bounded lattices. First, we present some new constructions of uninorms on an arbitrary bounded lattice L with some additional constraints on the neutral element. In particular, we obtain two idempotent uninorms on bounded lattices. Then we demonstrate that our new construction methods are different from some existing methods for the construction of uninorms on bounded lattices. In addition, some illustrative examples for the new constructions of uninorms on bounded lattices are provided. In particular, the results presented here provide a partial answer to a problem (as proposed by F. Karacal and R. Mesiar (2015) in [23]), which is "when L is a chain (in particular, when L = [0, 1) is the unit interval) then to any pair (T, S) of a t-norm on [0, e](2) and a t-conorm on [e, 1](2) there are related uninorms. For which bounded lattices a similar claim is valid?". (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：185 / 209
页数：25
相关论文
共 50 条
[1]   A characterization of residual implications derived from left-continuous uninorms [J].
Aguilo, I. ;
Suner, J. ;
Torrens, J. .
INFORMATION SCIENCES, 2010, 180 (20) :3992-4005
[2]  
Aguiló I, 2009, PROCEEDINGS OF THE JOINT 2009 INTERNATIONAL FUZZY SYSTEMS ASSOCIATION WORLD CONGRESS AND 2009 EUROPEAN SOCIETY OF FUZZY LOGIC AND TECHNOLOGY CONFERENCE, P333
[3]   Structure of n-uninorms [J].
Akella, Prabhakar .
FUZZY SETS AND SYSTEMS, 2007, 158 (15) :1631-1651
[4]  
[Anonymous], 2008, STUD FUZZ SOFT COMP
[5]  
Birkhoff G., 1967, Lattice Theory, Vthird
[6]  
Bodjanova S, 2014, I S INTELL SYST INFO, P61, DOI 10.1109/SISY.2014.6923558
[7]   On the structure of uninorms on bounded lattices [J].
Cayli, Gul Deniz .
FUZZY SETS AND SYSTEMS, 2019, 357 :2-26
[8]   Some properties of idempotent uninorms on a special class of bounded lattices [J].
Cayli, Gul Deniz ;
Drygas, Pawel .
INFORMATION SCIENCES, 2018, 422 :352-363
[9]   CONSTRUCTION OF UNINORMS ON BOUNDED LATTICES [J].
Cayli, Gul Deniz ;
Karacal, Funda .
KYBERNETIKA, 2017, 53 (03) :394-417
[10]   On a new class of uninorms on bounded lattices [J].
Cayli, Gul Deniz ;
Karacal, Funda ;
Mesiar, Radko .
INFORMATION SCIENCES, 2016, 367 :221-231
12345