Representations of Archimedean t-norms in interval-valued fuzzy set theory

被引：0
|
作者：
Deschrijver, Glad [1 ]
机构：
[1] Univ Ghent, Dept Appl Math & Comp Sci, Fuzziness & Uncertainty Modeling Res Unit, B-9000 Ghent, Belgium
来源：
NEW DIMENSIONS IN FUZZY LOGIC AND RELATED TECHNOLOGIES, VOL I, PROCEEDINGS | 2007年
关键词：
interval-valued fuzzy set; intuitionistic fuzzy set; t-norm; Archimedean; nilpotent; strict; representation;
D O I：
暂无
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper the Archimedean property and the nilpotency of t-norms on the lattice L(1) is investigated, where L(1) is the underlying lattice of interval-valued fuzzy set theory (Sambuc, 1975) and intuitionistic fuzzy set theory (Atanassov, 1983). We give some characterizations of continuous t-norms on L(1) which satisfy the residuation principle, T(D, D) subset of D, the Archimedean property and nilpotency.
引用
收藏
页码：53 / 60
页数：8
相关论文
共 50 条
  • [31] A bipolar-valued fuzzy set is an intersected interval-valued fuzzy set
    Hu, Bao Qing
    Yiu, Ka-fai Cedric
    INFORMATION SCIENCES, 2024, 657
  • [32] Lattice representations of interval-valued fuzzy sets
    Ranitovic, Marijana Gorjanac
    Petojevic, Aleksandar
    FUZZY SETS AND SYSTEMS, 2014, 236 : 50 - 57
  • [33] Interval-valued Atanassov intuitionistic t-norms and t-conorms endowed with the usual or admissible orders
    Bedregal, Benjamin
    Lima, Lucelia
    Rocha, Marcus
    Dimuro, Gracaliz
    Bustince, Humberto
    COMPUTATIONAL & APPLIED MATHEMATICS, 2023, 42 (01):
  • [34] Interval-valued Atanassov intuitionistic t-norms and t-conorms endowed with the usual or admissible orders
    Benjamín Bedregal
    Lucelia Lima
    Marcus Rocha
    Graçaliz Dimuro
    Humberto Bustince
    Computational and Applied Mathematics, 2023, 42
  • [35] Interval-valued pointwise sustaining degree fuzzy reasoning methods based on the left-continuous t-representable t-norms
    Luo, Minxia
    Xu, Donghui
    JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2022, 42 (06) : 5013 - 5029
  • [36] Combination of interval-valued fuzzy set and soft set
    Yang, Xibei
    Lin, Tsau Young
    Yang, Jingyu
    Li, Yan
    Yu, Dongjun
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (03) : 521 - 527
  • [37] Reverse triple I algorithms based on Schweizer-Sklar interval-valued t-norms
    Luo, Minxia
    Zhou, Xiaoling
    2015 10TH INTERNATIONAL CONFERENCE ON INTELLIGENT SYSTEMS AND KNOWLEDGE ENGINEERING (ISKE), 2015, : 414 - 419
  • [38] Interval valued L-fuzzy ideals based on t-norms and t-conorms
    Jagadeesha, B.
    Srinivas, Kedukodi Babushri
    Prasad, Kuncham Syam
    JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2015, 28 (06) : 2631 - 2641
  • [39] Computational aspects of fuzzy arithmetics based on Archimedean t-norms
    Wagenknecht, M
    Hampel, R
    Schneider, V
    FUZZY SETS AND SYSTEMS, 2001, 123 (01) : 49 - 62
  • [40] Characterization of Complete Fuzzy Preorders Defined by Archimedean t-Norms
    Montes, Ignacio
    Martinetti, Davide
    Diaz, Susana
    Montes, Susana
    INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGE-BASED SYSTEMS: THEORY AND METHODS, PT 1, 2010, 80 : 158 - +
12345