Fuzzy Galois connections categorically

被引：14
|
作者：
Gutierrez Garcia, Javier [2 ]
Mardones-Perez, Iraide [2 ]
de Prada Vicente, Maria Angeles [2 ]
Zhang, Dexue [1 ]
机构：
[1] Sichuan Univ, Dept Math, Chengdu 610064, Peoples R China
[2] Univ Pais Vasco Euskal Herriko Unibertsitatea, Dept Matemat, Bilbao 48080, Spain
来源：
MATHEMATICAL LOGIC QUARTERLY | 2010年 / 56卷 / 02期
关键词：
Unital quantale; category enriched over a unital quantale; Omega-adjunction; Omega-relation; covariant fuzzy Galois connection; contravariant fuzzy Galois connection; Girard quantale; SPACES;
D O I：
10.1002/malq.200810044
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper presents a systematic investigation of fuzzy (non-commutative) Galois connections in the sense of R. Belohlavek [1], from the point of view of enriched category theory. The results obtained show that the theory of enriched categories makes it possible to present the theory of fuzzy Galois connections in a succinct way; and more importantly, it provides a useful method to express and to study the link and the difference between the commutative and the non-commutative worlds. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
引用
收藏
页码：131 / 147
页数：17
相关论文
共 50 条
  • [1] GALOIS CONNECTIONS CATEGORICALLY
    HERRLICH, H
    HUSEK, M
    JOURNAL OF PURE AND APPLIED ALGEBRA, 1990, 68 (1-2) : 165 - 180
  • [2] Fuzzy Galois connections
    Bêlohlávek, R
    MATHEMATICAL LOGIC QUARTERLY, 1999, 45 (04) : 497 - 504
  • [3] Fuzzy Galois connections on fuzzy posets
    Yao, Wei
    Lu, Ling-Xia
    MATHEMATICAL LOGIC QUARTERLY, 2009, 55 (01) : 105 - 112
  • [4] Fuzzy Galois connections on fuzzy sets
    Gutierrez Garcia, Javier
    Lai, Hongliang
    Shen, Lili
    FUZZY SETS AND SYSTEMS, 2018, 352 : 26 - 55
  • [5] Relational fuzzy Galois connections
    Cabrera, Inma P.
    Cordero, Pablo
    Ojeda-Aciego, Manuel
    2017 JOINT 17TH WORLD CONGRESS OF INTERNATIONAL FUZZY SYSTEMS ASSOCIATION AND 9TH INTERNATIONAL CONFERENCE ON SOFT COMPUTING AND INTELLIGENT SYSTEMS (IFSA-SCIS), 2017,
  • [6] Triadic fuzzy Galois connections as ordinary connections
    Belohlavek, Radim
    Osicka, Petr
    FUZZY SETS AND SYSTEMS, 2014, 249 : 83 - 99
  • [7] Triadic fuzzy Galois connections as ordinary connections
    Belohlavek, Radim
    Osicka, Petr
    2012 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE), 2012,
  • [8] Representation of fuzzy subsets by Galois connections
    Antoni, Lubomir
    Krajci, Stanislav
    Kridlo, Ondrej
    FUZZY SETS AND SYSTEMS, 2017, 326 : 52 - 68
  • [9] Isotone fuzzy Galois connections with hedges
    Konecny, Jan
    INFORMATION SCIENCES, 2011, 181 (10) : 1804 - 1817
  • [10] Fuzzy Galois connections under weak conditions
    Frascella, A.
    FUZZY SETS AND SYSTEMS, 2011, 172 (01) : 33 - 50
12345