A survey of categorical properties of L-fuzzy relations

被引：2
作者：
Alcantara, Maigan S. da S. [1 ,2 ]
Dias, Thiago [1 ]
de Oliveira, Wilson R. [1 ]
Melo, Silvio de B. [2 ]
机构：
[1] Univ Fed Rural Pernambuco, Recife, PE, Brazil
[2] Univ Fed Pernambuco, Cidade Univ, Recife, PE, Brazil
来源：
FUZZY SETS AND SYSTEMS | 2021年 / 425卷
关键词：
Fuzzy sets; Fuzzy relations; Category theory; SET-THEORY; GEOMETRY; MODELS;
D O I：
10.1016/j.fss.2021.03.014
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
An IL-fuzzy relation is a relation valued on a complete lattice IL with a monoidal structure. This paper reviews four categories of IL-fuzzy relations each modelling an area where Fuzzy Set Theory can be applied. We review the notions of these multivalued binary relations and present some basic properties of the corresponding categories aiming at applications in areas such as Computing Science, Linear Logic and Quantum Mechanics. The emphasis is on the monoidal aspects of the categories. Monoidal categories are one of the most applied kinds of categories. A monoidal view of Fuzzy Relations may widen the spectrum of applications of Fuzzy Set Theory. (c) 2021 Elsevier B.V. All rights reserved.
引用
收藏
页码：62 / 82
页数：21
相关论文
共 60 条
  • [1] A categorical semantics of quantum protocols
    Abramsky, S
    Coecke, B
    [J]. 19TH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, PROCEEDINGS, 2004, : 415 - 425
  • [2] Abramsky S., 1996, CONCUR '96: Concurrency Theory. 7th International Conference. Proceedings, P1
  • [3] Abramsky S, 2012, PROC SYM AP, V71, P1
  • [4] [Anonymous], 2007, MATH QUANTUM COMPUTI
  • [5] [Anonymous], 2006, 1 COURSE FUZZY THEOR
  • [6] [Anonymous], 1999, FUZZY LOGIC INTELLIG
  • [7] [Anonymous], 2013, ON FUZZINESS
  • [8] Arbib M. A., 1975, Bulletin of the Australian Mathematical Society, V13, P169, DOI 10.1017/S0004972700024412
  • [9] Awodey S., 2010, Category Theory, V2nd
  • [10] Baez J.C., ARXIV PREPRINT ARXIV
123456