A unifying study between modal-like operators, topologies and fuzzy sets

被引:26
作者
Jarvinen, Jouni
Kortelainen, Jari
机构
[1] Lappeenranta Univ Technol, Lab Appl Math, FI-53851 Lappeenranta, Finland
[2] Turku Univ, Turku Ctr Comp Sci, FI-20014 Turku, Finland
关键词
modal-like operators; preorders; fuzzy sets; topologies; category theory;
D O I
10.1016/j.fss.2007.01.011
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
The paper presents the essential connections between modal-like operators, topologies and fuzzy sets. We show, for example, that each fuzzy set determines a preorder and an Alexandrov topology, and that similar correspondences hold also for the other direction. Further, a category for preorder-based fuzzy sets is defined, and it is shown that its equivalent subcategory of representatives is isomorphic to the categories of preordered sets and Alexandrov spaces. Moreover, joins, meets and complements for the objects in this category of representatives are determined. This suggests how to define for fuzzy subsets of a certain universe the lattice operations in a canonical way. (C) 2007 Elsevier B.V. All rights reserved.
引用
收藏
页码:1217 / 1225
页数:9
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