Journal
FUZZY SETS AND SYSTEMS
Volume 158, Issue 11, Pages 1217-1225Publisher
ELSEVIER
DOI: 10.1016/j.fss.2007.01.011
Keywords
modal-like operators; preorders; fuzzy sets; topologies; category theory
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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.
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