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Fuzzy objects in spaces with fuzzy partitions

Authors
  • Močkoř, Jiří1
  • Holčapek, Michal1
  • 1 University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, Ostrava 1, 701 03, Czech Republic , Ostrava 1 (Czechia)
Type
Published Article
Journal
Soft Computing
Publisher
Springer-Verlag
Publication Date
Nov 15, 2016
Volume
21
Issue
24
Pages
7269–7284
Identifiers
DOI: 10.1007/s00500-016-2431-4
Source
Springer Nature
Keywords
License
Yellow

Abstract

A theory of fuzzy objects is derived in the category SpaceFP of spaces with fuzzy partitions, which generalize classical fuzzy sets and extensional maps in sets with similarity relations. It is proved that fuzzy objects in SpaceFP can be characterized by some morphisms in the category of sets with similarity relations. A powerset object functor F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {F}}$$\end{document} in the category SpaceFP is introduced and it is proved that F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {F}}$$\end{document} defines a CSLAT-powerset theory in the sense of Rodabaugh.

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