@article{81331bf9da3440849b7e2db341f0ccb9,
title = "Relations in Fuzzy Class Theory: Initial steps",
abstract = "This paper studies fuzzy relations in the graded framework of Fuzzy Class Theory (FCT). This includes (i) rephrasing existing work on graded properties of binary fuzzy relations in the framework of Fuzzy Class Theory and (ii) generalizing existing crisp results on fuzzy relations to the graded framework. Our particular aim is to demonstrate that Fuzzy Class Theory is a powerful and easy-to-use instrument for handling fuzzified properties of fuzzy relations. This paper does not rephrase the whole theory of (fuzzy) relations; instead, it provides an illustrative introduction showing some representative results, with a strong emphasis on fuzzy preorders and fuzzy equivalence relations.",
keywords = "Fuzzy Class Theory, Fuzzy equivalence relation, Fuzzy preorder, Fuzzy relation, Graded properties, Similarity",
author = "Libor B{\v e}hounek and Ulrich Bodenhofer and Petr Cintula",
note = "Funding Information: The work of Libor Beˇhounek was supported by the Program “Information Society”, Project 1ET100300517. Parts of this paper were written while Ulrich Bodenhofer was still affiliated with Software Competence Center Hagenberg, A-4232 Hagenberg, Austria. Therefore, he acknowledges partial support by the Austrian Government, the State of Upper Austria, and the Johannes Kepler University Linz in the framework of the Kplus Competence Center Program. Funding Information: The work of Petr Cintula was partly supported by the grant No. B100300502 of the Grant Agency of the Academy of Sciences of the Czech Republic and partly by the Institutional Research Plan AV0Z10300504. Finally, the authors acknowledge partial support of the bilateral Czech–Austrian program KONTAKT/WTZ, project “Formal foundations of fuzzy preference modelling” (Czech No. 6-07-17, Austrian No. 02/2007).",
year = "2008",
month = jul,
day = "16",
doi = "10.1016/j.fss.2007.10.012",
language = "English",
volume = "159",
pages = "1729--1772",
journal = "Fuzzy Sets and Systems",
issn = "0165-0114",
publisher = "Elsevier",
number = "14",
}