How to construct fuzzy equivalence relations that satisfies reflectivity, symmetry and transitivity ? Could you please give me some examples of fuzzy equivalence relations?
@Joachim thanks a lot for reply
but in (Hu, Qinghua, Yu, Daren Xie, Zongxia. Information-preserving hybrid data reduction based on fuzzy-rough techniques. 2006)
R is a fuzzy equivalence relation if R satisfies
(1) Reflectivity: R(x,x)=1
(2) Symmetry: R(x,y)= R(y,x),
(3) Transitivity
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The fuzzy equivalence relation requires the properties of reflexivity, symmetry and transitivity, be satised. If it satises only the first two, that is, reflexivity and symmetry properties, it is termed as fuzzy compatible relation.
Though it is usually difficult to identify an equivalence relation directly, it is possible to identify a compatible relation in terms of an appropriate ‘distance function’ of the Minkowski class.
Please refer to section 4 of the attached PDF file. I have also attached a few other articles.
http://users.cis.fiu.edu/~iyengar/publication/J-(2003)%20-%20Classification%20of%20Heart%20Rate%20Data%20Using%20Artifictial%20Neural%20Network%20and%20Fuzzy%20Equivalence%20Relation%20-%20%5BJournal%20pattern%20recognition%5D.pdf.pdf
Article Fuzzy equivalence relations and their equivalence classes
Article Fuzzy equivalence relations
@Behrouz Ahmadi-Nedushan Thank you very much for the prompt reply.
I am confused, Is E (a fuzzy equivalence) the same as fuzzy equivalence relation (attached file)?
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