TY - GEN
T1 - Strict fuzzy orderings in a similarity-based setting
AU - Bodenhofer, Ulrich
AU - Demirci, Mustafa
PY - 2005
Y1 - 2005
N2 - This paper introduces and justifies a similaritybased concept of strict fuzzy orderings and provides constructions how fuzzy orderings can be transformed into strict fuzzy orderings and vice versa. We demonstrate that there is a meaningful correspondence between fuzzy orderings and strict fuzzy orderings. Unlike the classical case however, we do not obtain a general one-to-one correspondence. We observe that the strongest results are achieved if the underlying t-norm induces a strong negation, which, in particular, includes nilpotent t-norms and the nilpotent minimum.
AB - This paper introduces and justifies a similaritybased concept of strict fuzzy orderings and provides constructions how fuzzy orderings can be transformed into strict fuzzy orderings and vice versa. We demonstrate that there is a meaningful correspondence between fuzzy orderings and strict fuzzy orderings. Unlike the classical case however, we do not obtain a general one-to-one correspondence. We observe that the strongest results are achieved if the underlying t-norm induces a strong negation, which, in particular, includes nilpotent t-norms and the nilpotent minimum.
KW - Fuzzy equivalence relations
KW - Fuzzy orderings strict fuzzy orderings
UR - http://www.scopus.com/inward/record.url?scp=33745616606&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:33745616606
SN - 8476538723
SN - 9788476538722
T3 - Proceedings - 4th Conference of the European Society for Fuzzy Logic and Technology and 11th French Days on Fuzzy Logic and Applications, EUSFLAT-LFA 2005 Joint Conference
SP - 297
EP - 302
BT - Proceedings - 4th Conference of the European Society for Fuzzy Logic and Technology and 11th French Days on Fuzzy Logic and Applications, EUSFLAT-LFA 2005 Joint Conference
T2 - Joint 4th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2005 and 11th French Days on Fuzzy Logic and Applications, LFA 2005
Y2 - 7 September 2005 through 9 September 2005
ER -