@inproceedings { IIIA-2006-1226, title = {Real, rational and finite-chain semantics for fuzzy logics}, booktitle = {Actas del XIII Congreso Espa\~nol sobre Tecnolog\'{\i}as y L\'ogica Fuzzy ESTYLF 2006}, number = {20/22 Sept}, year = {2006}, pages = {83-88}, abstract = {In the seminal paper of Zadeh about Fuzzy Logic \cite{zadeh}, he defined fuzzy sets over the real unit interval but in real systems applications fuzzy sets over rational numbers in $[0,1]$ or over finite sets of values of a linguistic variable were also used. In this paper we try to analyze the differences between these different possible sets of truth-values in the setting of residuated multiple-valued logics underlying fuzzy sets. Moreover this analysis also clarifies the differences between t-norms in the strict sense (over $[0,1]$) and t-norm like over other linearly ordered sets, namely the rational interval and finite chains.}, author = {Francesc Esteva and Llu\'{\i}s Godo and Carles Noguera} }