TitleReal, rational and finite-chain semantics for fuzzy logics
Publication TypeConference Paper
Year of Publication2006
AuthorsEsteva F, Godo L, Noguera C
Conference NameActas del XIII Congreso Español sobre Tecnologías y Lógica Fuzzy ESTYLF 2006
Number20/22 Sept

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.