On the determination of left-continuous \(t\)-norms and continuous Archimedean \(t\)-norms on some segments. (English) Zbl 1083.39023

A \(t\)(riangular) norm is a function \(T:[0,1]^2\to [0,1]\) such that for all \(x,y,z\in [0,1]\) we have \(T(x,y)=T(y,x),\,T(T(x,y),z)=T(x,T(y,z)),\,T(x,1)=x\) and \(T(x,\cdot)\) is increasing. The author finds new sets of uniqueness for (continuous Archimedean and left continuous) \(t\)-norms. These sets of uniqueness are some vertical segments of \([0,1]^2\) and/or some level sets of the graph of the \(t\) norm.


39B22 Functional equations for real functions
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