NMŁ, a schematic extension of F. Esteva and L. Godo's logic MTL
The authors study an extension of the MTL logic of \textit{F. Esteva} and \textit{L. Godo} [ibid. 124, 271--288 (2001; Zbl 0994.03017)] by defining the new fuzzy logic NMŁ. The corresponding standard algebra is \(([0,1], *_J, \rightarrow_J, \max, \min, 0,1)\), where \(*_J : [0,1]^2\to[0,1]\) is defined as \((a*_J b) = 0\) if \(a + b \leq 1\), \((a*_J b) = (a + b - 2/3)\) if \(1/3 < 1 - a< b < 2/3\), \((a*_J b) = \min(a,b)\) otherwise for all \(a,b\in [0,1]\), and \(\rightarrow_ J : [0,1]^2\to[0,1]\) is defined as \((a\rightarrow_ J b) = 1\) if \(a\leq b\), \((a\rightarrow_ J b) = 2/3 -a +b\) if \(1/3 < b < a < 2/3\), \((a\rightarrow_ J b) = \max(1 - a,b)\) otherwise for all \(a,b\in [0,1]\). Note that \(*_J\) stands for the t-norm due to \textit{S. Jenei} [ibid. 110, 157--174 (2000; Zbl 0941.03059)]. As \textit{S. Jenei} and \textit{F. Montagna} [Stud. Log. 70, 183--192 (2002; Zbl 0997.03027)] have proved a completeness theorem for the MTL logic, here the authors prove an analogous result for the NMŁ logic.
scientific article; zbMATH DE number 2126004