On equivalent forms of fuzzy logic systems NM and IMTL

The nilpotent minima are important t-norrns in fuzzy logic and fuzzy reasoning. Two interesting formal systems-nilpotent minimum logic NM and L*-based on nilpotent minima have been proposed and have been intensively studied. In this paper, their equivalence is pointed out. Moreover, coincidence of two related algebraic structures-NM- and Ro-algebras-is also proved. In addition, we give an equivalent form of involutive monoidal t-norm-based logic IMTL. (C) 2002 Elsevier B.V. All rights reserved.