On equivalent forms of fuzzy logic systems NM and IMTL

Abstract

The nilpotent minima are important t-norms 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 R0-algebras - is also proved. In addition, we give an equivalent form of involutive monoidal t-norm-based logic IMTL. © 2002 Elsevier B.V. All rights reserved.