On equivalent forms of fuzzy logic systems NM and IMTL

  • Authors:

  • Daowu Pei

  • Affiliations:

  • Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China and Department of Mathematics, Yancheng Teachers College, Yancheng, Jiangsu 224002, People's Republic of Chi ...

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2003

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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.