Power of t-norms

  • Authors:

  • Carol L. Walker;Elbert A. Walker

  • Affiliations:

  • Department of Mathematics Sciences, New Mexico State University, P.O. Box 30001, Las Cruces, NM;Department of Mathematics Sciences, New Mexico State University, P.O. Box 30001, Las Cruces, NM

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2002

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Abstract

In this paper we consider the rth powers of a continuous t-norm for positive real numbers r, generalizing the notion of the diagonal (2nd power). We identify the increasing functions from the unit interval to itself that are realized as the rth power of some continuous t-norm. The strict and nilpotent cases are described in detail.