Distributivity of fuzzy numbers under t-norm based fuzzy arithmetic operations

  • Hong, Dug-Hun (School of Mechanical and Automotive Engineering, Catholic University of Daegu)
  • Published : 2003.02.28

Abstract

Computation with fuzzy numbers is a prospective branch of a fuzzy set theory regarding the data processing applications. In this paper we consider an open problem about distributivity of fuzzy quantities based on the extension principle suggested by Mare (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous t-norm which holds the distributivity under t-norm based fuzzy arithmetic operations.

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