# 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.

#### References

1. Analysis of Fuzzy Infornation v.2 Fuzzy numbers : an overview Dubois, D.;Prade, H.;J.C. Bezdek(Ed.0
2. Computation Over Fuzzy Quantities Mares, M.
3. Fuzzy Sets and Systems v.91 Weak arithmetics of fuzzy numbers Mares, M.
4. Kybermetika v.32 no.4 Fuzzy zero, algebraic equivalence: Yes or No? Mares, M.
5. Fuzzy Sets and System v.41 On generalization of Nguyen's theorem Fuller, R.;Keresztfalvi, T.
6. Journal of Mathematical Analysis and Applications v.64 A note on the extension principle for fuzzy sets Nguyen, H. T.
7. Introduction to fuzzy Arithmetic Theory and Application Kaufmann, A.;Gupta, M.M.
8. Fuzzy Reasoning and Fuzzy Optimazation Fuller, R.