CALCULATIONS ON THE SUPREMUM OF FUZZY NUMBERS VIA Lp METRICS

Taihe Fan (Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, 310018, China.)
Dan Wen (Wenling School, Wenling, Zhejiang, 317500, China.)

Journal of the Indonesian Mathematical Society
Volume 13 Number 2 (October 2007)

In this paper, it is proved that the supremum of a family of fuzzy number scan be finitely approximated via Lp metrics and the concrete approaches are given. As a byproduct, it is proved that the L1 metric d1 defined via cut-set is equivalent to ametric which can be calculated directly via membership functions. Since the Lp metrics are analytic in nature, the results in this paper may have interesting applications infuzzy analysis. For example, it may provide a method for the computation of various fuzzy-number-valued integrals.DOI : http://dx.doi.org/10.22342/jims.13.2.88.197-208