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Int. J. Fuzzy Log. Intell. Syst. 2010; 10(3): 242-246

Published online September 1, 2010

© The Korean Institute of Intelligent Systems

## Some Notes on Lp-metric Space of Fuzzy Sets

Yun Kyong Kim

### Abstract

It is well-known that the space Eⁿ of fuzzy numbers (i.e., normal, upper-semicontinuous, compact-supported and convex fuzzy subsets) in the n-dimensional Euclidean space Rⁿ is separable but not complete with respect to the Lp-metric.
In this paper, we introduce the space Fp(Rⁿ) that is separable and complete with respect to the Lp-metric. This will be accomplished by assuming p-th mean bounded condition instead of compact-supported condition and by removing
convex condition.

Keywords: Fuzzy numbers,Compact sets,Lp-metric

### Article

Int. J. Fuzzy Log. Intell. Syst. 2010; 10(3): 242-246

Published online September 1, 2010

## Some Notes on Lp-metric Space of Fuzzy Sets

Yun Kyong Kim

### Abstract

It is well-known that the space Eⁿ of fuzzy numbers (i.e., normal, upper-semicontinuous, compact-supported and convex fuzzy subsets) in the n-dimensional Euclidean space Rⁿ is separable but not complete with respect to the Lp-metric.
In this paper, we introduce the space Fp(Rⁿ) that is separable and complete with respect to the Lp-metric. This will be accomplished by assuming p-th mean bounded condition instead of compact-supported condition and by removing
convex condition.

Keywords: Fuzzy numbers,Compact sets,Lp-metric