International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Some Notes on Lp-metric Space of Fuzzy Sets

  • Kim, Yun-Kyong (Department of Information & Communication Engineering, Dongshin University)
  • Received : 2010.05.11
  • Accepted : 2010.08.24
  • Published : 2010.09.30
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Abstract

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

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References

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