Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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A note on distance measure and similarity measure defined by Choquet integral on interval-valued fuzzy sets

구간치 퍼지집합 상에서 쇼케이적분에 의해 정의된 거리측도와 유사측도에 관한 연구

  • Jang, Lee-Chae (Dept. of Mathematics and Computer Science, Konkuk University)
  • 장이채 (건국대학교 컴퓨터응용과학부 전산수학)
  • Published : 2007.08.25
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Abstract

Interval-valued fuzzy sets were suggested for the first time by Gorzafczany(1983) and Turksen(1986). Based on this, Zeng and Li(2006) introduced concepts of similarity measure and entropy on interval-valued fuzzy sets which are different from Bustince and Burillo(1996). In this paper, by using Choquet integral with respect to a fuzzy measure, we introduce distance measure and similarity measure defined by Choquet integral on interval-valued fuzzy sets and discuss some properties of them. Choquet integral is a generalization concept of Lebesgue inetgral, because the two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure.

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References

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