An extensional signed fuzzy measure of signed Rho-fuzzy measure

  • Authors:

  • Hsiang-Chuan Liu

  • Affiliations:

  • Department of Bioinformatics and Medical Informatics, Asia University, Graduate Institute of Acupuncture Science, China Medical University, Taichung, Taiwan, ROC

  • Venue:
  • ICCCI'10 Proceedings of the Second international conference on Computational collective intelligence: technologies and applications - Volume PartI
  • Year:
  • 2010

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Abstract

If some values of fuzzy density function are negative, none of non-negative fuzzy measure can be used, the signed fuzzy measures with real valued fuzzy density function are needed, a univalent signed fuzzy measure satisfying Liu's revised monotonicity, called signed Rho-measure, was proposed by author's previous work. In this paper, for any real valued fuzzy density function, it is proved that the well-known signed additive measure is a signed fuzzy measure satisfying the Liu's revised monotonicity, and a multivalent signed fuzzy measure with infinite many signed fuzzy measure solutions satisfying Liu's revised monotonicity, based on signed Rho-measure, called extensional signed Rho-fuzzy measure, is proposed, this new signed fuzzy measure is an generalization of not only signed Rho-fuzzy measure but also signed addition measure, obviously, it is more useful than above mentioned two signed fuzzy measures, some related properties are also discussed.