An Extensional Signed Fuzzy Measure of Signed Rho-Fuzzy Measure

摘要

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.