D型隶属函数与模糊度

D-TYPE MEMBERSHIP FUNCTION AND DEGREE OF FUZZINESS

研究D型隶属函数与O型隶属函数的关系,证明了确定X上一个D型隶属函数等价于确定X上一个O型隶属函数和X×X上一个O型隶属函数。并讨论了D型隶属函数与聚类的关系,对D型模糊集和O型模糊集分别定义了模糊度且研究了相应的性质。

The relation between D-type membership Function and O-type membership function has been studied.The determining of a D-type membership function on X is equivalent to the determining of anO-type membership function on X and an O-type membership function on X×X. The fuzzy clustering induced by D-type membership function is also discussed. The degrce of fuzziness on O-type fuzzy sets and D-type fuzzy sets are introduced. Some properties of these degrees are obtained. The degree of fuzziuess might be useful in uncertain reasoning.