摘要
Differrent kinds of operations have been proposed in fuzzy set theory although Zadeh's operation is the most popoular. We discuss a new kind of fuzzy set operations which is based on measurement. In the measure based operation, there are only two basic operators: operator for intersection and operator for union. These two operators are interrelated with each other, and conditional fuzzy measures(or conditional membership functions) are also included in these operators. Moreover, the operator for complement is not independently defined, and it is derived from the above two basic operators. The measure based operation brings to light some relations between Zadeh's operation and probabilistic operation. We show that both Zadeh's operation and probabilistic operation are special cases of measure based operators.We also discuss the problem of the law of excluded middle and the law of contradiction. It is shown that these laws still hold in fuzzy sets and this conclusion causes no difficulty in explaining the nature of fuzziness.
Differrent kinds of operations have been proposed in fuzzy set theory although Zadeh's operation is the most popoular. We discuss a new kind of fuzzy set operations which is based on measurement. In the measure based operation, there are only two basic operators: operator for intersection and operator for union. These two operators are interrelated with each other, and conditional fuzzy measures(or conditional membership functions) are also included in these operators. Moreover, the operator for complement is not independently defined, and it is derived from the above two basic operators. The measure based operation brings to light some relations between Zadeh's operation and probabilistic operation. We show that both Zadeh's operation and probabilistic operation are special cases of measure based operators.We also discuss the problem of the law of excluded middle and the law of contradiction. It is shown that these laws still hold in fuzzy sets and this conclusion causes no difficulty in explaining the nature of fuzziness.
