2.1.模糊集合¶

交换律: \(\mathbb{A} \cap \mathbb{B}\), \(\mathbb{A} \cup \mathbb{B}\)

结合律: \(\mathbb{A} \cap (\mathbb{B} \cap \mathbb{C}) = (\mathbb{A} \cap \mathbb{B}) \cap \mathbb{C}\), \(\mathbb{A} \cup (\mathbb{B} \cup \mathbb{C}) = (\mathbb{A} \cup \mathbb{B}) \cup \mathbb{C}\)

分配律: \(\mathbb{A} \cap (\mathbb{B} \cup \mathbb{C}) = (\mathbb{A} \cap \mathbb{B}) \cup (\mathbb{A} \cap \mathbb{C})\), \(\mathbb{A} \cup (\mathbb{B} \cap \mathbb{C}) = (\mathbb{A} \cup \mathbb{B}) \cap (\mathbb{A} \cup \mathbb{C})\)

对偶律: \(\overline{\mathbb{A} \cup \mathbb{B}} = \bar{\mathbb A} \cap \bar{\mathbb B}\) , \(\overline{\mathbb{A} \cap \mathbb{B}} = \bar{\mathbb A} \cup \bar{\mathbb B}\)

两极律: \(\mathbb{A} \cap \mathbb{E} = \mathbb{A}, \mathbb{A} \cup \mathbb{E} = \mathbb{E}\)

零一律: \(\mathbb{A} \cap \mathbb{\emptyset} = \mathbb{\emptyset}, \mathbb{A} \cup \mathbb{\emptyset} = \mathbb{A}\)

吸收律: \(\mathbb{A}\cap (\mathbb{A}\cup \mathbb{B}) = \mathbb{A}, \mathbb{A} \cup (\mathbb{A}\cap \mathbb{B}) = \mathbb{A}\)

等幂律: \(\mathbb{A} \cap \mathbb{A} = \mathbb{A}, \mathbb{A} \cup \mathbb{A} = \mathbb{A}\)

复原率: \(\bar{\bar{\mathbb A}} = {\mathbb A}\)