verdacidad \in \{ 0 , 1 \}

veracidad \in [ 0.0, 1.0 ]

X \in [a,b] ; a,b \in R

\mu(x) \to [0, 1]

x \in X

\mu \in [0,1]

A = \left\{ \int \frac{\mu(x)}{x} \right\}

A = \left\{ \int\limits_0^{10} \frac{ \exp \left[ - \frac{1}{2} \left( \frac{x-5}{3} \right)^2 \right] }{x} \right\}

A = \sum \frac{\mu(x)}{x}

A = \left\{ \frac{0}{1} + \frac{0.1}{2} + \frac{0.4}{3} + \frac{0.8}{4} + \frac{1}{5} + \frac{1}{6} + \frac{0.8}{7} + \frac{0.4}{8} + \frac{0.1}{9} + \frac{0}{10} \right\}

B \subseteq A; \forall b, b \in B \land b \in A

B \subseteq A \leftrightarrow \mu_B(x) \leq \mu_A(x);  \forall x \in X

C = A \cap B

\begin{aligned}
C = A \cap B \leftrightarrow \mu_C(x) & = \min (\mu_A(x), \mu_B(x)) \\
& = \mu_A(x) \land \mu_B(x) \forall x \in X
\end{aligned}

C = A \cup B

\begin{aligned}
C = A \cup B \leftrightarrow \mu_C(x) & = \max (\mu_A(x), \mu_B(x)) \\
& = \mu_A(x) \lor \mu_B(x) \forall x \in X
\end{aligned}

\overline{A}

\overline{A} \leftrightarrow \mu_{\sim A} = 1 - \mu_A(x) \forall x \in X

A \cup B = B \cup A

\max( \mu_A, \mu_B ) = \max( \mu_B, \mu_A )

A \cup ( B \cup C ) = ( A \cup B ) \cup C

\begin{aligned}
\max( \mu_A, \max ( \mu_B , \mu_C ) )  &= \max( \mu_A, \mu_B , \mu_C ) \\
& = \max( \max ( \mu_A,  \mu_B ) , \mu_C ) 
\end{aligned}

A \cup ( B \cap C ) = ( A \cup B ) \cap ( A \cup C )

\max( \mu_A, \min ( \mu_B , \mu_C ) )  = \min (  \max ( \mu_A,  \mu_B ) , \max (\mu_A , \mu_C ) )

A \cup \empty = A \\
A \cup X = X

\max ( \mu_A, 0 ) = \mu_A \\
\max ( \mu_A, 1 ) = 1 \\

A \cup A = A

\max ( \mu_A , \mu_A ) = \mu_A

A \cup \overline{A} = X

\overline{A \cup B} = \overline{B} \cap \overline{A}

1 - \max ( \mu_A, \mu_B ) = \min ( 1 - \mu_A, 1 - \mu_B )

A \cap B = B \cap A

\min( \mu_A, \mu_B ) = \min( \mu_B, \mu_A )

A \cap ( B \cap C ) = ( A \cap B ) \cap C

\begin{aligned}
\min( \mu_A, \min ( \mu_B , \mu_C ) )  &= \min( \mu_A, \mu_B , \mu_C ) \\
& = \min( \min ( \mu_A,  \mu_B ) , \mu_C ) 
\end{aligned}

A \cap ( B \cup C ) = ( A \cap B ) \cup ( A \cap C )

\min( \mu_A, \max ( \mu_B , \mu_C ) )  = \max (  \min ( \mu_A,  \mu_B ) , \min (\mu_A , \mu_C ) )

A \cap \empty = \empty \\
A \cap X = A

\min ( \mu_A, 0 ) = 0 \\
\min ( \mu_A, 1 ) = \mu_A \\

A \cap A = A

\min ( \mu_A , \mu_A ) = \mu_A

A \cap \overline{A} = \empty

\overline{A \cap B} = \overline{B} \cup \overline{A}

1 - \min ( \mu_A, \mu_B ) = \max ( 1 - \mu_A, 1 - \mu_B )

A \subseteq B \land B \subseteq C \rightarrow A \subseteq C

\mu_A \leq \mu_B \land \mu_B \leq \mu_C \rightarrow \mu_A \leq \mu_C 

\overline{ \overline{ A } } = A

\mu_{\overline{\overline{A}}} = 1 - \mu_{\overline{A}} = 1 - ( 1 - \mu_A ) = \mu_A