\item Fuzzy logic is an extension of Boolean logic
\item Fuzzy logic is an extension of multivalued logic
\item Natural language rules
\item Aristotle, later Lofti A. Zadeh in 1965 and 1973
\item Japan, later on west
@ -137,11 +137,12 @@
\begin{frame}{Formal Definitions}
\begin{block}{Definition}
Let $U$ be the \textit{universe of discourse} and $x$ be the element in it. The \textit{membership function}$\mu_A$ is defined as:
$$\mu_A:X\rightarrow[0,1]$$
Let $U$ be the \textit{universe of discourse} and $x$ be the element in it. The \textit{membership function}$f^A$ assigning \textit{degree of membership}$\mu_A$:
$$f^A(x): \:\in U \rightarrow\mu_A(x)\in[0,1]$$
%$$\mu_A:U\rightarrow[0,1]$$
\end{block}
\begin{block}{Definition}
A fuzzy set $A$ is expressed as a set of ordered pairs, given that $\mu_A(x)$ is a degree, to which $x$ a member of $A$:
A fuzzy set $A$ is expressed as a set of ordered pairs (tuples), given that $\mu_A(x)$ is a degree, to which $x$ a member of $A$: