\documentclass[12pt]{article}
\usepackage{amsmath,amsthm,amssymb}
\theoremstyle{definition}
\newtheorem*{example}{مثال}
\newtheorem*{solution}{حل}
\usepackage[a4paper,margin=2cm]{geometry}
\usepackage{setspace}
\usepackage{pgfplots}
\usetikzlibrary{patterns}
\pgfplotsset{compat=1.16}
\tikzstyle{hollowdot}=[draw,fill=white,circle,inner sep=0pt,minimum size=3pt]
\tikzstyle{soliddot}=[draw,fill=black,circle,inner sep=0pt,minimum size=3pt]
\usepackage{float}
\onehalfspacing

\begin{document}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
xmin=0,xmax=3,
ymin=0,ymax=1,
xtick={0.5,1,1.25,1.5,2},
xticklabels={$0.1$,$.2$,$.25$,$.3$,$0.4$},
ytick={0,0.5},
yticklabels={$0$,$1$},
yticklabel style={font=\footnotesize},
every axis x label/.style={at={(ticklabel* cs:1)},anchor=west,},
every axis y label/.style={at={(ticklabel* cs:1)},anchor=south east,},
xlabel=$x$,
ylabel=$y$,
axis on top,
clip=false
]
\draw[dashed,help lines] (1,0.5) |- (1,0);
\draw[dashed,help lines] (1.25,0.5) |- (1.25,0);
\draw[dashed,help lines] (1.5,0.5) |- (1.5,0);
\draw[dashed,help lines] (0,0.5) |- (1,0.5);
\draw [very thick, black] (0.5,0)to (1,0.5)to(1.5,0.5)to(2,0)node [above] {$$};
\draw [ultra thin, black] (0.5,0)to (1.25,0.5)to(2,0)node [above] {$$};
\end{axis}
\end{tikzpicture}
\end{figure}
\textbf{$$\tilde{A}=(0.1,0.2,0.3,0.4; 1.0)$$}
$$\tilde{B}=(0.1,0.25,0.4;1.0)$$

\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
xmin=0,xmax=3,
ymin=0,ymax=1,
xtick={0.5,1,1.5,2},
xticklabels={$0.1$,$0.2$,$0.3$,0.4},
ytick={0,0.5},
yticklabels={$0$,$1$},
yticklabel style={font=\footnotesize},
every axis x label/.style={at={(ticklabel* cs:1)},anchor=west,},
every axis y label/.style={at={(ticklabel* cs:1)},anchor=south east,},
xlabel=$x$,
ylabel=$y$,
axis on top,
clip=false
]
\draw[dashed,help lines] (1,0.5) |- (1,0);
\draw[dashed,help lines] (1.5,0.5) |- (1.5,0);
\draw[dashed,help lines] (0,0.5) |- (1,0.5);
\draw [very thick, black] (0.5,0)to (1,0.5)to(1.5,0.5)to(2,0)node [above] {$$};
\end{axis}
\end{tikzpicture}
\end{figure}
$$\tilde{A}=(0.1,0.2,0.3,0.4; 1.0)$$
$$\tilde{B}=(0.1,0.2,0.3,0.4;1.0)$$

\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
xmin=0,xmax=4,
ymin=0,ymax=1,
xtick={0.5,1,1.5,2,2.5,3,3.5,4},
xticklabels={$.1$,$.2$,$.3$,$.4$,$.5$,$.6$,$.7$,1},
ytick={0,0.5},
yticklabels={$0$,$1$},
yticklabel style={font=\footnotesize},
every axis x label/.style={at={(ticklabel* cs:1)},anchor=west,},
every axis y label/.style={at={(ticklabel* cs:1)},anchor=south east,},
xlabel=$x$,
ylabel=$y$,
axis on top,
clip=false
]
\draw[dashed,help lines] (1,0.5) |- (1,0);
\draw[dashed,help lines] (1.5,0.5) |- (1.5,0);
%\draw[dashed,help lines] (2,0.5) |- (2,0);
\draw[dashed,help lines] (0,0.5) |- (2.75,0.5);
\draw [ultra thin, black] (0.5,0)to (1,0.5)to(1.5,0.5)to(2,0)node [above] {$$};
\draw [very thick, black] (2,0)to (2.75,0.5)to(3.5,0)node [above] {$$};
\draw[dashed,help lines] (2.75,0.5) |- (2.75,0);
\end{axis}
\end{tikzpicture}
\end{figure}
$$\tilde{A}=(0.1,0.2,0.3,0.4; 1.0)$$
\textbf{$$\tilde{B}=(0.4,0.55,0.55;0.7,1.0)$$}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
xmin=0,xmax=4,
ymin=0,ymax=1,
xtick={0.5,1,1.5,2,2.5,3,3.5},
xticklabels={$.1$,$.2$,$.3$,$.4$,$.5$,$.6$,$.7$},
ytick={0,0.5},
yticklabels={$0$,$1$},
yticklabel style={font=\footnotesize},
every axis x label/.style={at={(ticklabel* cs:1)},anchor=west,},
every axis y label/.style={at={(ticklabel* cs:1)},anchor=south east,},
xlabel=$x$,
ylabel=$y$,
axis on top,
clip=false
]
\draw[dashed,help lines] (1,0.5) |- (1,0);
\draw[dashed,help lines] (1.5,0.5) |- (1.5,0);
\draw[dashed,help lines] (0,0.5) |- (2.75,0.5);
\draw [ultra thin, black] (0.5,0)to (1,0.5)to(1.5,0.5)to(2,0)node [above] {$$};
\draw[dashed,help lines] (0,0.5) |- (2.75,0.5);
\draw [very thick, black] (2,0)to (2.5,0.5)to(3,0.5)to(3.5,0)node [above] {$$};
\draw[dashed,help lines] (3,0.5) |- (3,0);
\draw[dashed,help lines] (2.5,0.5) |- (2.5,0);
\end{axis}
\end{tikzpicture}
\end{figure}
$$\tilde{A}=(0.1,0.2,0.3,0.4; 1.0)$$
\textbf{$$\tilde{B}=(0.4,0.5,0.6,0.7;1.0)$$}
\end{document}