Algorithm 1: single passIT2FCM-ACO
Input: X, c, $t_{max},$ m1, m2, min_impro, $\rho$, $\epsilon$, $\alpha$, ns, $\underset{\_}{w},\overline{w}$ Output: U, V, Jm $z_{max}\in N$ and $z_{max}=$1000, min_impro= 10−5 Initialize fuzzifier m1 = 1.7, m2 = 2.6, $J_{min}=inf,$ ACO parameters: $\rho =$ 0.005, $\epsilon =$0.01, $\alpha =$ 1.0 Initialize ${\underset{\_}{p}}_{ij}=1,{\overline{p}}_{ij}i=1,\dots ,candj=1,\dots ,n$
00	Load X as ns sized samples, $X=\left\{X_1,\dots \dots ,X_s\right\}$
01	Initialize ${\underset{\_}{w}}_j=ones\left(c,n_s\right),{\overline{w}}_j,=ones\left(c,n_s\right)$
02	For first PDA since there are no previous c weighted points for $n_{s+c}$, c=0.
03	for $l=1tos$ do
04	for z=1 to $z_{max}$ do
05	Repeat
06	for j=1 to $n_{s+c}$
07	for i=1, …., c
08	set ${\underset{\_}{u}}_{ij}={\underset{\_}{p}}_{ij}/{\displaystyle \sum }_{\mathrm{k}=1}^c{\underset{\_}{p}}_{kj}+N\left(0,\sigma \right)$
09	if ${\underset{\_}{u}}_{ij}<0then{\underset{\_}{u}}_{ij}=0$ end if
10	if ${\underset{\_}{u}}_{ij}>1then{\underset{\_}{u}}_{ij}=1$ end if
11	randomly set ${\overline{u}}_{ij}={\overline{p}}_{ij}/{\displaystyle \sum }_{\mathrm{k}=1}^c{\overline{p}}_{kj}+N\left(0,\sigma \right)$
12	if ${\overline{u}}_{ij}<0then{\overline{u}}_{ij}=0$ end if
13	if ${\overline{u}}_{ij}>1then{\overline{u}}_{ij}=1$ end if
14	end for
15	for i=1, …., c
16	${\underset{\_}{u}}_{ij}={\underset{\_}{u}}_{ij}/{\displaystyle \sum }_{\mathrm{k}=1}^c{\underset{\_}{u}}_{kj}$
17	${\overline{u}}_{ij}={\overline{u}}_{ij}/{\displaystyle \sum }_{k=1}^c{\overline{u}}_{kj}$
18	end for
19	end for
20	until ${\displaystyle \sum }_{\mathrm{j}=1}^{n_{s+c}}{\underset{\_}{u}}_{ij}>0and{\displaystyle \sum }_{\mathrm{j}=1}^{n_{s+c}}{\overline{u}}_{ij}>0,\forall 1\le i\le c$
21	compute type-1 fuzzy set of cluster centroids where $V_L, V_R, u_{ij}^L, u_{ij}^R, w_j^L, w_j^R$ recomputed using procedure defined in algorithm 2.
22	update $\tilde{U}=\left[{\underset{\_}{u}}_{ij}, {\overline{u}}_{ij}\right]$
23	obtain the crisp value of cluster centroids $\tilde{V}=V_L+V_R/2$
24	compute crisp value of fuzzy partition matrix using $u_{ij}=u_{ij}^L+u_{ij}^R/2$
25	type reduce weights $w_j=w_j^L+w_j^R/2$
26	calculate objective function using “Equation (12)”
27	Type reduce objective function ${\tilde{J}}_m=J_{m_1}+J_{m_2}/2$
28	if $\tilde{J}<J_{min}^m$ then $J_{min}^m=\tilde{J}$ end if
29	for i=1, …., c
30	for j = 1, …, $n_{s+c}$
31	update pheromone matrices $\tilde{P}$
32	${\underset{\_}{p}}_{ij}=w_j{\underset{\_}{p}}_{ij}\times \left(1-\rho \right)+{\underset{\_}{u}}_{ij}/{\left(\tilde{J}-J_{min}+\epsilon \right)}^{\alpha }$
33	${\overline{p}}_{ij}=w_j{\overline{p}}_{ij}\times \left(1-\rho \right)+{\overline{u}}_{ij}/{\left(\tilde{J}-J_{min}+\epsilon \right)}^{\alpha }$
34	end for
35	end for
36	if t > 1, if $\left|\tilde{J}\left(t\right)-\tilde{J}\left(t-1\right)\right|<$min_impro break; end if, end if
37	end for
38	compute lower and upper values of weight of c condensed data points
39	$\underset{\_}{w}{’}_j={\displaystyle \sum }_{j=1}^{n_{s+c}}\left({\underset{\_}{u}}_{ij}\right)w_j$, $1\le i\le c$, $w_j=1\forall 1\le j\le n_s$
40	set ${\underset{\_}{w}}_j=$ $\underset{\_}{w}{’}_j$
41	$\overline{w}{’}_j={\displaystyle \sum }_{j=1}^{n_{s+c}}\left({\overline{u}}_{ij}\right)w_j$, $1\le i\le c$, $w_j=1\forall 1\le j\le n_s$
42	set ${\overline{w}}_j=$ $\overline{w}{’}_j$
43	End