Incremental Interval Type-2 Fuzzy Clustering of Data Streams using Single Pass Method

. 2020 Jun 5;20(11):3210. doi: 10.3390/s20113210

Algorithm 2: Type-reducing weighted cluster lefts proposed algorithm
00	For arbitrary fuzzifier m
01	compute lefts $v^{'} = ({v^{'}}_{i 1}, \dots \dots, {v^{'}}_{i d})$ using $\frac{\sum_{j = 1}^{n_{s + c}} w_{j} {(u_{i j})}^{m} x_{j}}{\sum_{j = 1}^{n_{s + c}} w_{j} {(u_{i j})}^{m}}$
02	where $u_{i j} = {\underline{u}}_{i j} + {\bar{u}}_{i j} / 2$ and $w_{j} = {\underline{w}}_{j} + {\bar{w}}_{j} / 2$
03	sort the n data patterns in each of d attributes (l=1, …, d) in ascending order
04	compute $V_{R}$
05	for all data patterns
06	find interval index k $(1 \leq k \leq n_{s + c} - 1)$ such that $x_{k l} \leq v ’_{i l} \leq x_{(k + 1) l}$
07	for all data patterns
08	if $(j \leq k)$ then
09	set primary membership $u_{i j}^{R_{1}} = {\underline{u}}_{i j}$ and set weight $w_{j}^{R_{1}} = {\underline{w}}_{j}, \forall x_{j}$ else
10	set primary membership $u_{i j}^{R_{2}} = {\bar{u}}_{i j}$ and set weight $w_{j}^{R_{2}} = {\bar{w}}_{j}, \forall x_{j}$
11	end if
12	end for
13	$u_{i j}^{R} = (u_{i j}^{R_{1}} \cup u_{i j}^{R_{2}})$ and $w_{j}^{R} = (w_{j}^{R_{1}} \cup w_{j}^{R_{2}})$
14	end for
15	$V_{L}$ is calculated using the same procedure as above replacing the “if statement” as follows
16	for all data patterns
17	if $(j \leq k)$ then
18	set primary membership $u_{i j}^{L_{1}} = {\bar{u}}_{i j}$ and set weight $w_{j}^{L_{1}} = {\bar{w}}_{j}, \forall x_{j}$ else
19	set primary membership $u_{i j}^{L_{2}} = {\underline{u}}_{i j}$ and set weight $w_{j}^{L_{2}} = {\underline{w}}_{j}, \forall x_{j}$
20	end if
21	end for
22	$u_{i j}^{L} = (u_{i j}^{L_{1}} \cup u_{i j}^{L_{2}})$ and $w_{j}^{L} = (w_{j}^{L_{1}} \cup w_{j}^{L_{2}})$
23	compute maximum value of $V_{R}$ and $V_{L}$ using equation (13)