IEEE Computational Intelligence Magazine - November 2020 - 64

data sources include both modern healthcare records and TCM
records of the residents. Those characteristics are used as input
features for grouping, and the value of each feature is normalized, e.g., real values (such as height and weight) are normalized
to [0,1], and exclusive labels (such as sex and illness) are represented by binary variables. In this study, we use a total of 1148
features for grouping. However, for most residents, many features can be absent.
A. An Improved Fuzzy c-Means Clustering Method

For such a high-dimension grouping problem with many missing values, classical hard clustering methods such as K-means
clustering [22] are not very effective. In this study, we use an
improved fuzzy c-means (FCM) clustering method [23]. In
brief, FCM groups a set of data points by minimizing the overall fuzzy-membership-weighted distance of the data points
from cluster centroids:
c

n

min J (U,V ) = 1 / / u mij d 2ij (1)
cn i = 1 j = 1

	

where n is the number of data points, c is the number of clusters,
uij is the membership degree of the jth data point to the ith
cluster subject to R i u ij = 1, d ij is the distance between the jth
data point and the ith cluster centroid, m is a control parameter
with a default value of 2, U = (u ij) c #n is the weight matrix, and
V = [v 1, v 2, f, v c] is the set of cluster centroid vectors.
Xu and Wu [24] extended the standard FCM to intuitionistic FCM based on new distance measures defined on
intuitionistic fuzzy sets (IFS) [25] that capture more uncertainty information. Here, we use Pythagorean fuzzy sets
(PFS) [26], which allow for a larger body of membership

TABLE 1 Physical characteristics for grouping community
residents.
NUMBER OF
INDICATORS

grades than IFS, to further improve clustering. Formally, let S
be an arbitrary non-empty set, a PFS is a mathematical
object of the form:
P = {G x, n P (x), o P (x) H | x ! S}	(2)

	

where n P (x) : S " [0, 1] and o P (x) : S " [0, 1] are respectively the membership degree and non-membership degree of the
element x to S in P. PFS extends IFS in that the membership
degrees satisfy n 2P (x) + o 2P (x) # 1. The hesitant degree of
x ! X is expressed as:
1 - n 2P (x) - o 2P (x) (3)

r P ( x) =

	

In our improved Pythagorean FCM, data points and cluster
centroids are represented by Pythagorean fuzzy number (PFN)
vectors, where the distance between two PFN b 1 = P (n b1, o b1)
and b 2 = P (n b2, o b2) is calculated as [27]:
	

(n 2b1-n 2b2) 2 + (o 2b1-o 2b 2) 2 + (r 2b1-r 2b2) 2
	(4)
2

| b 1, b 2 |=

and the distance d ij in Eq. (1) between a D-dimensional data
point x j and a cluster centroid v i is calculated as:
	

x j, v i =

2

(5)

Algorithm 1 Pythagorean fuzzy c-means clustering algorithm.

 1 Initialize a c # n matrix U and a set V (0) of c cluster centroids;
 2 Let k = 0;

CHARACTERISTICS

BASIC HEALTH
METRICS

AGE, SEX, OCCUPATION,
HEIGHT, WEIGHT, HEART RATE,
BLOOD PRESSURE, VITAL
CAPACITY, ...

121

TCM CONSTITUTIONS

MILD, YANG DEFICIENCY, YIN
DEFICIENCY, PHLEGM DAMPNESS, WET & HEAT, QI STAGNATION, QI DEFICIENCY, BLOOD
STASIS, SPECIAL

9

SHIRE JINYIN, PIXU SHIYUN,
XUEXU FENGZAO, SHIRE YUZU,
SHIRE SHANGYIN, QIZHI
XUEYU, QIXU BUZU, GANSHEN
BUZU, ...

50

PAST ILLNESSES

DISEASES AND THE CORRESPONDING INDICATORS

484

13     v i ! * b d,

CURRENT ILLNESSES

DISEASES AND THE CORRESPONDING INDICATORS

484

14    k ! k + 1;
15  return (U, V);

 3 while V (k+1), V (k) 2 e do
 4   for j = 1 to n do
 5     if 7i l : 1 # i l # c : x j, v i l = 0 then
 6       for i = 1 to c do
(k)
 7         if i = i l then u ij ! 1;
(k)
 8         else u ij ! 0;
 9     else
10       for i = 1 to c do
1

(k)

64

x jd, v id
D

Algorithm 1 presents the Pythagorean FCM method,
which minimizes the objective function J(U, V ) by iteratively updating the fuzzy membership weights according to
the distances between data points and centroids (Line 11) and
updating the centroids according to the membership and

TYPE

TCM SYNDROMES [21]

/ Dd = 1

11          u ij !

2

m-1
/ e xx j,, vv i o
j
il
i l= 1
c

;

12   for i = 1 to c do

IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2020

(k)

/ nj = 1 u (ijk) n 2 / nj = 1 u (ijk) o 2
,
/ nj = 1 u (ijk)
/ nj = 1 u (ijk)
bd

bd

| 1 # d # D 4;
IEEE Computational Intelligence Magazine - November 2020

Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - November 2020
