Intuitionistic hesitancy membership function

Description

Intuitionistic hesitancy membership values with membership and non-membership values as input

Usage

hmemIFS(m, nm)

Arguments

Value

IFS hesistancy values

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
a<-mn(x)
b<-std(x)
m<-memG(a,b,x)
lam<-0.5
nm<-nonmemS(m,lam)
hmemIFS(m,nm)
#       [,1]       [,2]       [,3]
#[1,]0.09921264 0.05810582 0.03270001
#[2,]0.09915966 0.03100937 0.05966479
#[3,]0.04565299 0.09939456 0.04565299
#[4,]0.04565299 0.09939456 0.04565299

Pythagorean hesitancy membership function

Description

Pythagorean hesitancy membership values with membership and non-membership values as input

Usage

hmemPFS(m, nm)

Arguments

Value

PFS hesistancy values

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
a<-mn(x)
b<-std(x)
m<-memG(a,b,x)
lam<-0.5
nm<-nonmemS(m,lam)
hmemPFS(m,nm)
#       [,1]      [,2]      [,3]
#[1,] 0.7651357 0.5875871 0.4417361
#[2,] 0.7649349 0.4302263 0.5953393
#[3,] 0.5213768 0.7658251 0.5213768
#[4,] 0.5213768 0.7658251 0.5213768

Spherical indeterminacy membership function

Description

Spherical indeterminacy membership values with membership and non-membership values as input

Usage

imemSFS(m, nm)

Arguments

Value

SFS indeterminacy membership values

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
a<-mn(x)
b<-std(x)
m<-memG(a,b,x)
lam<-0.5
nm<-nonmemS(m,lam)
imemSFS(m,nm)
#        [,1]       [,2]       [,3]
#[1,] 0.09921264 0.05810582 0.03270001
#[2,] 0.09915966 0.03100937 0.05966479
#[3,] 0.04565299 0.09939456 0.04565299
#[4,] 0.04565299 0.09939456 0.04565299

Left foot values

Description

Left foot value for triangular or trapezoidal membership function

Usage

leftfootfinding(x, n)

Arguments

Value

Left foot values for the input data set x.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
leftfootfinding(x,5)
#[1] 10 5 10 10

Left shoulder values

Description

Left shoulder value for trapezoidal membership function

Usage

leftshoulderfinding(a, b)

Arguments

Value

Left shoulder values for the input data set x.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
mid<-midvalue(x)
leftshoulderfinding(2.5,mid)
#[1] 14.0 10.5 12.0 15.0

Gaussian membership function

Description

Gaussian membership function with mean, standard deviation, and data set

Usage

memG(a, b, x)

Arguments

Value

Gaussian membership values for the input data set x.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
a<-mn(x)
b<-std(x)
memG(a,b,x)
#       [,1]      [,2]      [,3]
#[1,] 0.5169457 0.7958771 0.8941586
#[2,] 0.5179406 0.9000876 0.7891159
#[3,] 0.8464817 0.5134171 0.8464817
#[4,] 0.8464817 0.5134171 0.8464817

Triangular membership function

Description

Triangular membership function with leftfooting, midvalue, rightfooting, and data set

Usage

memT(a, b, c, x)

Arguments

Value

Triangular membership values for the input data set x.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
a<-leftfootfinding(x,5)
b<-midvalue(x)
c<-rightfootfinding(x,5)
memT(a,b,c,x)
#       [,1]      [,2]      [,3]
#[1,] 0.3076923 0.4705882 0.5882353
#[2,] 0.5000000 0.5714286 0.4285714
#[3,] 0.8888889 0.9090909 0.8888889
#[4,] 0.1333333 0.1333333 0.1333333

Trapezoidal membership function

Description

Trapezoidal membership function with leftfooting, leftshoulder, rightshoulder, rightfooting, and data set

Usage

memTP(a, b, c, d, x)

Arguments

Value

Trapezoidal membership values for the input data set x.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
a<-leftfootfinding(x,5)
mid<-midvalue(x)
b<-leftshoulderfinding(2.5,mid)
c<-rightshoulderfinding(mid,2.5)
d<-rightfootfinding(x,5)
memTP(a,b,c,d,x)
#       [,1]      [,2]      [,3]
#[1,] 0.5000000 0.6666667 0.8333333
#[2,] 0.7272727 0.8888889 0.6666667
#[3,] 1.0000000 1.0000000 1.0000000
#[4,] 0.2000000 0.2000000 0.2000000

Middle values

Description

Middle value for triangular or trapezoidal membership function

Usage

midvalue(x)

Arguments

Value

Middle values for the input data set x.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
midvalue(x)
#[1] 16.5 13.0 14.5 17.5

Mean values

Description

Mean values of the data set for gaussian membership function

Usage

mn(x)

Arguments

Value

Mean values for individual row of the input data set X.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
mn(x)
#[1] 17.66667 14.00000 14.33333 15.33333

Sugeno and Terano's non membership function

Description

Sugeno and Terano's non membership function with membership values and lambda value

Usage

nonmemS(m, lam)

Arguments

Value

Sugeno and Terano's non membership for the data set x.

References

M. Sugeno and T. Terano. A model of learning based on fuzzy information. Kybernetes, 1977.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
a<-mn(x)
b<-std(x)
m<-memG(a,b,x)
lam<-0.5
nonmemS(m,lam)
#        [,1]      [,2]       [,3]
#[1,] 0.3838416 0.1460171 0.07314142
#[2,] 0.3828998 0.0689030 0.15121934
#[3,] 0.1078653 0.3871883 0.10786528
#[4,] 0.1078653 0.3871883 0.10786528

Yager's non membership function

Description

Yager's non membership function with membership values and lambda value

Usage

nonmemY(m, lam)

Arguments

Value

Yager's non membership for the data set x.

References

R. R. Yager. On the measure of fuzziness and negation part i: membership in the unit interval. 1979.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
a<-mn(x)
b<-std(x)
m<-memG(a,b,x)
lam<-0.5
nonmemY(m,lam)
#         [,1]        [,2]        [,3]
#[1,] 0.078966962 0.011638215 0.002959405
#[2,] 0.078578801 0.002628666 0.012471988
#[3,] 0.006392896 0.080354498 0.006392896
#[4,] 0.006392896 0.080354498 0.006392896

Right foot values

Description

Right foot value for triangular or trapezoidal membership function

Usage

rightfootfinding(x, n)

Arguments

Value

Right foot values for the input data set x.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
rightfootfinding(x,5)
#[1] 25 20 20 25

Right shoulder values

Description

right shoulder value for trapezoidal membership function

Usage

rightshoulderfinding(b, c)

Arguments

Value

Right shoulder values for the input data set x.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
mid<-midvalue(x)
rightshoulderfinding(mid,2.5)
#[1] 19.0 15.5 17.0 20.0

Spherical refusal membership function

Description

Spherical refusal membership values with membership,non-membership and indeterminacy values as input

Usage

rmemSFS(m, nm, im)

Arguments

Value

SFS refusal membership values

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
a<-mn(x)
b<-std(x)
m<-memG(a,b,x)
lam<-0.5
nm<-nonmemS(m,lam)
im<-imemSFS(m,nm)
rmemSFS(m,nm,im)
#       [,1]      [,2]      [,3]
#[1,] 0.7586762 0.5847071 0.4405241
#[2,] 0.7584805 0.4291073 0.5923419
#[3,] 0.5193742 0.7593476 0.5193742
#[4,] 0.5193742 0.7593476 0.5193742

IFS similarity measure simBA

Description

IFS similarity measure values using simBA computation technique with membership, and non-membership of two objects or set of objects.

Usage

simBA(ma, na, mb, nb, p, t, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

F. E. Boran and D. Akay. A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Information sciences, 255:45 - 57, 2014.

Examples

#When data set y consist of only one row use k=1
x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
p<-2
t<-2
k<-1
simBA(ma,na,mb,nb,p,t,k)
#0.7072291 0.6947466 0.8919850 0.8919850

#When data set y having more than one rows
#use k = the number of rows of data set y
x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,24,21,12,6,11),nrow=2)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
p<-2
t<-2
sim<-c()
for(k in 1:nrow(y)){sim<-rbind(sim,simBA(ma,na,mb,nb,p,t,k))}
sim
#       [,1]      [,2]      [,3]      [,4]
#[1,] 0.7072291 0.6947466 0.8919850 0.8919850
#[2,] 0.9410582 0.9843247 0.7380007 0.7380007

IFS similarity measure simC

Description

IFS similarity measure values using simC computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simC(ma, na, mb, nb, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

S.-M. Chen. Measures of similarity between vague sets. Fuzzy sets and Systems, 74(2):217 - 223, 1995.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simC(ma,na,mb,nb,k)
#[1] 0.7005061 0.7011282 0.8783314 0.8783314

IFS similarity measure simDC

Description

IFS similarity measure values using simDC computation technique with membership,non-membership, and hesitancy values of two objects or set of objects.

Usage

simDC(ma, na, mb, nb, ha, hb, p, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

L. Dengfeng and C. Chuntian. New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern recognition letters, 23(1-3):221 - 225, 2002.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ha<-hmemIFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
hb<-hmemIFS(mb,nb)
p<-2
k<-1
simDC(ma,na,mb,nb,ha,hb,p,k)
#[1] 0.3553975 0.3558802 0.5378438 0.5378438

IFS similarity measure simGK

Description

IFS similarity measure values using simGK computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simGK(ma, na, mb, nb, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

H. Garg and K. Kumar. Distance measures for connection number sets based on set pair analysis and its applications to decision-making process. Applied Intelligence, 48(10):3346 - 3359, 2018.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simGK(ma,na,mb,nb,k)
#[1] 0.1523230 0.1534360 0.6786289 0.6786289

IFS similarity measure simHK

Description

IFS similarity measure values using simHK computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simHK(ma, na, mb, nb, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

D. H. Hong and C. Kim. A note on similarity measures between vague sets and between elements. Information sciences, 115(1-4):83 - 96, 1999.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simHK(ma,na,mb,nb,k)
#[1] 0.9702837 0.9702706 0.9874349 0.9874349

IFS similarity measure simHY1

Description

IFS similarity measure values using simHY1 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simHY1(ma, na, mb, nb, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

W.-L. Hung and M.-S. Yang. On similarity measures between intuitionistic fuzzy sets. International journal of intelligent systems, 23(3):364 - 383, 2008.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simHY1(ma,na,mb,nb,k)
#[1] 0.5562031 0.5673731 0.8158479 0.8158479

IFS similarity measure simHY2

Description

IFS similarity measure values using simHY2 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simHY2(ma, na, mb, nb, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

W.-L. Hung and M.-S. Yang. On similarity measures between intuitionistic fuzzy sets. International journal of intelligent systems, 23(3):364 - 383, 2008.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simHY2(ma,na,mb,nb,k)
#[1] 0.7247430 0.7253651 0.9021400 0.9021400

IFS similarity measure simHY3

Description

IFS similarity measure values using simHY3 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simHY3(ma, na, mb, nb, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

W.-L. Hung and M.-S. Yang. On similarity measures between intuitionistic fuzzy sets. International journal of intelligent systems, 23(3):364 - 383, 2008.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simHY3(ma,na,mb,nb,k)
#[1] 0.5460424 0.5468474 0.8109329 0.8109329

IFS similarity measure simHY4

Description

IFS similarity measure values using simHY4 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simHY4(ma, na, mb, nb, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

W.-L. Hung and M.-S. Yang. On similarity measures between intuitionistic fuzzy sets. International journal of intelligent systems, 23(3):364 - 383, 2008.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simHY4(ma,na,mb,nb,k)
#[1] 0.7063744 0.7070477 0.8955969 0.8955969

IFS similarity measure simJJLY

Description

IFS similarity measure values using simJJLY computation technique with membership,non-membership, and hesitancy values of two objects or set of objects.

Usage

simJJLY(ma, na, mb, nb, ha, hb, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

Q. Jiang, X. Jin, S.-J. Lee, and S. Yao. A new similarity/distance measure between intuitionistic fuzzy sets based on the transformed isosceles triangles and its applications to pattern recognition. Expert Systems with Applications, 116:439–453, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ha<-hmemIFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
hb<-hmemIFS(mb,nb)
k<-1
simJJLY(ma,na,mb,nb,ha,hb,k)
#[1] 0.7239098 0.7245767 0.8981760 0.8981760

SFS similarity measure simKKDKS

Description

SFS similarity measure values using simKKDKS computation technique with membership,non-membership, and indeterminacy membership values of two objects or set of objects.

Usage

simKKDKS(ma, na, mb, nb, ia, ib, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

M. J. Khan, P. Kumam, W. Deebani,W. Kumam, and Z. Shah. Distance and similarity measures for spherical fuzzy sets and their applications in selecting mega projects. Mathematics, 8(4):519, 2020.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
k<-1
simKKDKS(ma,na,mb,nb,ia,ib,k)
#[1] 0.5726216 0.3223250 0.2791418 0.2791418

IFS similarity measure simL

Description

IFS similarity measure values using simL computation technique with membership,non-membership, and hesitancy values of two objects or set of objects.

Usage

simL(ma, na, mb, nb, ha, hb, p, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

H.-W. Liu. New similarity measures between intuitionistic fuzzy sets and between elements. Mathematical and Computer Modelling, 42(1-2):61 - 70, 2005.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ha<-hmemIFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
hb<-hmemIFS(mb,nb)
k<-1
p<-2
simL(ma,na,mb,nb,ha,hb,p,k)
#[1] 0.7022635 0.6896045 0.8890488 0.8890488

IFS similarity measure simM

Description

IFS similarity measure values using simM computation technique with membership,non-membership, and hesitancy values of two objects or set of objects.

Usage

simM(ma, na, mb, nb, p, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

H. B. Mitchell. On the dengfeng–chuntian similarity measure and its application to pattern recognition. Pattern Recognition Letters, 24(16):3101 - 3104, 2003.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ha<-hmemIFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
hb<-hmemIFS(mb,nb)
p<-2
k<-1
simM(ma,na,mb,nb,p,k)
#[1] 0.3840287 0.3837673 0.3849959 0.3849959

PFS similarity measure simNNNG1

Description

PFS similarity measure values using simNNNG1 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simNNNG1(ma, na, mb, nb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

X. T. Nguyen, V. D. Nguyen, V. H. Nguyen, and H. Garg. Exponential similarity measures for pythagorean fuzzy sets and their applications to pattern recognition and decision-making process. Complex & Intelligent Systems, 5(2):217 - 228, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simNNNG1(ma,na,mb,nb,k)
#[1] 0.5885775 0.5995230 0.8202927 0.8202927

PFS similarity measure simNNNG2

Description

PFS similarity measure values using simNNNG2 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simNNNG2(ma, na, mb, nb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

X. T. Nguyen, V. D. Nguyen, V. H. Nguyen, and H. Garg. Exponential similarity measures for pythagorean fuzzy sets and their applications to pattern recognition and decision-making process. Complex & Intelligent Systems, 5(2):217 - 228, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simNNNG2(ma,na,mb,nb,k)
#[1] 0.7761019 0.7803072 0.9079870 0.9079870

IFS similarity measure simNSCA

Description

IFS similarity measure values using simNSCA computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simNSCA(ma, na, mb, nb, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

R. T. Ngan, B. C. Cuong, M. Ali, et al. H-max distance measure of intuitionistic fuzzy sets in decision making. Applied Soft Computing, 69:393 - 425, 2018.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
y<-matrix(c(11,24,21,12,6,11,15,21),nrow=1)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simNSCA(ma,na,mb,nb,k)
#[1] 0.6928792 0.6934970 0.8754130 0.8754130

PFS similarity measure simP

Description

PFS similarity measure values using simP computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simP(ma, na, mb, nb, a, b, p, t, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

X. Peng. New similarity measure and distance measure for pythagorean fuzzy set. Complex & Intelligent Systems, 5(2):101 - 111, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
a<-2
b<-2
p<-2
t<-2
k<-1
simP(ma,na,mb,nb,a,b,p,t,k)
#[1] 0.7007663 0.6879639 0.8834981 0.8834981

PFS similarity measure simPG1

Description

PFS similarity measure values using simPG1 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simPG1(ma, na, mb, nb, p, l, t, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

X. Peng and H. Garg. Multiparametric similarity measures on pythagorean fuzzy sets with applications to pattern recognition. Applied Intelligence, 49(12):4058 - 4096, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
p<-2
l<-2
t<-2
k<-1
simPG1(ma,na,mb,nb,p,l,t,k)
#[1] 0.6027082 0.5857886 0.8375740 0.8375740

PFS similarity measure simPG2

Description

PFS similarity measure values using simPG2 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simPG2(ma, na, mb, nb, p, l, t, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

X. Peng and H. Garg. Multiparametric similarity measures on pythagorean fuzzy sets with applications to pattern recognition. Applied Intelligence, 49(12):4058 - 4096, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
p<-2
l<-2
t<-2
k<-1
simPG2(ma,na,mb,nb,p,l,t,k)
#[1] 0.5203669 0.5000073 0.7998594 0.7998594

PFS similarity measure simPYY1

Description

PFS similarity measure values using simPYY1 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simPYY1(ma, na, mb, nb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

X. Peng, H. Yuan, and Y. Yang. Pythagorean fuzzy information measures and their applications. International Journal of Intelligent Systems, 32(10):991 - 1029, 2017.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simPYY1(ma,na,mb,nb,k)
#[1] 0.7253069 0.7257693 0.8985028 0.8985028

PFS similarity measure simPYY2

Description

PFS similarity measure values using simPYY2 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simPYY2(ma, na, mb, nb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

X. Peng, H. Yuan, and Y. Yang. Pythagorean fuzzy information measures and their applications. International Journal of Intelligent Systems, 32(10):991 - 1029, 2017.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simPYY2(ma,na,mb,nb,k)
#[1] 0.4082725 0.4321653 0.7383688 0.7383688

PFS similarity measure simPYY3

Description

PFS similarity measure values using simPYY3 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simPYY3(ma, na, mb, nb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

X. Peng, H. Yuan, and Y. Yang. Pythagorean fuzzy information measures and their applications. International Journal of Intelligent Systems, 32(10):991 - 1029, 2017.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simPYY3(ma,na,mb,nb,k)
#[1] 0.6973456 0.7033537 0.8813094 0.8813094

SFS similarity measure simSGFDK1

Description

SFS similarity measure values using simSGFDK1 computation technique with membership,non-membership, and indeterminacy membership values of two objects or set of objects.

Usage

simSGFDK1(ma, na, mb, nb, ia, ib, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

S. A. S. Shishavan, F. K. Gundogdu, E. Farrokhizadeh, Y. Donyatalab, and C. Kahraman. Novel similarity measures in spherical fuzzy environment and their applications. Engineering Applications of Artificial Intelligence, 94:103837, 2020.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
k<-1
simSGFDK1(ma,na,mb,nb,ia,ib,k)
#[1] 0.5765316 0.5799590 0.9132581 0.9132581

SFS similarity measure simSGFDK2

Description

SFS similarity measure values using simSGFDK2 computation technique with membership,non-membership, indeterminacy membership, and refusal membership values of two objects or set of objects.

Usage

simSGFDK2(ma, na, mb, nb, ia, ib, ra, rb, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

S. A. S. Shishavan, F. K. Gundogdu, E. Farrokhizadeh, Y. Donyatalab, and C. Kahraman. Novel similarity measures in spherical fuzzy environment and their applications. Engineering Applications of Artificial Intelligence, 94:103837, 2020.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
ra<-rmemSFS(ma,na,ia)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
rb<-rmemSFS(mb,nb,ib)
k<-1
simSGFDK2(ma,na,mb,nb,ia,ib,ra,rb,k)
#[1] 0.5582521 0.5488739 0.8922309 0.8922309

SFS similarity measure simSGFDK3

Description

SFS similarity measure values using simSGFDK3 computation technique with membership,non-membership, and indeterminacy membership values of two objects or set of objects.

Usage

simSGFDK3(ma, na, mb, nb, ia, ib, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

S. A. S. Shishavan, F. K. Gundogdu, E. Farrokhizadeh, Y. Donyatalab, and C. Kahraman. Novel similarity measures in spherical fuzzy environment and their applications. Engineering Applications of Artificial Intelligence, 94:103837, 2020.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
k<-1
simSGFDK3(ma,na,mb,nb,ia,ib,k)
#[1] 0.5433799 0.5440421 0.8018367 0.8018367

SFS similarity measure simSGFDK4

Description

SFS similarity measure values using simSGFDK4 computation technique with membership,non-membership, indeterminacy membership, and refusal membership values of two objects or set of objects.

Usage

simSGFDK4(ma, na, mb, nb, ia, ib, ra, rb, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

S. A. S. Shishavan, F. K. Gundogdu, E. Farrokhizadeh, Y. Donyatalab, and C. Kahraman. Novel similarity measures in spherical fuzzy environment and their applications. Engineering Applications of Artificial Intelligence, 94:103837, 2020.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
ra<-rmemSFS(ma,na,ia)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
rb<-rmemSFS(mb,nb,ib)
k<-1
simSGFDK4(ma,na,mb,nb,ia,ib,ra,rb,k)
#[1] 0.5433799 0.4910220 0.6803727 0.6803727

SFS similarity measure simSGFDK5

Description

SFS similarity measure values using simSGFDK5 computation technique with membership,non-membership, and indeterminacy membership values of two objects or set of objects.

Usage

simSGFDK5(ma, na, mb, nb, ia, ib, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

S. A. S. Shishavan, F. K. Gundogdu, E. Farrokhizadeh, Y. Donyatalab, and C. Kahraman. Novel similarity measures in spherical fuzzy environment and their applications. Engineering Applications of Artificial Intelligence, 94:103837, 2020.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
k<-1
simSGFDK5(ma,na,mb,nb,ia,ib,k)
#[1] 0.6563487 0.6447030 0.8547821 0.8547821

SFS similarity measure simSGFDK6

Description

SFS similarity measure values using simSGFDK6 computation technique with membership,non-membership, indeterminacy membership, and refusal membership values of two objects or set of objects.

Usage

simSGFDK6(ma, na, mb, nb, ia, ib, ra, rb, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

S. A. S. Shishavan, F. K. Gundogdu, E. Farrokhizadeh, Y. Donyatalab, and C. Kahraman. Novel similarity measures in spherical fuzzy environment and their applications. Engineering Applications of Artificial Intelligence, 94:103837, 2020.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
ra<-rmemSFS(ma,na,ia)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
rb<-rmemSFS(mb,nb,ib)
k<-1
simSGFDK6(ma,na,mb,nb,ia,ib,ra,rb,k)
#[1] 0.6563487 0.6334610 0.7893601 0.7893601

SFS similarity measure simSGFDK7

Description

SFS similarity measure values using simSGFDK7 computation technique with membership,non-membership, and indeterminacy membership values of two objects or set of objects.

Usage

simSGFDK7(ma, na, mb, nb, ia, ib, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

S. A. S. Shishavan, F. K. Gundogdu, E. Farrokhizadeh, Y. Donyatalab, and C. Kahraman. Novel similarity measures in spherical fuzzy environment and their applications. Engineering Applications of Artificial Intelligence, 94:103837, 2020.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
k<-1
simSGFDK7(ma,na,mb,nb,ia,ib,k)
#[1] 0.9670246 0.9661003 0.9976603 0.9976603

SFS similarity measure simSGFDK8

Description

SFS similarity measure values using simSGFDK8 computation technique with membership,non-membership, indeterminacy membership, and refusal membership values of two objects or set of objects.

Usage

simSGFDK8(ma, na, mb, nb, ia, ib, ra, rb, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

S. A. S. Shishavan, F. K. Gundogdu, E. Farrokhizadeh, Y. Donyatalab, and C. Kahraman. Novel similarity measures in spherical fuzzy environment and their applications. Engineering Applications of Artificial Intelligence, 94:103837, 2020.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
ra<-rmemSFS(ma,na,ia)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
rb<-rmemSFS(mb,nb,ib)
k<-1
simSGFDK8(ma,na,mb,nb,ia,ib,ra,rb,k)
#[1] 0.8558748 0.8421080 0.8994662 0.8994662

IFS similarity measure simSWLX

Description

IFS similarity measure values using simSWLX computation technique with membership,non-membership, and hesitancy values of two objects or set of objects.

Usage

simSWLX(ma, na, mb, nb, ha, hb, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

Y. Song, X. Wang, L. Lei, and A. Xue. A new similarity measure between intuitionistic fuzzy sets and its application to pattern recognition. In Abstract and Applied Analysis, volume 2014. Hindawi, 2014.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ha<-hmemIFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
hb<-hmemIFS(mb,nb)
k<-1
simSWLX(ma,na,mb,nb,ha,hb,k)
#[1] 0.9241207 0.9180258 0.9853267 0.9853267

IFS similarity measure simSY

Description

IFS similarity measure values using simSY computation technique with membership,non-membership, and hesitancy values of two objects or set of objects.

Usage

simSY(ma, na, mb, nb, ha, hb, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

L. Shi and J. Ye. Study on fault diagnosis of turbine using an improved cosine similarity measure for vague sets. Journal of Applied Sciences, 13(10):1781 - 1786, 2013.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ha<-hmemIFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
hb<-hmemIFS(mb,nb)
k<-1
simSY(ma,na,mb,nb,ha,hb,k)
#[1] 0.8982202 0.8904059 0.9890627 0.9890627

PFS similarity measure simWW1

Description

PFS similarity measure values using simWW1 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simWW1(ma, na, mb, nb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

G.Wei and Y.Wei. Similarity measures of pythagorean fuzzy sets based on the cosine function and their applications. International Journal of Intelligent Systems, 33(3):634 - 652, 2018.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simWW1(ma,na,mb,nb,k)
#[1] 0.9360206 0.9342653 0.9953501 0.9953501

PFS similarity measure simWW2

Description

PFS similarity measure values using simWW2 computation technique with membership,non-membership, and hesitancy values of two objects or set of objects.

Usage

simWW2(ma, na, mb, nb, ha, hb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

G.Wei and Y.Wei. Similarity measures of pythagorean fuzzy sets based on the cosine function and their applications. International Journal of Intelligent Systems, 33(3):634 - 652, 2018.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ha<-hmemPFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
hb<-hmemPFS(mb,nb)
k<-1
simWW2(ma,na,mb,nb,ha,hb,k)
#[1] 0.7061971 0.6841839 0.9511029 0.9511029

PFS similarity measure simWW3

Description

PFS similarity measure values using simWW3 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simWW3(ma, na, mb, nb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

G.Wei and Y.Wei. Similarity measures of pythagorean fuzzy sets based on the cosine function and their applications. International Journal of Intelligent Systems, 33(3):634 - 652, 2018.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simWW3(ma,na,mb,nb,k)
#[1] 0.7362461 0.7150021 0.9511755 0.9511755

PFS similarity measure simWW4

Description

PFS similarity measure values using simWW4 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simWW4(ma, na, mb, nb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

G.Wei and Y.Wei. Similarity measures of pythagorean fuzzy sets based on the cosine function and their applications. International Journal of Intelligent Systems, 33(3):634 - 652, 2018.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simWW4(ma,na,mb,nb,k)
#[1] 0.8971627 0.8883797 0.9843815 0.9843815

PFS similarity measure simWW5

Description

PFS similarity measure values using simWW5 computation technique with membership,non-membership, and hesitancy values of two objects or set of objects.

Usage

simWW5(ma, na, mb, nb, ha, hb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

G.Wei and Y.Wei. Similarity measures of pythagorean fuzzy sets based on the cosine function and their applications. International Journal of Intelligent Systems, 33(3):634 - 652, 2018.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ha<-hmemPFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
hb<-hmemPFS(mb,nb)
k<-1
simWW5(ma,na,mb,nb,ha,hb,k)
#[1] 0.7362461 0.7150021 0.9511755 0.9511755

PFS similarity measure simWW6

Description

PFS similarity measure values using simWW6 computation technique with membership,non-membership, and hesitancy values of two objects or set of objects.

Usage

simWW6(ma, na, mb, nb, ha, hb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

G.Wei and Y.Wei. Similarity measures of pythagorean fuzzy sets based on the cosine function and their applications. International Journal of Intelligent Systems, 33(3):634 - 652, 2018.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ha<-hmemPFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
hb<-hmemPFS(mb,nb)
k<-1
simWW6(ma,na,mb,nb,ha,hb,k)
#[1] 0.7362461 0.7150021 0.9511755 0.9511755

SFS similarity measure simWWLWW1

Description

SFS similarity measure values using simWWLWW1 computation technique with membership,non-membership, and indeterminacy membership values of two objects or set of objects.

Usage

simWWLWW1(ma, na, mb, nb, ia, ib, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

G. Wei, J. Wang, M. Lu, J. Wu, and C. Wei. Similarity measures of spherical fuzzy sets based on cosine function and their applications. IEEE Access, 7:159069 - 159080, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
k<-1
simWWLWW1(ma,na,mb,nb,ia,ib,k)
#[1] 0.9357619 0.9339882 0.9953291 0.9953291

SFS similarity measure simWWLWW10

Description

SFS similarity measure values using simWWLWW10 computation technique with membership,non-membership, indeterminacy membership, and refusal membership values of two objects or set of objects.

Usage

simWWLWW10(ma, na, mb, nb, ia, ib, ra, rb, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

G. Wei, J. Wang, M. Lu, J. Wu, and C. Wei. Similarity measures of spherical fuzzy sets based on cosine function and their applications. IEEE Access, 7:159069 - 159080, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
ra<-rmemSFS(ma,na,ia)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
rb<-rmemSFS(mb,nb,ib)
k<-1
simWWLWW10(ma,na,mb,nb,ia,ib,ra,rb,k)
#[1] 0.04488958 0.04334510 0.08280306 0.08280306

SFS similarity measure simWWLWW2

Description

SFS similarity measure values using simWWLWW2 computation technique with membership,non-membership, indeterminacy membership, and refusal membership values of two objects or set of objects.

Usage

simWWLWW2(ma, na, mb, nb, ia, ib, ra, rb, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

G. Wei, J. Wang, M. Lu, J. Wu, and C. Wei. Similarity measures of spherical fuzzy sets based on cosine function and their applications. IEEE Access, 7:159069 - 159080, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
ra<-rmemSFS(ma,na,ia)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
rb<-rmemSFS(mb,nb,ib)
k<-1
simWWLWW2(ma,na,mb,nb,ia,ib,ra,rb,k)
#[1] 0.7092608 0.6874359 0.9519182 0.9519182

SFS similarity measure simWWLWW3

Description

SFS similarity measure values using simWWLWW3 computation technique with membership,non-membership, and indeterminacy membership values of two objects or set of objects.

Usage

simWWLWW3(ma, na, mb, nb, ia, ib, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

G. Wei, J. Wang, M. Lu, J. Wu, and C. Wei. Similarity measures of spherical fuzzy sets based on cosine function and their applications. IEEE Access, 7:159069 - 159080, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
k<-1
simWWLWW3(ma,na,mb,nb,ia,ib,k)
#[1] 0.7362461 0.7150021 0.9511755 0.9511755

SFS similarity measure simWWLWW4

Description

SFS similarity measure values using simWWLWW4 computation technique with membership,non-membership, and indeterminacy membership values of two objects or set of objects.

Usage

simWWLWW4(ma, na, mb, nb, ia, ib, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

G. Wei, J. Wang, M. Lu, J. Wu, and C. Wei. Similarity measures of spherical fuzzy sets based on cosine function and their applications. IEEE Access, 7:159069 - 159080, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
k<-1
simWWLWW4(ma,na,mb,nb,ia,ib,k)
#[1] 0.8946430 0.8856546 0.9840049 0.9840049

SFS similarity measure simWWLWW5

Description

SFS similarity measure values using simWWLWW5 computation technique with membership,non-membership, indeterminacy membership, and refusal membership values of two objects or set of objects.

Usage

simWWLWW5(ma, na, mb, nb, ia, ib, ra, rb, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

G. Wei, J. Wang, M. Lu, J. Wu, and C. Wei. Similarity measures of spherical fuzzy sets based on cosine function and their applications. IEEE Access, 7:159069 - 159080, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
ra<-rmemSFS(ma,na,ia)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
rb<-rmemSFS(mb,nb,ib)
k<-1
simWWLWW5(ma,na,mb,nb,ia,ib,ra,rb,k)
#[1] 0.7362461 0.7150021 0.9511755 0.9511755

SFS similarity measure simWWLWW6

Description

SFS similarity measure values using simWWLWW6 computation technique with membership,non-membership, indeterminacy membership, and refusal membership values of two objects or set of objects.

Usage

simWWLWW6(ma, na, mb, nb, ia, ib, ra, rb, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

G. Wei, J. Wang, M. Lu, J. Wu, and C. Wei. Similarity measures of spherical fuzzy sets based on cosine function and their applications. IEEE Access, 7:159069 - 159080, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
ra<-rmemSFS(ma,na,ia)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
rb<-rmemSFS(mb,nb,ib)
k<-1
simWWLWW6(ma,na,mb,nb,ia,ib,ra,rb,k)
#[1] 0.7362461 0.7150021 0.9511755 0.9511755

SFS similarity measure simWWLWW7

Description

SFS similarity measure values using simWWLWW7 computation technique with membership,non-membership, and indeterminacy membership values of two objects or set of objects.

Usage

simWWLWW7(ma, na, mb, nb, ia, ib, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

G. Wei, J. Wang, M. Lu, J. Wu, and C. Wei. Similarity measures of spherical fuzzy sets based on cosine function and their applications. IEEE Access, 7:159069 - 159080, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
k<-1
simWWLWW7(ma,na,mb,nb,ia,ib,k)
#[1] 0.04488958 0.04334510 0.08280306 0.08280306

SFS similarity measure simWWLWW8

Description

SFS similarity measure values using simWWLWW8 computation technique with membership,non-membership, and indeterminacy membership values of two objects or set of objects.

Usage

simWWLWW8(ma, na, mb, nb, ia, ib, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

G. Wei, J. Wang, M. Lu, J. Wu, and C. Wei. Similarity measures of spherical fuzzy sets based on cosine function and their applications. IEEE Access, 7:159069 - 159080, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
k<-1
simWWLWW8(ma,na,mb,nb,ia,ib,k)
#[1] 0.06899567 0.06819133 0.09416530 0.09416530

SFS similarity measure simWWLWW9

Description

SFS similarity measure values using simWWLWW9 computation technique with membership,non-membership, indeterminacy membership, and refusal membership values of two objects or set of objects.

Usage

simWWLWW9(ma, na, mb, nb, ia, ib, ra, rb, k)

Arguments

Value

The SFS similarity values of data set y with data set x

References

G. Wei, J. Wang, M. Lu, J. Wu, and C. Wei. Similarity measures of spherical fuzzy sets based on cosine function and their applications. IEEE Access, 7:159069 - 159080, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ia<-imemSFS(ma,na)
ra<-rmemSFS(ma,na,ia)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
ib<-imemSFS(mb,nb)
rb<-rmemSFS(mb,nb,ib)
k<-1
simWWLWW9(ma,na,mb,nb,ia,ib,ra,rb,k)
#[1] 0.04488958 0.04334510 0.08280306 0.08280306

IFS similarity measure simY

Description

IFS similarity measure values using simY computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simY(ma, na, mb, nb, k)

Arguments

Value

The IFS similarity values of data set y with data set x

References

J. Ye. Cosine similarity measures for intuitionistic fuzzy sets and their applications. Mathematical and computer modelling, 53(1-2):91 - 97, 2011.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simY(ma,na,mb,nb,k)
#[1] 0.9024655 0.8950394 0.9898896 0.9898896

PFS similarity measure simZ

Description

PFS similarity measure values using simZ computation technique with membership,non-membership, and hesitancy values of two objects or set of objects.

Usage

simZ(ma, na, mb, nb, ha, hb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

X. Zhang. A novel approach based on similarity measure for pythagorean fuzzy multiple criteria group decision making. International Journal of Intelligent Systems, 31(6):593 - 611, 2016.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ha<-hmemPFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
hb<-hmemPFS(mb,nb)
k<-1
simZ(ma,na,mb,nb,ha,hb,k)
#[1] 0.6128632 0.6335697 0.7722389 0.7722389

PFS similarity measure simZHFLL1

Description

PFS similarity measure values using simZHFLL1 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simZHFLL1(ma, na, mb, nb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

Q. Zhang, J. Hu, J. Feng, A. Liu, and Y. Li. New similarity measures of pythagorean fuzzy sets and their applications. IEEE Access, 7:138192 - 138202, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simZHFLL1(ma,na,mb,nb,k)
#[1] 0.4742565 0.4823949 0.7745995 0.7745995

PFS similarity measure simZHFLL2

Description

PFS similarity measure values using simZHFLL2 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simZHFLL2(ma, na, mb, nb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

Q. Zhang, J. Hu, J. Feng, A. Liu, and Y. Li. New similarity measures of pythagorean fuzzy sets and their applications. IEEE Access, 7:138192 - 138202, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
k<-1
simZHFLL2(ma,na,mb,nb,k)
#[1] 0.6572330 0.6610095 0.8652155 0.8652155

PFS similarity measure simZHFLL3

Description

PFS similarity measure values using simZHFLL3 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simZHFLL3(ma, na, mb, nb, ha, hb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

Q. Zhang, J. Hu, J. Feng, A. Liu, and Y. Li. New similarity measures of pythagorean fuzzy sets and their applications. IEEE Access, 7:138192 - 138202, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ha<-hmemPFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
hb<-hmemPFS(mb,nb)
k<-1
simZHFLL3(ma,na,mb,nb,ha,hb,k)
#[1] 0.4742565 0.4823949 0.7745995 0.7745995

PFS similarity measure simZHFLL4

Description

PFS similarity measure values using simZHFLL4 computation technique with membership, and non-membership values of two objects or set of objects.

Usage

simZHFLL4(ma, na, mb, nb, ha, hb, k)

Arguments

Value

The PFS similarity values of data set y with data set x

References

Q. Zhang, J. Hu, J. Feng, A. Liu, and Y. Li. New similarity measures of pythagorean fuzzy sets and their applications. IEEE Access, 7:138192 - 138202, 2019.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
y<-matrix(c(11,21,6),nrow=1)
a<-mn(x)
b<-std(x)
a1<-mn(y)
b1<-std(y)
lam<-0.5
ma<-memG(a,b,x)
na<-nonmemS(ma,lam)
ha<-hmemPFS(ma,na)
mb<-memG(a1,b1,y)
nb<-nonmemS(mb,lam)
hb<-hmemPFS(mb,nb)
k<-1
simZHFLL4(ma,na,mb,nb,ha,hb,k)
#[1] 0.4742565 0.4823949 0.7745995 0.7745995

Standard deviation values

Description

Standard deviation of the data set for gaussian membership function

Usage

std(x)

Arguments

Value

Standard deviation values for individual row of the input data set X.

Examples

x<-matrix(c(12,9,14,11,21,16,15,24,20,17,14,11),nrow=4)
std(x)
#[1] 4.9328829 4.3588989 0.5773503 7.5055535