# DwablphiTra: (\varphi,theta)-wabl/ldev/rdev distance between trapezoidal... In FuzzyStatTra: Statistical Methods for Trapezoidal Fuzzy Numbers

## Description

This function calculates the (\varphi,θ)-wabl/ldev/rdev distance between the trapezoidal fuzzy numbers contained in two matrixes, which should be given in the desired format. For this, the function first checks if the input matrixes R and S are in the correct form (tested by checkingTra).

## Usage

 1 DwablphiTra(R, S, a = 1, b = 1, theta = 1) 

## Arguments

 R matrix of dimension r x 4 containing r trapezoidal fuzzy numbers characterized by their four values inf0,inf1,sup1,sup0. The function first calls checkingTra to check if the matrix R has the correct format. S matrix of dimension s x 4 containing s trapezoidal fuzzy numbers characterized by their four values inf0,inf1,sup1,sup0. The function first calls checkingTra to check if the matrix S has the correct format. a number >0, by default a=1. It is the first parameter of a beta distribution which corresponds to a weighting measure on [0,1]. b number >0, by default b=1. It is the second parameter of a beta distribution which corresponds to a weighting measure on [0,1]. theta number >0, by default theta=1. It is the weight of the ldev and rdev in the (\varphi,θ)-wabl/ldev/rdev distance.

See examples

## Value

The function returns a matrix of dimension r x s containing the (\varphi,θ)-wabl/ldev/rdev distances between the trapezoidal fuzzy numbers of the matrix R and the trapezoidal fuzzy numbers of the matrix S.

## Note

In case you find (almost surely existing) bugs or have recommendations for improving the functions comments are welcome to the above mentioned mail addresses.

## Author(s)

Asun Lubiano <lubiano@uniovi.es>, Sara de la Rosa de Saa <rosasara@uniovi.es>

## References

[1] Sinova, B.; de la Rosa de Saa, S.; Gil, M.A.: A generalized L1-type metric between fuzzy numbers for an approach to central tendency of fuzzy data, Information Sciences 242, pp. 22-34 (2013)

[2] Sinova, B.; Gil, M.A.; Van Aelst, S.: M-estimates of location for the robust central tendency of fuzzy data, IEEE Transactions on Fuzzy Systems 24(4), pp. 945-956 (2016)

checkingTra, Dwablphi, Wablphi

## Examples

  1 2 3 4 5 6 7 8 9 10 # Example 1: F=SimulCASE1(10) S=SimulCASE1(20) DwablphiTra(F,S,5,1,1) # Example 2: F=matrix(c(1,1,0,2,3,4,5,6),nrow=2) S=SimulCASE1(8) DwablphiTra(F,S) 

### Example output

           [,1]      [,2]     [,3]      [,4]      [,5]      [,6]     [,7]
[1,] 1.8778077 1.6418693 4.534212 2.2273118 1.6699782 1.9482797 2.995212
[2,] 2.0104611 1.6438636 4.672189 2.3593366 1.7926609 1.9075699 3.133189
[3,] 1.9344934 1.6996545 4.596221 2.3151821 1.7318475 1.9910511 3.057221
[4,] 1.7529012 2.8542228 3.417769 2.7654236 1.8069623 3.1657679 1.879027
[5,] 2.2685644 3.3273230 4.121525 3.2385239 2.2800626 3.6388682 2.582530
[6,] 0.4050334 0.9880618 3.036775 0.9209407 0.1572470 1.2996069 1.497775
[7,] 2.9012091 4.0063109 3.366858 3.9175117 2.9590504 4.3178560 2.273426
[8,] 1.4608949 0.4641029 3.712098 0.4679989 1.4036109 0.2740161 2.088660
[9,] 1.4795334 0.4704364 3.730736 0.4659700 1.4221680 0.3116673 2.107298
[10,] 0.8439320 0.9543722 3.415872 1.2400093 0.6642849 1.2618791 1.886227
[,8]     [,9]     [,10]    [,11]     [,12]    [,13]     [,14]
[1,] 1.7630455 2.360587 1.9682496 3.270429 1.5415550 3.563610 2.0067235
[2,] 1.8828380 2.498563 2.1062263 3.299843 1.6795317 3.701587 2.2176031
[3,] 1.9814162 2.422596 2.0302586 3.327214 1.6049566 3.625619 2.2007803
[4,] 2.9907513 1.244144 0.8518067 4.469383 1.1947784 2.447167 2.8881591
[5,] 3.4638515 1.947899 1.5555621 4.942484 1.6702378 3.150923 3.3587709
[6,] 1.1400233 2.376160 1.7341580 2.603223 0.7488830 3.532526 1.1375881
[7,] 4.1428393 1.197093 1.2886808 5.621471 2.3003875 2.396256 4.0293162
[8,] 0.3882268 3.719996 3.0779947 1.383192 2.0749773 4.876363 0.4249487
[9,] 0.3917535 3.738635 3.0966332 1.323033 2.0936159 4.895002 0.4275885
[10,] 1.0541303 2.452242 1.8124279 2.580283 0.8067983 3.608185 0.9374147
[,15]     [,16]     [,17]     [,18]     [,19]    [,20]
[1,] 1.5198018 0.9883003 0.6109738 0.5655990 2.4078553 2.492614
[2,] 1.7030831 1.0656831 0.7201853 0.7742878 2.5554996 2.630591
[3,] 1.7058147 1.0459231 0.6055344 0.7551129 2.5209208 2.554623
[4,] 2.5412205 1.7387108 1.4745578 1.3649245 2.9748528 1.376171
[5,] 3.0141799 2.2118111 1.9538948 1.8354164 3.4456703 2.079926
[6,] 0.7192959 0.5697308 1.0188108 1.1092434 1.2374464 2.836294
[7,] 3.6931555 2.8907989 2.6266428 2.5000324 4.1196227 1.325276
[8,] 0.7212579 1.4816786 1.7354430 1.9566018 0.6646160 4.180131
[9,] 0.7251968 1.5000725 1.7540816 1.9595801 0.6132078 4.198770
[10,] 0.6429667 0.4734616 0.8112431 0.6237568 1.3206529 2.911952
[1] "input defines no trapezoidal fuzzy numbers - four values must increase"


FuzzyStatTra documentation built on May 2, 2019, 10:59 a.m.