IFTOPSIS {IFMCDM}

Implementation of the Intuitionistic Fuzzy Technique for Order of Preference by Similarity to Ideal Solution for Fuzzy Multi-Criteria Decision Making Problems

Description

The IFTOPSIS - Intuitionistic Fuzzy Technique for Order of Preference by Similarity to Ideal Solution for Fuzzy Multi-Criteria Decision Making. Reference describing the method: Roszkowska, Kusterka-Jefmańska, Jefmański (2021) doi:10.3390/e23050563

Usage

IFTOPSIS(
  data,
  d = "e",
  w = rep(3/ncol(data), ncol(data)/3),
  z = rep("b", ncol(data)/3),
  p = "dataBounds",
  ap = "dataBounds"
)

Arguments

data

The data matrix (m x n*3) with the values of mi ni and pi (three columns for each intuitionistic fuzzy representation of criteria for each alternative), where m is the number of alternatives and n is the number of criteria.

d

Distance "euclidean" or "hamming".

w

A vector of length n, containing the crisp weights for the criteria (one value for intuitionistic fuzzy representation)

z

A vector of length n, with preferences type for each criterion with "b" (benefit) and "c" (cost).

p

Ideal point calculation type with one of two values: "dataBounds" – ideal point contains max and min values from the dataset – see details; "idealBounds" – ideal point contains 1 and 0’s - see details.

ap

Anti-ideal point calculation type with one of two values: "dataBounds" – anti-ideal point contains min and max from the dataset – see details; "idealBounds" – anti-ideal point contains 0 and 1’s - see details.

Details

For p="dataBounds" the actual ideal point is calculated for benefits as maximum from all values for mi and min for ni (pi = 1- mi - ni); in the case of costs, minimal value for mi and max for ni (pi = 1- mi - ni). For p="idealBounds" for benefitss is 1 for mi and 0 for ni (pi = 1- mi - ni ). In the case of costs it is 0 for mi and 1 for ni (pi = 1- (mi - ni). For ap="dataBounds" the actual anti-ideal point is calculated for benefit criteria as minimum of all values for mi, maximum of all values for ni and pi = 1- (mi + ni); in the case of cost criteria, maximum of all values for mi, minimum of all values for ni and pi = 1- (mi + ni). For ap="idealBounds" in the case of benefit criteria it is 0 for mi, 1 for ni, 0 for pi; in the case of cost criteria it is 1 for mi, 0 for ni and 0 for pi.

Value

IFTOPSIS returns a data frame that contains the scores of the Intuitionistic Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (IFTOPSIS) and the ranking of the alternatives.

References

Roszkowska E, Kusterka-Jefmańska M, Jefmański B. Intuitionistic Fuzzy TOPSIS as a Method for Assessing Socioeconomic Phenomena on the Basis of Survey Data. Entropy. 2021; 23(5):563. doi:10.3390/e23050563

Xu, Z. Some Similarity Measures of Intuitionistic Fuzzy Sets and Their Applications to Multiple Attribute Decision Making. Fuzzy Optimization and Decision Making. 2007; 6: 109–121. doi:10.1007/s10700-007-9004-z

Examples

set.seed(823)
data<-sample(1:7,26*13*8,replace=TRUE)
dim(data)<-c(26*13,8)
nrColumns<-8
primary<-data.frame(name=rep(LETTERS,each=13),data)
f<-IFconversion(primary)
m<-IFTOPSIS(f)
print(m)