IFSM {IFMCDM}

Implementation of the Intuitionistic Fuzzy Synthetic Measure Method for Fuzzy Multi-Criteria Decision Making Problems

Description

The IFSM - Intuitionistic Fuzzy Synthetic Measure Method for Fuzzy Multi-Criteria Decision Making Problems. Reference describing the method: Jefmański, Roszkowska, Kusterka-Jefmańska (2021) doi:10.3390/e23121636

Usage

IFSM(
  data,
  d = "e",
  w = rep(3/ncol(data), ncol(data)/3),
  z = rep("b", ncol(data)/3),
  p = "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.

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).

Value

IFSM returns a data frame that contains the scores of the Intuitionistic Fuzzy Synthetic Measure (IFSM) and the ranking of the alternatives.

References

Jefmański B, Roszkowska E, Kusterka-Jefmańska M. Intuitionistic Fuzzy Synthetic Measure on the Basis of Survey Responses and Aggregated Ordinal Data. Entropy. 2021; 23(12):1636. doi:10.3390/e23121636

Roszkowska E, Jefmański B, Kusterka-Jefmańska M. On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights. Entropy. 2022; 24(8):1081. doi:10.3390/e24081081

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)
print(f)
m<-IFSM(f)
print(m)