Package 'IFMCDM'

Title: Intuitionistic Fuzzy Multi-Criteria Decision Making Methods
Description: Implementation of two multi-criteria decision making methods (MCDM): Intuitionistic Fuzzy Synthetic Measure (IFSM) and Intuitionistic Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (IFTOPSIS) for intuitionistic fuzzy data sets for multi-criteria decision making problems. References describing the methods: Jefmański (2020) <doi:10.1007/978-3-030-52348-0_4>; Jefmański, Roszkowska, Kusterka-Jefmańska (2021) <doi:10.3390/e23121636>.
Authors: Andrzej Dudek [aut, cre] , Bartłomiej Jefmański [aut] , Marta Kusterka-Jefmańska [aut] , Ewa Roszkowska [aut]
Maintainer: Andrzej Dudek <[email protected]>
License: GPL (>= 2)
Version: 0.1.17
Built: 2025-01-22 03:56:09 UTC
Source: https://github.com/a-dudek-ue/ifmcdm

Help Index

The sample intuitionistic fuzzy dataset

Description

The sample intuitionistic fuzzy dataset

Usage

data_IF

Format

An object of class matrix (inherits from array) with 5 rows and 9 columns.

Examples

set.seed(61222)
data(data_IF)
m<-IFSM(data_IF)
print(m)

Aggregation of primary data into Intuitionistic Representation

Description

The IFconversion - Aggregation of primary data into Intuitionistic Representation. Reference describing the method: Jefmański (2020) doi:10.1007/978-3-030-52348-0_4

Usage

IFconversion(
  primary,
  u = round(mean(c(min(primary[, -1], na.rm = TRUE), max(primary[, -1], na.rm =
    TRUE)))),
  u_is_neutral = TRUE
)

Arguments

primary

dataset with object names (not aggregated) in first column
u

cut level
u_is_neutral

if exact value of variable is equal to u (cut_level) the variable is treated as neutral (TRUE) or negative (FALSE)

Value

IFconversion returns the decision matrix (m x n*3) with the values of the mi ni and pi (three columns for each fuzzy representation), for the n criteria

References

Jefmański Bartłomiej, Intuitionistic Fuzzy Synthetic Measure for Ordinal Data. in: Classification and Data Analysis: Theory and Applications / Jajuga Krzysztof, Batóg Jacek, Walesiak Marek (eds.), Studies in Classification, Data Analysis, and Knowledge Organization, 2020, Cham, Springer, 53-72. doi:10.1007/978-3-030-52348-0_4

Examples

set.seed(61222)
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)
inth<-IFconversion(primary)

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)

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)