Package 'fcmfd'

Hard Cluster Assignment

Description

Assigns each observation to the cluster with the highest membership value.

Usage

cluster_assignment(object)

Arguments

object

An object of class "fcmTFN".

Value

A factor indicating cluster labels.

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Cluster Sizes

Description

Computes the size of each cluster using both hard assignments and fuzzy memberships.

Usage

cluster_size(object)

Arguments

object

An object of class "fcmTFN".

Details

Hard size is obtained by assigning each observation to the cluster with the highest membership degree.

Fuzzy size is computed as the sum of membership degrees for each cluster.

Value

A data.frame containing:

Cluster

Cluster label.

Hard_Size

Number of observations assigned to the cluster.

Fuzzy_Size

Sum of membership degrees.

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Fuzzy C-Means Clustering for Triangular Fuzzy Numbers

Description

Performs fuzzy clustering on ordinal Likert-type data represented as triangular fuzzy numbers (TFNs).

Usage

fcmTFN(
  data,
  type = "symmetric",
  option = "B",
  dictionary = NULL,
  k_values = 2:6,
  m = 2,
  epsilon = 1e-06,
  max_iter = 1000,
  verbose = TRUE
)

Arguments

data	A data.frame or matrix containing ordinal Likert-type responses. Rows represent observations (respondents) and columns represent variables (items or dimensions). All values must be integers within the range defined by the selected scale option.
type	A character string specifying the type of fuzzy dictionary to use. Must be one of "symmetric" for predefined symmetric triangular fuzzy numbers, or "asymmetric" for a user-defined custom dictionary. Defaults to "symmetric".
option	A character string indicating the Likert scale option. Must be one of "A" (5-point scale, 1–5), "B" (7-point scale, 1–7), "C" (10-point scale, 1–10), or "D" (11-point scale, 0–10). Defaults to "B".
dictionary	An optional numeric matrix with 3 columns (l, c, r) representing the lower bound, modal value, and upper bound of each triangular fuzzy number. Required when type = "asymmetric"; ignored when type = "symmetric". Defaults to NULL.
k_values	A numeric vector specifying the candidate numbers of clusters to evaluate. The algorithm runs independently for each value of k. Defaults to 2:6.
m	Fuzzifier parameter (m > 1) specifying the fuzzifier parameter, which controls the degree of membership overlap between clusters. Higher values produce softer partitions. Defaults to 2.
epsilon	A positive numeric value specifying the convergence tolerance. The algorithm stops when the change in the objective function between iterations falls below this threshold. Defaults to 1e-06.
max_iter	A positive integer specifying the maximum number of iterations allowed per run. If convergence is not reached within this limit, a warning is issued. Defaults to 1000.
verbose	A logical value. If TRUE, progress messages are printed to the console during execution, including iteration count and convergence status for each value of k. Defaults to TRUE.

Details

The function automatically determines the optimal number of clusters based on the Xie-Beni validity index.

Value

An object of class '"fcmTFN"' and '"fcm"'.

References

Coppi, R., D'Urso, P., & Giordani, P. (2012). Fuzzy and possibilistic clustering for fuzzy data. <doi:10.1016/j.csda.2010.09.013>

Xie, X. L., & Beni, G. (1991). A validity measure for fuzzy clustering. <doi:10.1109/34.85677>

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Extract Membership Matrix

Description

Returns the fuzzy membership matrix obtained from the Fuzzy C-Means clustering process.

Usage

membership(object)

Arguments

object

An object of class "fcmTFN".

Value

A matrix where rows represent observations and columns represent clusters.

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Membership Quality Assessment

Description

Evaluates the quality of fuzzy assignments for each cluster using membership-based measures.

Usage

membership_quality(object)

Arguments

object

An object of class "fcmTFN".

Details

This function computes both cluster-specific metrics based on hardened assignments (maximum membership rule) and global partition criteria to evaluate how well-defined the fuzzy boundaries are.

Value

A list containing:

cluster_summary

Data frame with one row per cluster containing:

• Hard_Size: number of observations primarily assigned to the cluster.

• Avg_Membership: average membership of those observations.

• Avg_Margin: average difference between the largest and second-largest memberships, indicating the clarity of assignment.

partition_coefficient

Global partition coefficient (PC).

partition_entropy

Global partition entropy (PE).

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Plot Fuzzy Dictionary

Description

Plots the triangular fuzzy numbers defining the Likert-scale dictionary.

Usage

plot_dictionary(object, show_title = TRUE, ...)

Arguments

object	An object of class "fcmTFN".
show_title	Logical. If TRUE (default), displays the plot title.
...	Additional graphical parameters.

Value

Invisibly returns NULL.

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Plot Cluster Prototypes

Description

Visualizes cluster prototypes as interval plots using triangular fuzzy numbers (l, c, r).

Usage

plot_prototypes(
  object,
  cluster = 1,
  view = c("single", "global"),
  use_var_names = FALSE,
  var_names = NULL,
  show_title = TRUE,
  ...
)

Arguments

object	An object of class "fcmTFN".
cluster	Integer cluster to plot when view = "single".
view	Character string indicating the visualization mode. Either "single" or "global".
use_var_names	Logical.
var_names	Optional character vector of variable names.
show_title	Logical. If TRUE (default), displays the plot title.
...	Additional graphical parameters.

Value

Invisibly returns NULL.

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Plot Xie-Beni Index

Description

Plots the Xie-Beni validity index across candidate numbers of clusters.

Usage

plot_xb(object, mark_optimal = TRUE, type = "b", show_title = TRUE, ...)

Arguments

object	An object of class "fcmTFN".
mark_optimal	Logical. Whether to highlight the optimal k.
type	Character string indicating the plotting style (default = "b").
show_title	Logical. If TRUE (default), displays the plot title.
...	Additional graphical parameters.

Value

Invisibly returns NULL.

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Print Method for fcmTFN Objects

Description

Displays a concise summary of a fitted fuzzy C-means model using triangular fuzzy numbers.

Usage

print_fcmTFN(x, ...)

Arguments

x	An object of class "fcmTFN".
...	Additional arguments (not used).

Value

The input object (invisibly).

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Prototype Results

Description

Returns cluster prototypes either as a flat matrix or as a list of tables containing l, c, r values for each variable.

Usage

prototype_results(
  object,
  use_var_names = FALSE,
  var_names = NULL,
  format = c("flat", "table")
)

Arguments

object	An object of class "fcmTFN".
use_var_names	Logical.
var_names	Optional variable names.
format	Character string indicating the output format: "flat" (default) returns the original matrix representation, while "table" returns one table per cluster.

Value

If format = "flat", a data.frame containing prototype values.

If format = "table", a named list of data.frames, one for each cluster.

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Simulated Likert 1–7 Survey Dataset

Description

A simulated Likert-type dataset with three well-separated clusters, specifically designed for testing fuzzy clustering of ordinal data.

Usage

sim_likert7

Format

A data frame with 300 rows and 12 variables:

Q1

Simulated survey response measured on a 1–7 Likert scale.

Q10

Simulated survey response measured on a 1–7 Likert scale.

Q11

Simulated survey response measured on a 1–7 Likert scale.

Q12

Simulated survey response measured on a 1–7 Likert scale.

Q2

Simulated survey response measured on a 1–7 Likert scale.

Q3

Simulated survey response measured on a 1–7 Likert scale.

Q4

Simulated survey response measured on a 1–7 Likert scale.

Q5

Simulated survey response measured on a 1–7 Likert scale.

Q6

Simulated survey response measured on a 1–7 Likert scale.

Q7

Simulated survey response measured on a 1–7 Likert scale.

Q8

Simulated survey response measured on a 1–7 Likert scale.

Q9

Simulated survey response measured on a 1–7 Likert scale.

Details

The dataset contains 300 observations divided into three distinct clusters of 100 observations each. Data generation was based on three latent profiles centered approximately at:

• Low agreement: $\approx$ 2

• Moderate agreement: $\approx$ 4

• High agreement: $\approx$ 6

Source

Simulated data generated for package examples.

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Student Wellbeing During COVID-19

Description

Survey data on subjective well-being, optimism, gratitude, emotional closeness, worry, and depression, collected from university students.

Usage

students_wellbeing

Format

A data frame with 651 rows and 9 variables:

Q13.1	Satisfaction with life overall.
Q13.2	Satisfaction with life at the present moment.
Q13.3	Satisfaction with oneself.
Q13.4	Satisfaction with physical appearance.
Q13.5	Satisfaction with ability to communicate with others.
Q13.6	Satisfaction with overall health.
Q13.7	Satisfaction with achievements in life so far.
Q13.8	Satisfaction with the college.
Q13.9	Satisfaction with college classmates.

Details

All variables are measured on an 11-point ordinal scale ranging from 0 to 10, where higher values indicate greater satisfaction.

Source

Martinez, L., Valencia, I., Trofimoff, V., & Valenzuela, L. S. (2020). Students wellbeing during COVID-19. <doi:10.17632/w9brygpwg7.2>

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Summary for fcmTFN Objects

Description

Displays a summary of the Fuzzy C-Means clustering results for triangular fuzzy numbers.

Usage

## S3 method for class 'fcmTFN'
summary(object, ...)

Arguments

object	An object of class "fcmTFN".
...	Additional arguments (not used).

Value

Prints a formatted summary of the clustering result.

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