Fuzzy C-Means for Fuzzy Data

Implements a fuzzy clustering approach for ordinal Likert-type data using triangular fuzzy numbers (TFNs). The package extends the classical fuzzy C-means algorithm to better handle uncertainty in ordinal scales and includes automatic selection of the number of clusters using the Xie-Beni validity index. References: Coppi, R., D'Urso, P., and Giordani, P. (2012), "Fuzzy and possibilistic clustering for fuzzy data", . Xie, X. L. and Beni, G. (1991), "A validity measure for fuzzy clustering", .

title: "fcmfd" output: github_document

fcmfd

Fuzzy C-Means Clustering for Ordinal Data using Triangular Fuzzy Numbers

Overview

The fcmfd package implements fuzzy clustering for ordinal Likert-type data using Triangular Fuzzy Numbers (TFNs).

It is designed for datasets where responses are measured on discrete ordinal scales (e.g., 1-5, 1–7, 1-10 or 0–10), providing a robust alternative to traditional clustering approaches.

Features

• Fuzzy C-Means clustering adapted to TFNs
• Automatic selection of the optimal number of clusters
• Xie–Beni validity index
• Support for Likert-type data
• Cluster assignment and prototype extraction
• Visualization tools

Installation

# install.packages("devtools")
devtools::install_github("yourusername/fcmfd")

Example

library(fcmfd)

# Load dataset
data(sim_likert7)

# Run clustering
result <- fcmTFN(
  data = sim_likert7,
  option = "B",
  k_values = 2:6
)

# Summary
summary(result)

# Cluster assignment
clusters <- cluster_assignment(result)
table(clusters)

# Plot Xie–Beni index
plot_xb(result)

Included Datasets

• sim_likert7 Simulated dataset with a 1–7 Likert scale

Methodological Background

The package combines:

• Fuzzy C-Means clustering
• Triangular Fuzzy Numbers representation
• Xie–Beni cluster validity index

to provide a framework tailored for ordinal data.

Uses Cases

• Survey analysis
• Social sciences
• Customer satisfaction
• Quality of life studies
• Likert-type data clustering

References

Coppi, R., D'Urso, P., & Giordani, P. (2011). Fuzzy clustering of fuzzy data. Computational Statistics & Data Analysis. https://doi.org/10.1016/j.csda.2010.09.013

Xie, X. L., & Beni, G. (1991). A validity measure for fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence. https://doi.org/10.1109/34.85677

Author

José Ortigas

License

MIT