fcmfd
================

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# fcmfd

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

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## 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.

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## 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

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## Installation

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

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## Example

``` r
library(fcmfd)

# Load dataset
data(sim_likert_0_10)

# Run clustering
result <- fcmTFN(
  data = sim_likert_0_10,
  option = "B",
  k_values = 2:6
)

# Summary
summary(result)

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

# Plot Xie–Beni index
plot_xb(result)
```

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## Included Datasets

- **sim_likert7** Simulated dataset with a 1–7 Likert scale

- **sim_likert_0_10** Simulated dataset with a 0–10 Likert scale and
  latent cluster structure

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## 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.

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## Uses Cases

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

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## 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>

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## Author

José Ortigas

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## License

MIT
