# Using the Full Consistency Method (FUCOM) for Multi-Criteria Decision-Making

## Introduction

The Full Consistency Method (FUCOM) is a Multi-Criteria Decision-Making (MCDM) method developed to determine the optimal weights of criteria, ensuring that the deviation from full consistency is minimized. This vignette provides a step-by-step guide on how to use the fucom package to apply the FUCOM method and interpret the results.

Example: Applying the FUCOM Method

Below is an example demonstrating how to apply the FUCOM method using the fucom package to calculate optimized weights for a set of criteria.

First, define the criteria to be evaluated, along with their respective ranks and priorities. In this example, we are evaluating eight criteria with the following priority values: criteria_rank <- c (“Criterion 1”, “Criterion 2”, “Criterion 3”, “Criterion 4”, “Criterion 5”, “Criterion 6”, “Criterion 7”, “Criterion 8”) criteria_priority <- c (1, 1, 1, 2, 4, 4, 4, 4)

    library(fucom)

    criteria_rank <- c("Criterion 1", "Criterion 2", "Criterion 3",
                       "Criterion 4", "Criterion 5", "Criterion 6",
                       "Criterion 7", "Criterion 8")

    criteria_priority <- c(1, 1, 1, 2, 4, 4, 4, 4)

    results <- fucom_method(criteria_rank, criteria_priority)

    # Display the results
    results$weights  # Optimized weights
    #> [1] 2.012639e-04 3.303488e-05 1.319787e-02 2.872265e-01 2.708919e-01
    #> [6] 2.444394e-01 1.438934e-01 4.011656e-02
    results$Phi      # Comparative priority (Phi) values
    #> [1] 1 1 2 2 1 1 1
    results$w        # Mathematical transitivity condition (w)
    #> [1] 1 2 4 2 1 1
    results$DFC      # Minimum deviation from full consistency (DFC)
    #> [1] 5.093228

Interpret the Results

The output includes:

    Weights: Optimized weights for each criterion, where the sum equals 1.
    Phi Values: Comparative priority values between the criteria.
    Transitivity Condition (w): Ensures the consistency of the comparative priorities.
    DFC: The deviation from full consistency, which should be minimized.

Conclusion

This vignette demonstrated how to use the fucom package to apply the FUCOM method in multi-criteria decision-making. By optimizing the weights of criteria based on their priorities, the method ensures consistency in the decision-making process.

For more detailed information on the FUCOM method, you can refer to the original paper: https://doi.org/10.3390/sym10090393.