Define generic for coefficients

Description

A generic function to retrieve coefficients from model objects.

Usage

coefficients(object, ...)

Arguments

Value

A data frame of coefficients and related statistics.

Examples

# Simulate data and fit a fuzzy linear model
set.seed(123)
X_crisp <- matrix(round(runif(300, 2, 10)), nrow = 100, ncol = 3)
beta <- c(1.5, -0.8, 2.0)
Y_crisp <- round(X_crisp %*% beta + rnorm(100, mean = 0, sd = 1))
X_fuzzy <- fuzzify_crisp_matrix(X_crisp, spread = 1)
Y_fuzzy <- fuzzify_crisp_vector(Y_crisp, spread = 1)
object <- fuzzy_lm(X_fuzzy, Y_fuzzy, p = 3)

# Extract coefficients
coefficients(object)

Accessor for Coefficients

Description

Accessor for Coefficients

Usage

## S3 method for class 'fuzzy_lm'
coefficients(object, ...)

Arguments

Value

A data frame of coefficients and statistics.

Examples

# Simulate data and fit a fuzzy linear model
set.seed(123)
X_crisp <- matrix(round(runif(300, 2, 10)), nrow = 100, ncol = 3)
beta <- c(1.5, -0.8, 2.0)
Y_crisp <- round(X_crisp %*% beta + rnorm(100, mean = 0, sd = 1))
X_fuzzy <- fuzzify_crisp_matrix(X_crisp, spread = 1)
Y_fuzzy <- fuzzify_crisp_vector(Y_crisp, spread = 1)
object <- fuzzy_lm(X_fuzzy, Y_fuzzy, p = 3)

# Extract coefficients
coefficients(object)

Compute confidence intervals for regression coefficients

Description

Compute confidence intervals for regression coefficients

Usage

compute_ci(beta_hat, se_beta, df, alpha = 0.05)

Arguments

Value

A list containing lower and upper bounds of confidence intervals.

Examples

beta_hat <- c(0.5, 1.2)  # Example regression coefficients
se_beta <- c(0.1, 0.2)  # Example standard errors
df <- 30  # Example degrees of freedom
ci <- compute_ci(beta_hat, se_beta, df)
print(ci)

Compute p-values for regression coefficients

Description

Compute p-values for regression coefficients

Usage

compute_p_values(t_values, df)

Arguments

Value

Numeric vector of p-values for each coefficient.

Examples

t_values <- c(2.5, 3.0)  # Example t-values
df <- 30  # Example degrees of freedom
p_values <- compute_p_values(t_values, df)
print(p_values)

Compute Predictions from Fuzzy Linear Model

Description

Compute Predictions from Fuzzy Linear Model

Usage

compute_pred(object, X_fuzzy)

Arguments

Value

A list of fuzzy predictions.

Examples

# Example setup
X_fuzzy <- list(
  list(list(l = 1, x = 2, r = 3), list(l = 4, x = 5, r = 6)),
  list(list(l = 2, x = 3, r = 4), list(l = 5, x = 6, r = 7))
)
beta_hat <- c(0.5, 1.2, -0.8)  # Example regression coefficients
object <- list(beta_hat = beta_hat)

# Compute predictions
predictions <- compute_pred(object, X_fuzzy)
print(head(predictions, 6))

Compute Residuals for Fuzzy Linear Model

Description

Compute Residuals for Fuzzy Linear Model

Usage

compute_res(Y_fuzzy, Y_pred)

Arguments

Value

A list of fuzzy residuals.

Examples

# Example setup
Y_fuzzy <- list(
  list(l = 2, x = 3, r = 4),
  list(l = 5, x = 6, r = 7)
)
Y_pred <- list(
  list(l = 1.5, x = 2.5, r = 3.5),
  list(l = 4.5, x = 5.5, r = 6.5)
)

# Compute residuals
residuals <- compute_res(Y_fuzzy, Y_pred)
print(head(residuals, 6))

Compute t-values for regression coefficients

Description

Compute t-values for regression coefficients

Usage

compute_t_values(beta_hat, Y_fuzzy, Y_pred, XtX_inv)

Arguments

Value

Numeric vector of t-values for the regression coefficients.

Examples

# Example setup
beta_hat <- c(0.5, 1.2)  # Example regression coefficients
Y_fuzzy <- list(
  list(l = 2.1, x = 2.3, r = 2.5),
  list(l = 3.1, x = 3.3, r = 3.5),
  list(l = 4.1, x = 4.3, r = 4.5)
)  # Example fuzzy response
Y_pred <- list(
  list(l = 2.0, x = 2.2, r = 2.4),
  list(l = 3.0, x = 3.2, r = 3.4),
  list(l = 4.0, x = 4.2, r = 4.4)
)  # Example predicted values
XtX_inv <- matrix(c(0.1, 0.2, 0.2, 0.4), ncol = 2)  # Example XtX_inv matrix
t_values <- compute_t_values(beta_hat, Y_fuzzy, Y_pred, XtX_inv)
print(t_values)

Fuzzify a matrix of crisp values

Description

Converts a numeric matrix into a list of triangular fuzzy numbers.

Usage

fuzzify_crisp_matrix(crisp_matrix, spread = 1)

Arguments

Value

A list of lists representing rows of triangular fuzzy numbers.

Examples

set.seed(123)
matrix <- matrix(runif(9, 5, 15), nrow = 3, ncol = 3)
fuzzify_crisp_matrix(matrix, spread = 1.5)

Fuzzify a single crisp value

Description

Converts a crisp value into a triangular fuzzy number with a specified spread.

Usage

fuzzify_crisp_value(crisp_value, spread = 1)

Arguments

Value

A list representing the triangular fuzzy number with components l, x, and r.

Examples

fuzzify_crisp_value(10, spread = 2)

Fuzzify a vector of crisp values

Description

Converts a numeric vector into a list of fuzzified values using a triangular fuzzy membership function.

Usage

fuzzify_crisp_vector(crisp_vector, spread = 1, var_name = "Outcome")

Arguments

Value

A list of fuzzified values, where each value is represented as a list with components l, x, and r.

Examples

crisp_vector <- c(10, 20, 30)
fuzzify_crisp_vector(crisp_vector, spread = 1, var_name = "Variable")

Add two triangular fuzzy numbers

Description

Performs the addition of two triangular fuzzy numbers.

Usage

fuzzy_add(X, Y)

Arguments

Value

A list representing the sum of the two fuzzy numbers.

Examples

X <- list(l = 1, x = 2, r = 3)
Y <- list(l = 2, x = 3, r = 4)
fuzzy_add(X, Y)

Multiply a crisp scalar by a triangular fuzzy number

Description

Scales a triangular fuzzy number by a crisp scalar.

Usage

fuzzy_crisp_mult(scalar, fuzzy_num)

Arguments

Value

A list representing the scaled fuzzy number.

Examples

scalar <- 3
fuzzy_num <- list(l = 1, x = 2, r = 3)
fuzzy_crisp_mult(scalar, fuzzy_num)

Compute the squared distance between two fuzzy numbers

Description

Calculates the squared distance between two triangular fuzzy numbers using Diamond's metric.

Usage

fuzzy_d_squared(X, Y)

Arguments

Value

Numeric. The squared distance between X and Y.

Examples

X <- list(l = 1, x = 2, r = 3)
Y <- list(l = 2, x = 3, r = 4)
fuzzy_d_squared(X, Y)

Fuzzy Linear Regression

Description

Fits a fuzzy linear regression model given fuzzified predictors and response variables.

Usage

fuzzy_lm(X_fuzzy, Y_fuzzy, p, X_crisp = NULL)

Arguments

Value

A list object of class fuzzy_lm containing:

Examples

# Simulate complex data for fuzzy linear regression
set.seed(123)

# Generate a dataset with 100 observations and 4 predictors
n <- 100
X_crisp <- data.frame(
  Age = round(runif(n, 20, 70)),            # Random ages between 20 and 70
  Income = round(runif(n, 20000, 120000)),  # Random incomes between 20k and 120k
  Education = round(runif(n, 10, 20)),      # Random years of education between 10 and 20
  Experience = round(runif(n, 1, 40))       # Random years of work experience between 1 and 40
)

# Define true coefficients
beta <- c(5.0, 1.2, -0.5, 0.8, 0.05)  # Intercept and coefficients for the predictors

# Generate the crisp response variable with noise
Y_crisp <- round(beta[1] + as.matrix(X_crisp) %*% beta[-1] + rnorm(n, mean = 0, sd = 50))

# Fuzzify the predictor and response variables
X_fuzzy <- fuzzify_crisp_matrix(as.matrix(X_crisp), spread = 10)  # Larger spread for predictors
Y_fuzzy <- fuzzify_crisp_vector(Y_crisp, spread = 20)             # Larger spread for responses

# Fit the fuzzy linear model
object <- fuzzy_lm(X_fuzzy, Y_fuzzy, p = 4, X_crisp = X_crisp)

# Print the coefficients
print("Fuzzy Linear Model Coefficients:")
print(object$Coefficients)

# Example residuals and predictions
print("Example Residuals:")
print(head(object$Residuals, 6))

print("Example Predictions:")
print(head(object$Predictions, 6))

Multiply two triangular fuzzy numbers

Description

Computes the scalar product of two triangular fuzzy numbers.

Usage

fuzzy_mults(X, Y)

Arguments

Value

A scalar representing the sum of the product of the corresponding components.

Examples

X <- list(l = 1, x = 2, r = 3)
Y <- list(l = 2, x = 3, r = 4)
fuzzy_mults(X, Y)

Generic Plot Function

Description

This is a generic plot function that dispatches to specific plot methods based on the class of the object provided. It is used to create plots for objects such as fuzzy_lm.

Usage

plot(object, ...)

Arguments

Value

Depends on the class of object. Typically, a plot or visualization is returned.

Examples

# Example with fuzzy_lm:
set.seed(123)
x_crisp <- seq(4, 12, length.out = 20)
beta <- 1.5
intercept <- 2
y_crisp <- intercept + beta * x_crisp + rnorm(length(x_crisp), mean = 0, sd = 0.5)

# Fuzzify data
spread_x <- 0.5
spread_y <- 1.0
X_fuzzy <- fuzzify_crisp_matrix(matrix(x_crisp, ncol = 1), spread = spread_x)
Y_fuzzy <- fuzzify_crisp_vector(y_crisp, spread = spread_y)

# Fit fuzzy regression model
object <- fuzzy_lm(X_fuzzy, Y_fuzzy, p = 1)

# Plot

plot(object, X_fuzzy = X_fuzzy, Y_fuzzy = Y_fuzzy)

Plot Fuzzy Regression Results

Description

Visualizes the results of a fuzzy regression model. For simple regression (1 predictor), it generates a 2D plot with fuzzy intervals and regression lines. For multiple regression (2 predictors), it generates a 3D plot with cubes representing fuzzy intervals and a regression plane.

Usage

## S3 method for class 'fuzzy_lm'
plot(object, ...)

Arguments

Value

A ggplot2 object for simple regression or a plotly object for multiple regression.

Examples

# Example 1: Simple Regression
# See above for setup example

# Example 2: Multiple Regression
set.seed(123)
n <- 100
x1_crisp <- runif(n, 5, 15)
x2_crisp <- runif(n, 10, 20)
beta <- c(3, 1.5, -0.8)
y_crisp <- beta[1] + beta[2] * x1_crisp + beta[3] * x2_crisp + rnorm(n, mean = 0, sd = 2)

X_fuzzy <- fuzzify_crisp_matrix(cbind(x1_crisp, x2_crisp), spread = 0.5)
Y_fuzzy <- fuzzify_crisp_vector(y_crisp, spread = 1.0)
object <- fuzzy_lm(X_fuzzy, Y_fuzzy, p = 2)

plot(object, X_fuzzy = X_fuzzy, Y_fuzzy = Y_fuzzy)

Define generic for predictions

Description

Define generic for predictions

Usage

predictions(object, ...)

Arguments

Value

A list of fuzzy predictions.

Examples

# Simulate data and fit a fuzzy linear model
set.seed(123)
X_crisp <- matrix(round(runif(300, 2, 10)), nrow = 100, ncol = 3)
beta <- c(1.5, -0.8, 2.0)
Y_crisp <- round(X_crisp %*% beta + rnorm(100, mean = 0, sd = 1))
X_fuzzy <- fuzzify_crisp_matrix(X_crisp, spread = 1)
Y_fuzzy <- fuzzify_crisp_vector(Y_crisp, spread = 1)
object <- fuzzy_lm(X_fuzzy, Y_fuzzy, p = 3)

# Extract predictions
head(predictions(object))

Accessor for Predictions

Description

Accessor for Predictions

Usage

## S3 method for class 'fuzzy_lm'
predictions(object, ...)

Arguments

Value

A list of fuzzy predictions.

Examples

# Simulate data and fit a fuzzy linear model
set.seed(123)
X_crisp <- matrix(round(runif(300, 2, 10)), nrow = 100, ncol = 3)
beta <- c(1.5, -0.8, 2.0)
Y_crisp <- round(X_crisp %*% beta + rnorm(100, mean = 0, sd = 1))
X_fuzzy <- fuzzify_crisp_matrix(X_crisp, spread = 1)
Y_fuzzy <- fuzzify_crisp_vector(Y_crisp, spread = 1)
object <- fuzzy_lm(X_fuzzy, Y_fuzzy, p = 3)

# Extract predictions
head(predictions(object))

Define generic for residuals

Description

A generic function to retrieve residuals from model objects.

Usage

residuals(object, ...)

Arguments

Value

A list of fuzzy residuals.

Examples

# Simulate data and fit a fuzzy linear model
set.seed(123)
X_crisp <- matrix(round(runif(300, 2, 10)), nrow = 100, ncol = 3)
beta <- c(1.5, -0.8, 2.0)
Y_crisp <- round(X_crisp %*% beta + rnorm(100, mean = 0, sd = 1))
X_fuzzy <- fuzzify_crisp_matrix(X_crisp, spread = 1)
Y_fuzzy <- fuzzify_crisp_vector(Y_crisp, spread = 1)
object <- fuzzy_lm(X_fuzzy, Y_fuzzy, p = 3)

# Extract residuals
head(residuals(object))

Accessor for Residuals

Description

Accessor for Residuals

Usage

## S3 method for class 'fuzzy_lm'
residuals(object, ...)

Arguments

Value

A list of fuzzy residuals.

Examples

# Simulate data and fit a fuzzy linear model
set.seed(123)
X_crisp <- matrix(round(runif(300, 2, 10)), nrow = 100, ncol = 3)
beta <- c(1.5, -0.8, 2.0)
Y_crisp <- round(X_crisp %*% beta + rnorm(100, mean = 0, sd = 1))
X_fuzzy <- fuzzify_crisp_matrix(X_crisp, spread = 1)
Y_fuzzy <- fuzzify_crisp_vector(Y_crisp, spread = 1)
object <- fuzzy_lm(X_fuzzy, Y_fuzzy, p = 3)

# Extract residuals
head(residuals(object))

Summary for Fuzzy Linear Regression

Description

Summary for Fuzzy Linear Regression

Usage

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

Arguments

Value

Prints a summary of the fuzzy linear regression results.

Examples

# Simulate data and fit a fuzzy linear model
set.seed(123)
X_crisp <- matrix(round(runif(300, 2, 10)), nrow = 100, ncol = 3)
beta <- c(1.5, -0.8, 2.0)
Y_crisp <- round(X_crisp %*% beta + rnorm(100, mean = 0, sd = 1))
X_fuzzy <- fuzzify_crisp_matrix(X_crisp, spread = 1)
Y_fuzzy <- fuzzify_crisp_vector(Y_crisp, spread = 1)
object <- fuzzy_lm(X_fuzzy, Y_fuzzy, p = 3)

# Summarize the model
summary(object)