library(frbs)

## The four hill function
## Set seed of random numbers
set.seed(2)

## Create the four hill function
fun <- function(input.xy){
  z <- 1 / (input.xy[1]^4 + input.xy[2]^4
  -2 * input.xy[1]^2 - 2 * input.xy[2]^2 + 3)
}

## Generate data
input.xy <- expand.grid(seq(-2, 2, 0.14),
  seq(-2, 2, by = 0.14))
  
## Calculate the function  
z <- apply(input.xy, 1, fun)

## Create data in a data.frame that contains three columns ("X", "Y", and "Z")
data <- cbind(input.xy, z)
colnames(data)<- c("X", "Y", "Z")

## Randomize the data
data <- data[sample(nrow(data)), ]

## Split the data to training and testing data
cut.indx <- round(0.8 * nrow(data))
data.tra <- data[1 : cut.indx, ]
data.tst <- data[(cut.indx + 1) : nrow(data), 
  1 : 2]
  
## Save actual values for validation  
real.val <- data[(cut.indx + 1) : nrow(data), 
  3, drop = FALSE]
  
## Calculate range of data
#range.data <- apply(data, 2, range)
range.data <- matrix(c(-2, 2, -2, 2, min(data[, 3]), max(data[, 3])), nrow = 2)

## Set parameters
method.type <- "WM"
control <- list(num.labels = 5, 
  type.mf = "GAUSSIAN", type.defuz = "WAM", 
  type.tnorm = "MIN", type.snorm = "MAX", 
  type.implication.func = "LUKASIEWICZ",
  name = "fourhill") 

## Construct an FRBS model (called mod.reg)  
mod.reg <- frbs.learn(data.tra, range.data,
  method.type, control)

## We can also convert and display the frbsPMML format
fourHillpmml <- frbsPMML(mod.reg)
  
## Convert the model and save it to "modRegress.pmml"
write.frbsPMML(fourHillpmml, "modRegress")

## Import the frbsPMML format back to the FRBS model
objectReg <- read.frbsPMML("modRegress.frbsPMML")

## Predict new data (called data.tst)
res.test <- predict(objectReg, data.tst)

## Calculate the mean square error
err.MSE <- mean((real.val - res.test)^2)
print(err.MSE)