demo/FRBS.Mamdani.Manual.R

In frbs: Fuzzy Rule-Based Systems for Classification and Regression Tasks

 ## This example shows how to use frbs without 
 ## learning process.
 ## Note: some variables might be shared for other examples.

 ## Define shape and parameters of membership functions of input variables.
 ## Please see fuzzifier function to contruct the matrix.
 # varinp.mf <- matrix(c(2, 0, 20, 40, NA, 4, 20, 40, 60, 80, 3, 60, 80, 100, NA,
                       # 2, 0, 35, 75, NA, 3, 35, 75, 100, NA,
                       # 2, 0, 20, 40, NA, 1, 20, 50, 80, NA, 3, 60, 80, 100, NA,
                       # 2, 0, 20, 40, NA, 4, 20, 40, 60, 80, 3, 60, 80, 100, NA),
                       # nrow = 5, byrow = FALSE)

 varinp.mf <- matrix(c(4, 0, 0, 20, 40, 4, 20, 40, 60, 80, 4, 60, 80, 100, 100,
                       4, 0, 0, 35, 75, 4, 35, 75, 100, 100,
                       4, 0, 0, 20, 40, 1, 20, 50, 80, NA, 4, 60, 80, 100, 100,
                       5, 25, 15, NA, NA, 5, 50, 15, NA, NA, 5, 75, 15, NA, NA),
                       nrow = 5, byrow = FALSE)

 ## Define number of fuzzy terms of input variables.
 ## Suppose, we have 3, 2, 3, and 3 numbers of fuzzy terms 
 ## for first, second, third and fourth variables, respectively.
 num.fvalinput <- matrix(c(3, 2, 3, 3), nrow=1)
 
 ## Give the names of the fuzzy terms of each input variable.
 ## It should be noted that the names of the fuzzy terms must be unique,
 ## so we put a number for making it unique.
 varinput.1 <- c("a1", "a2", "a3")
 varinput.2 <- c("b1", "b2")
 varinput.3 <- c("c1", "c2", "c3")
 varinput.4 <- c("d1", "d2", "d3")
 names.varinput <- c(varinput.1, varinput.2, varinput.3, varinput.4)

 ## Set interval of data.
 range.data <- matrix(c(0,100, 0, 100, 0, 100, 0, 100, 0, 100), nrow=2)

 ## Set weighted average method to be used as defuzzification method.
 type.defuz <- "WAM"
 ## We are using standard t-norm and s-norm.
 type.tnorm <- "MIN"
 type.snorm <- "MAX"
 type.implication.func <- "ZADEH"

 ## Give the name of simulation.
 name <- "Sim-0"

 ## Provide new data for testing. 
 newdata<- matrix(c(25, 40, 35, 15, 45, 75, 78, 70), nrow= 2, byrow = TRUE)
 ## the names of variables
 colnames.var <- c("input1", "input2", "input3", "input4", "output1")

 ###################################################################
 ## 1. The following codes show how to generate a fuzzy model using the frbs.gen function
 ## 1a. Using Mamdani Model 
 ####################################################################
 ## Define number of fuzzy terms of output variable.
 ## In this case, we set the number of fuzzy terms to 3.
 num.fvaloutput <- matrix(c(3), nrow=1)

 ## Give the names of the fuzzy terms of the output variable.
 ## Note: the names of the fuzzy terms must be unique.
 varoutput.1 <- c("e1", "e2", "e3")
 names.varoutput <- c(varoutput.1)

 ## Define the shapes and parameters of the membership functions of the output variables.
 varout.mf <- matrix(c(4, 0, 0, 20, 40, 4, 20, 40, 60, 80, 4, 60, 80, 100, 100),
                       nrow = 5, byrow = FALSE)

 ## Set type of model which is 1 or 2 for Mamdani or Takagi Sugeno Kang model, respectively.
 ## In this case, we choose Mamdani model.
 type.model <- "MAMDANI"
 
 ## Define the fuzzy IF-THEN rules; 
 ## there are two kinds of model: Mamdani and Takagi Sugeno Kang model
 ## if we use the Mamdani model then the consequent part is a linguistic term,
 ## but if we use Takagi Sugeno Kang then we build a matrix representing 
 ## linear equations in the consequent part.
 ## In this example we are using the Mamdani model 
 ## (see the type.model parameter). 
 ## Note:
 ## "a1", "and", "b1, "->", "e1" means that "IF inputvar.1 is a1 and inputvar.2 is b1 THEN outputvar.1 is e1" 
 ## Make sure that each rule has a "->" sign. 
 rule <- matrix(c("very a1","and","b1","and","slightly c1","and","d1","->","e1",
                  "a2","and","b2","and","very c2","and","dont_care", "->", "e2", 
                  "extremely a3","and","b2","and","c2","and","d1", "->", "e3"), 
                  nrow=3, byrow=TRUE) 

 ## Generate a fuzzy model with frbs.gen.
 object <- frbs.gen(range.data, num.fvalinput, names.varinput, num.fvaloutput, varout.mf, 
					names.varoutput, rule, varinp.mf, type.model, type.defuz, type.tnorm, 
                  type.snorm, func.tsk = NULL, colnames.var, type.implication.func, name)
 
 ## We can plot the membership function
 plotMF(object)

 ## Predicting using new data.
 res <- predict(object, newdata)$predicted.val