frbs (version 3.2-0)

# fuzzifier: Transforming from crisp set into linguistic terms

## Description

Fuzzification refers to the process of transforming a crisp set into linguistic terms.

## Usage

fuzzifier(data, num.varinput, num.labels.input, varinp.mf)

## Arguments

data

a matrix of data containing numerical elements.

num.varinput

number of input variables.

num.labels.input

the number of labels of the input variables.

varinp.mf

a matrix containing the parameters to form the membership functions. See the Detail section.

## Value

A matrix of the degree of each linguistic terms based on the shape of the membership functions

## Details

In this function, there are five shapes of membership functions implemented, namely TRIANGLE, TRAPEZOID, GAUSSIAN, SIGMOID, and BELL. They are represented by a matrix that the dimension is ($$5, n$$) where $$n$$ is a multiplication the number of linguistic terms/labels and the number of input variables. The rows of the matrix represent: The first row is the type of membership function, where 1 means TRIANGLE, 2 means TRAPEZOID in left side, 3 means TRAPEZOID in right side, 4 means TRAPEZOID in the middle, 5 means GAUSSIAN, 6 means SIGMOID, and 7 means BELL. And, the second up to fifth row indicate the corner points to construct the functions.

• TRIANGLE has three parameters ($$a, b, c$$), where $$b$$ is the center point of the TRIANGLE, and $$a$$ and $$c$$ are the left and right points, respectively.

• TRAPEZOID has four parameters ($$a, b, c, d$$).

• GAUSSIAN has two parameters ($$mean$$ and $$variance$$).

• SIGMOID has two parameters ($$\gamma$$ and $$c$$) for representing steepness of the function and distance from the origin, respectively.

• BELL has three parameters ($$a, b, c$$).

For example:

varinp.mf <- matrix(c(2,1,3,2,3,0,30,60,0,40,20,50,80,

30,80,40,70,100,60,100,0,0,100,0,100), nrow=5, byrow=TRUE)

defuzzifier, rulebase, and inference