I need to classify objects using fuzzy logic. Each object is characterized by four functions - {size, shape, color, texture}. Each function is smoothed out by linguistic terms and some membership function. The problem is that I cannot figure out how to defuzzify so that I can know which class the unknown object belongs to. Using the conclusion of Mamdani Max-Min, can anyone help in solving this problem?
Objects = {Dustbin, Can, Bottle, Cup} or are designated as {1,2,3,4} respectively. Fuzzy sets for each function:
Function: Size
$\tilde{Size_{Large}}$ = {1//1,1/2,0/3,0.6/4} for crisp values in range 10cm - 20 cm
$\tilde{Size_{Small}}$ = {0/1,0/2,1/3,0.4/4} (4cm - 10cm)
The form:
$\tilde{Shape_{Square}}$ = {0.9/1, 0/2,0/3,0/4} for crisp values in range 50-100
$\tilde{Shape_{Cylindrical}}$ = {0.1/1, 1/2,1/3,1/4} (10-40)
Function: Color
$\tilde{Color_{Reddish}}$ = {0/1, 0.8/2, 0.6/3,0.3/4} say red values in between 10-50 (not sure, assuming)
$\tilde{Color_{Greenish}}$ = {1/1, 0.2/2, 0.4/3, 0.7/4} say color values in 100-200
Function: Texture
$\tilde{Tex_{Coarse}}$ = {0.2/1, 0.2/2,0/3,0.5/4} if texture crisp values 10-20
$\tilde{Tex_{Shiny}}$ = {0.8/1, 0.8/2, 1/3, 0.5/4} 30-40
. If then other classification rules -
R1: IF the object is large in size and cylindrical in shape, and greenish in color and rough in texture. THEN Dustbin Object
,
Object type Size Shape Color Texture
Dustbin : Large cylindrical greenish coarse
Can : small cylindrical reddish shiny
Bottle: small cylindrical reddish shiny
Cup : small cylindrical greenish shiny
X = {12 , 52, 120, 11}. ? , ?