基于模糊的体系测定膝关节与骨关节炎的严重级(4)

Fuzzy-Based System for Determining the Severity Level of Knee Osteoarthritis

F. Centre of Area Defuzzification method

In centre of area (COA) defuzzification, the crisp value u is taken to be the geometrical centre of the output fuzzy value µOUT (u), where µOUT(u) is formed by taking the union of the contributions of all the rules whose degree of membership function is greater than zero. The centroid methods are based on finding the balance point of the whole geometric figure. The defuzzified output is defined as

N

u

1

i

OUT

ui

i N

(1)

i 1

OUT

ui

where the summation is carried out over discrete values of the universe of discourse, µi, sampled at N points.

Centre of Sums Defuzzification

In the centre of sum defuzzification method, the overlapping areas of multiple rules are taken into account more than once. The defuzzification output is defined as

Nn

u

i 1ui

k 1 k

ui

N

n

(2)

i 1 k 1

k

ui

where N represents the number of sample points and n represents the number of rules.

Mean of Maximum (MOM) Defuzzification

This is the another method to defuzzify the output by taking the crisp value with the highest degree of membership in µOUT, When there is more than one element with the maximum value in the universe of discourse, then the mean value of the maximum is taken or randomly select one of them. Suppose there is M such maxima in a discrete universe of discourse. The crisp output can be obtained as:

M

u mM

(3)

m 1Where um is the mth element in the universe of discourse in which the membership function

OUT

u

is at its maximum value, and M is the total number of such elements. The height of a fuzzy set A, i.e. h(A) is the largest membership grade obtained by any element in that set.

The defuzzification yields a crisp, non-fuzzy control action from an inferred fuzzy control action. In this research work, the centroid method is used as the defuzzification strategy.

V. FLC Design

During fuzzification, the fuzzy input variable, KneePain ranging from 1 to 10 is converted into four linguistic grades namely Grade1, Grade2, Grade3 and Grade4.

Similarly, the input variable Age ranging from 45 to 75 is converted into five linguistic variables namely: VeryYoung, Young, MiddleAge, Old and VeryOld. The other two fuzzy input variables; Stiffness and Crepitus and the output variable SeverityLevel ranging from 1 to 10 are converted into five linguistic levels namely: VeryMild, Mild, Moderate, Severe and VerySevere. The triangular membership function is used to perform the scale mapping

The behavior of the control surfaces is defined by the rules that join the fuzzy variables together. In this work, 500 rules were framed with the assistance of a Rheumatologist. All the rules are presented in the form of a rule base matrix, where the antecedents are the KneePain, Stiffness, Swelling and Crepitus and the consequent of the rules is SeverityLevel.

The non-fuzzy crisp output from the FLC is obtained by carrying out defuzzification using the centre of gravity method.

u

i

i

xi

i

i

(4)

where

i

Is a running point in a discrete universe function and u‘ is the crisp output value.xi

x

is its membership value in the membership

VI. Model Simulation

A total of 500 rules were generated for this research represented by 4 linguistically designed input with the kneepain‘ having four (4) membership function and the remaining three input variables: stiffness‘, crepitus‘ and age‘ are all having five membership function each. This number results from the membership function say (x) raise to the number of input-variable, since the variable kneepain‘ has four membership functions and the other three have five MFs each, then the total number of rules = 53 x 4 = 500. Rules generation in fuzzy system follows human reasoning pattern which make it more flexible in composition. It is just like a dialogue taking into cognizance the pros and cons on a circumstance. In the rule viewer provided by the Fuzzy inference System (FIS) in fig. 2, sliding the red line changes the input values and, and generate a new output response, also, the inputs can be set explicitly using the edit field.