Computational Intelligence: Synergies of Fuzzy Logic, Neural Networks and Evolutionary Computing

Appendix B

MATLAB® Programs for Fuzzy Logic

B.1.1 Membership Functions

The Fuzzy Logic Toolbox provides a number of membership functions. The most widely used MFs are triangular, Gaussian, bell-shaped and trapezoidal. trimf(), trapmf(), gaussmf() and gbellmf() are built-in functions for triangular, trapezoidal, Gaussian and bell-shaped MFs. The general forms of use with parameters are described below:

y = trimf(x, [a b c])
y = trapmf(x, [a b c d ])
y = gaussmf(x, [a c]), 
y = gbellmf(x, [a b c])

Different parametric membership functions are discussed in Section 2.4 of Chapter 2. The triangular membership function trimf() depends on three parameters a, b and c. The parameters a, b and c locate the ‘feet’ of the triangle and the parameter c locates the peak. The trapezoidal function trapmf() depends on four scalar parameters a, b, c and d. The parameters a and d locate the ‘feet’ of the trapezoid and the parameters b and c locate the ‘shoulders’. The symmetric Gaussian membership function gaussmf() depends on two parameters a and c. The parameter c is the centre of the function and the width is determined by the parameter a of the Gaussian function. The generalized bell function gbellmf() depends on three parameters a, b and c. The parameter b is usually positive. The parameter c locates the centre and the parameter a determines the width of the membership function. Sample plots of these MFs are shown in Figure B.1.1.

Figure B.1.1 (a) Triangular MF = [3 6 8]; (b) Gaussian MF = ...