Fuzzy Systems Toolbox, Fuzzy Logic Toolbox [Software Review]

MATLAB@ (derived from m i x moratory) is a technical computing environment whose basic data element is a self-dimensioning matrix. It combines fast numerical capabilities with excellent graphics using a command syntax that is quite intuitive. MATLAB@ is useful for developing and modifying algorithms, particularly those which are heavy in matrix operations. Many of the MATLAB@ commands are based on execution of function programs contained in " M-files, " which contain source code. This yields a highly open and extensible environment whereby the user can redefine certain existing commands or create new ones by suitably editing the M-files. MATLAB@ is a product of The Mathworks, Inc., and numerous sets of application specific routines, called " toolboxes, " have been developed and marketed by that company for use with MATLAB@. Here, we review the two commercially available MATLAB@ taol-boxes for creating and using fuzzy inference systems. They are the " Fuzzy Systems Toolbox, " by PWS Publishing Company, and " Fuzzy Logic Toolbox, " by The Mathworks, Inc. We examined both the Macintosh and UNIX versions of the two toolboxes, but all the computational experiments described in the following were done using the UNIX version, which was executed on a shared SUN Sparc 20 computer with graphics, transmitted across a reasonably heavily used local ethernet network. This toolbox provides a command line approach to building fuzzy sets and fuzzy rule-based systems. A continuous fuzzy set can be represented in either of two ways using FST. The more general option is to specify n support and membership grades for the fuzzy set using a pair of 1 x n arrays. Piecewise linear interpolation between successive (support, grade) points gives the complete membership function. For example, the support array s = [I 2 3 41 and grade array g = [0 .2 .6 01 describe a fuzzy set that assigns the grade of 0.4 to the support value 2.5. The less general, but more convenient, option of specifying a fuzzy set is through the use of parameters. The six parametric families available allow users to specify singleton or interval crisp sets and fuzzy sets with membership functions in the shape of triangles, trapezoids, " bumps, " and " flat bumps. " Fuzzy sets corresponding to numbers " near " a given number, or " large " relative to a given support, are easily obtmned. It is possible to plot the antecedent fuzzy sets …