Interval Type-2 Fuzzy Logic Systems

Queries about the software can be made to "qilian@sipi.usc.edu".

Copyright (c) 2000 by the University of Southern California. All rights reserved.

This software is experimental in nature and is provided on an "as is" basis only. The University 
SPECIFICALLY DISCLAIMS ALL WARRANTIES INCLUDING, WITHOUT LIMITATION, 
THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A 
PARTICULAR PURPOSE.

This software may be used for non-commercial purposes only, so long as this copyright notice is
reproduced with each such copy made.

The software in this folder focuses on the computations and designs of interval type-2 FLSs.

Each M-file is keyed into a  chapter of the book Uncertain Rule-Based Fuzzy Logic Systems: Introduction and 
New Directions, by Jerry M. Mendel, and published by Prentice-Hall, 2000. 


Description of M-files 

Here, we provide brief descriptions of the M-files that appear in this directory. For more help on any specific file, 
type "help (filename)" at MATLAB prompt.

I. Plotting

					plot2d1.m: Function to plot two-dimensional representation of the FOU of an interval type-2 fuzzy set. 
The area between the upper and lower member-ship functions is shaded uniformly to indicate that all the 
secondary grades are unity.


II. Operations

					interval_meet.m: Function to compute the meet (or product) of n interval type-1 sets, as described 
in Theorem 7-2.

					interval_sum.m: Function to compute an affine combination of n interval type-1 sets, as described 
in Theorem 7-4.

					interval_wtdavg.m: Function used to implement the iterative procedure de-scribed in Theorem 9-1 
to compute the maximum and minimum of a weighted average, where both the   and the   are interval sets.


III. Interval Singleton Mamdani Type-2 FLS

					sfls.m: Compute the output(s) of an interval singleton type-2 FLS when the antecedent membership 
functions are Gaussian primary membership functions with uncertain means.

					train_sfls.m: Tune the parameters of an interval singleton type-2 FLS when the antecedent membership 
functions are Gaussian primary membership func-tions with uncertain means, using some inputÐoutput training data.

					svd_qr_sfls.m: Rule-reduction of an interval singleton type-2 FLS when the antecedent membership 
functions are Gaussian primary membership functions with uncertain means, using some inputÐoutput training data.



IV. Interval Type-1 Non-Singleton Mamdani Type-2 FLS

					nsfls1.m: Compute the output(s) of an interval type-1 non-singleton type-2 FLS when the antecedent
membership functions are Gaussian primary mem-bership functions with uncertain means and the input sets 
are type-1 Gaussian.

					train_nsfls1.m: Tune the parameters of an interval type-1 non-singleton type-2 FLS when the antecedent 
membership functions are Gaussian primary membership functions with uncertain means and input sets are type-1 
Gaussian, using some inputÐoutput training data.

					svd_qr_nsfls1.m: Rule-reduction of an interval type-1 non-singleton type-2 FLS when the antecedent 
membership functions are Gaussian primary mem-bership functions with uncertain means and input sets are type-1 Gaussian, using some inputÐoutput training data.


V. Interval Type-2 Non-Singleton Mamdani Type-2 FLS

					nsfls2.m: Compute the output(s) of an interval type-2 non-singleton type-2 FLS when the antecedent 
membership functions are Gaussian primary membership functions with uncertain means and the input 
membership functions are Gaussian primary membership functions with uncertain standard deviations.

					train_nsfls2.m: Tune the parameters of an interval type-2 non-singleton type-2 FLS when the
antecedent membership functions are Gaussian primary membership functions with uncertain means and 
the input membership functions are Gaussian primary membership functions with uncertain standard deviations, 
using some inputÐoutput training data.

					svd_qr_nsfls2.m: Rule-reduction of an interval type-2 non-singleton type-2 FLS when the antecedent 
membership functions are Gaussian primary membership functions with uncertain means and the input membership functions are Gaussian primary membership functions with uncertain standard deviations, using some inputÐoutput 
training data.


VI. Interval Type-2 TSK FLS

					tsk_type2.m: Compute the output(s) of an interval type-2 TSK FLS A2-C1 (type-2 antecedents and 
type-1 consequent) when the antecedent membership functions are Gaussian primary membership functions
with uncertain means.

					train_tsk_type2.m: Tune the parameters of an interval type-2 TSK FLS A2-C1 when the antecedent 
membership functions are Gaussian primary membership functions with uncertain means, using some 
inputÐoutput training data.


VII. Miscellaneous

		adapt.m: Function used to implement the iterative procedure described in Theorem 9-1 to compute the 
maximum and minimum of a weighted average, where the "y_i" s are crisp numbers and the "w_i"s are 
interval sets that take values from some real interval "[w_lower,w_upper]". 

					gausstype2.m: Computes upper and lower membership functions for a Gaussian primary membership 
functions with uncertain means.

					leftpoint.m: Computes c1 the left point of the consequent fuzzy set.

					rightpoint.m: Computes r1 the right point of the consequent fuzzy set.

					







