funclist.m

FISMAT accommodates different arithmetic operators, fuzzification and defuzzification algorithm, imp

% FSTB : Fuzzy Systems Toolbox for MATLAB.
%
% File : funclist.m - List of functions available.

% NOTE: This is out-of-date.
% 
% see http://isabel.csc.umist.ac.uk/FUZZY/HTML/funclist.html
%
% for an updated version.

% Generating, modifying and visiualising sets :
% 
% - modlrset(L,R,par,resx) :
%     Creating a (discrete) fuzzy set in LR representation form. 
% - modsuset() :
%     Symetric unimodal trapecoids. Mouse supported. Only two points required.
% - modtrset() :
%     Trapecoidal sets. Mouse supported.
% - modgauss() :
%     Gaussian normal distributed fuzzy sets.
% - plot_set(set) :
%     Plotting a fuzzy set.
% - plot_num(n1,n2,n3)
%     Plotting three fuzzy numbers.
% - con2dis(set,Nel)
%     conversion between the compact trapezoid and discrete form of a set.
% - modi_set(set,mod) :
%     Modification of a fuzzy sets shape. (normalisation, dilation, concen.)
% - get_fit(xi,x,set)
%     picks a (fit-) value from a set.
% - set_fit(xi,fv,x,set)
%     sets a particular (fit-) value of the set.

% Logical operations on sets : (accepting both main forms for sets)
%
% - fuz_or(method,ua,ub) 
%     method: bounded sum, maximum, algebraic sum.
% - fuz_and(method,ua,ub)
%     method: minimum, bounded difference, algebraic product.
% - fuz_fand(gamma,ua,ub) :
%     Fuzzy-and from Werners min <-> algebr.mean.
% - fuz_for(gamma,ua,ub) :
%     General fuzzy-or from Werners(1984) max <-> average.
% - fuz_not(ua) :
%     complement of a set.

pause % Strike any key to continue...
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% Arithmetic with fuzzy numbers:

% - fuz_add(f1,f2) :
%     Addition of two fuzzy numbers.
% - fuz_sub(f1,f2) :
%     Subtraction of two fuzzy numbers.
% - fuz_div(f1,f2) :
%     Division of two fuzzy numbers.
% - fuz_exp(f1) :
%     Exponential function of a fuzzy number.
% - fuz_log(f1) :
%     natural logarithm of a fuzzy number.
% - fuz_over(f1,f2) :
% - fuz_inv(f1) :
%     Inversion of a fuzzy number.
% - fuz_sign(f1) :
%     Determine the sign of a fuzzy number.
% - fuz_sire(f1) :
%     Sign reversal of a fuzzy number.

pause % Strike any key to continue.
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% Operations only using the compact trapezoidal form:

% - show_op(op,par,op2,par2) :
%     Function to create 3D and contour plots of the following operations:
% - gamma_a(gamma,ua,ub) :
%     compensatory-and from Zimmermann,Zysno (1982).
% - gamma_b(gamma,ua,ub) :
%     Convexcombination from minimum- and maximum- operator.
% - gamma_ct(gamma,ua,ub) :
%     gamma operator from the magazine ct 3/91.
% - and the following t- and co-t (or s-) norms :

%  see for example Zimmermannn,H.-J.[1992]:
% 'Fuzzy Set Theory and its Applications', Kluwer Academic Publishers, 2.Ed.

% twdp  - drastic product.             swds - drastic sum.  
% t1bd  - bounded difference.          s1bs - bounded sum.
% t15ep - Einstein product.           s15es - Einstein sum.
% t2ap  - algebraic product.           s2as - algebraic sum.
% t25hp - Hamacher product.           s25hs - Hamacher sum.
% t3mi  - minimum.                     s3ma - maximum.

% Note: the last two letters are the abbreviation of the names.

% sumop  - summing up two sets.
% lukand - Lukasiewicz AND

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% For control are some special functions are provided:

% - fuzzsiyi(set,x)
%     fuzzification for the special set form from Siler/Ying.
% - fuzzifi(set,x)
%     fuzzification for sets/library of sets in compact trapecoidal form.
% - match(X,xi,setlib)
%     fuzzification for discrete sets.
% - ctr_surf(ctr,ts,bo,steps)
%     Control surface for a two dimensional controller.
% - ctr_func(ctr,ts,bo)
%     Input-Output function for a one dimensional fuzzy or neural controller.
% - fuzzy11(), fuzzy21(), fuzzy31()
%     Simulink files to implement a general fuzzy (or neural net) controller
%     with 1, 2, 3 inputs.
% - rtinf(rt,e,de,andop,orop)
%     Inference for a controller with two inputs defined in a rule-table.
% - defucogx()
%     Defuzzification with the centre of gravity method.

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% - accumulu(B,accop)
%     accumulation of all fuzzy results to one fuzzy conclusion using 
%   various operators.
% - aggregat(Ae,Ade,FAMbank,aggop)
%     aggregation of all facts in the premise to one result using various
%     operators.
% - inferenc(A,B,FAMbank,infop)
%     inference using various operators.
% - apsumcog(FAMbank,A,moments,areas)
%     optimised controller type with algebraic-product inference (correlation
%     product encoding), summing output fuzzy-sets and COG defuzzification.
% - apsumhei(FAMbank,A,moments,areas)
%     optimised controller type with algebraic-product inference (correlation
%     product encoding), summing output fuzzy-sets and Height-Method for 
%     defuzzification.
%   

% Methods to Neural Networks and Fuzzy Systems (Kosko 1992)
%
% - corminen()
%     correlation minimum encoding. 
% - corproen()
%     correlation product encoding. 
% - maxminco()
%     max-minimum composition.
% - maxproco()
%     max-product composition. 

% - ucl()
%     stochastic Unsupervised-Competive-Learning (UCL)
% - dcl()
%     stochastic unsupervised Differential-Competive-Learning (DCL)

% - psc()
%     Product-Space-Clustering (PSC) to generate FAM rules.

pause % Strike any key to continue.
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