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Questions related to Fuzzy Systems
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How can I obtain the membership functions associated to sign function in order to design a Takagi-Sugeno fuzzy model? Thank you.
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Sorry for the late response. You can read about the "Stone–Weierstrass Theorem". By applying the theorem, if the fuzzy system contains a sufficient number of rules, then it is possible to choose the parameters of the fuzzy system such that the defuzzification mapping will uniformly approximate a smooth function with arbitrary accuracy.
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How can i generate the rules matrix of a fuzzy system that has two outputs and the outputs are logically combined using the "and" operator. (In MATLAB envirement)?
p--->q and r
The fuzzy system has 3 rules like above. The membership functions are triangular, and the linguistic variables are "Low", "Medium" and "High".
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fis = mamfis;
fis = addInput(fis, [0 1], 'Name', 'p');
fis = addMF(fis, 'p', 'trimf', [-0.5 0.0 0.5], 'Name', 'L');
fis = addMF(fis, 'p', 'trimf', [ 0.0 0.5 1.0], 'Name', 'M');
fis = addMF(fis, 'p', 'trimf', [ 0.5 1.0 1.5], 'Name', 'H');
fis = addOutput(fis, [-1 0], 'Name', 'q');
fis = addMF(fis, 'q', 'trimf', [-1.5 -1.0 -0.5], 'Name', 'NB');
fis = addMF(fis, 'q', 'trimf', [-1.0 -0.5 0.0], 'Name', 'NM');
fis = addMF(fis, 'q', 'trimf', [-0.5 0.0 0.5], 'Name', 'NS');
fis = addOutput(fis, [0 1], 'Name', 'r');
fis = addMF(fis, 'r', 'trimf', [-0.5 0.0 0.5], 'Name', 'PS');
fis = addMF(fis, 'r', 'trimf', [ 0.0 0.5 1.0], 'Name', 'PM');
fis = addMF(fis, 'r', 'trimf', [ 0.5 1.0 1.5], 'Name', 'PB');
rules = [...
"p==L => q=NB, r=PS"; ...
"p==M => q=NM, r=PM"; ...
"p==H => q=NS, r=PB"; ...
];
fis = addRule(fis, rules);
figure
subplot(211)
opt1 = gensurfOptions('OutputIndex', 1, 'NumGridPoints', 21);
gensurf(fis, opt1), grid on
subplot(212)
opt2 = gensurfOptions('OutputIndex', 2, 'NumGridPoints', 21);
gensurf(fis, opt2), grid on
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Evaluation metrics in fuzzy systems.
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Any type of error metrics such as MSE, IAE, ISE, ITAE, MAE etc
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In his name is the judge
Hi
I have to use tsk fuzzy system in python for my research.
Please recommend me a library for tsk ( not mamdani ) fuzzy system in python.
Also if this library exist please Introduce me a source for learning it in python.
wish you best
Take refuge in the right.
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thank you dear Kishore Bingi
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In his name is the judge
Hi
In order to design controler for my damper ( wich is tlcgd), i want to use fuzzy system.
So i have to optimize rules for fuzzy controler. i want to know for optimizition rules of fuzzy systems wich one is the best genetiz algorithm or Artificial neural network?
Wish you best
Take refuge in the right.
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I strongly recommend the usage of a floating fuzzy control algorithm since it allows you to change the range of your membership function in real-time so you can adapt your controller at each time step.
Regards.
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I have just designed a fuzzy system, and now I want to redesign it based on the fractional order. However, I have no idea where to start from and what to do. Could you please tell me what I should do and mention any related sources to study?
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Dear s.Milad:
You can benefit from this valuable article about your topic:
"Fuzzy Fractional-Order PID Controller for Fractional Model of Pneumatic Pressure System".
Abstract:
This article presents a fuzzy fractional-order PID (FFOPID) controller scheme for a pneumatic pressure regulating system. The industrial pneumatic pressure systems are having strong dynamic and nonlinearity characteristics; further, these systems come across frequent load variations and external disturbances. Hence, for the smooth and trouble-free operation of the industrial pressure system, an effective control mechanism could be adopted. The objective of this work is to design an intelligent fuzzy-based fractional-order PID control scheme to ensure a robust performance with respect to load variation and external disturbances. A novel model of a pilot pressure regulating system is developed to validate the effectiveness of the proposed control scheme. Simulation studies are carried out in a delayed nonlinear pressure regulating system under different operating conditions using fractional-order PID (FOPID) controller with fuzzy online gain tuning mechanism. The results demonstrate the usefulness of the proposed strategy and confirm the performance improvement for the pneumatic pressure system. To highlight the advantages of the proposed scheme a comparative study with conventional PID and FOPID control schemes is made.
I hope it will be helpful...
Best wishes....
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Are there sources explain how ANFIS code can be generated to optimize it by Particle Swarm Optimization (PSO)?
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I am interested to use SAFIS and DENFIS model for my machine learning project. Can anyone help me with the coding or suggest any methods using MATLAB or Python?
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This is good question
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We know that, a particular variable may have some inherent sub-domains out of which few of them may be intersecting or non intersecting. If such variable exists in a nonlinear objective function then it is hardly possible to optimize this function. Thus we need to create a unified domain by utilizing such subdomains. Then the function under study can be easily solved. However, we knew that fuzzy system can give an approximated solution of a function which is associated to the variables of impreciseness( non-random uncertainty). Thus using fuzzy system we may create almost nearly an unified domain.
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You may able to model your problem using disjunctive programming (https://en.wikipedia.org/wiki/Extended_Mathematical_Programming#Disjunctive_programming). AMPL/GAMS should support that.
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firstly my fuzzy system is based on 5 image features dental x-ray images, consisting of 120 preapical images. features are described as below:
1-Entropy, Edge-Value, and Intensity: [30:55]
2-Local Binary Patterns - LBP: [140:160]
3-Red-Green-Blue - RGB: [82:140]
4-Gradient Feature: [0.3:0.45]
5-Patch Level Feature: [0.01:0.33]
output range: [1:5]
based on the article:
I achieved the membership function parameters of my fuzzy system (the number of my parameters to optimize were 48).
then created a cost function to optimize the values in order to minimize the Errors. but it gained a poor accuracy (about 13%) and a great number of MAE and MSE (MAE=1.27 and MSE= 2.22).
Is there a better.
Do you know a better way to optimize my system?
my programming software: MATLAB2019
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what's your opinion about Fuzzy logic future?
do you think Fuzzy logic would be develop like machine learning in nowadays ?
and let's start a discussion about Advanced Application of fuzzy logic and fuzzy systems...
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As long as we want to model all relative concepts (Velocity, heat, age, evaluation, small, high, success, light, clean etc ..) mathematically and according to expert opinion, and Fuzzy will remain popular. In a world where control of a system (Air conditioning, temperature, velocity, intersection etc ..) is not required, there will be no Fuzzy. So fuzzy will always be. I have at least 10 articles from different areas where I use Fuzzy logic.
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Besides the Schneider Electric PLCs that are programmed with EcoStruxure Control Expert or Unity Pro, Do you know of any other PLC(s) that include fuzzy control functions?
It would be interesting to know which manufacturers have been following the IEC 61131-7 standard, to know the state of the art of the application of fuzzy systems in industrial processes.
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Mathematically, it seems neutrosophic logic is more generalized than intuitionistic fuzzy logic. But, when it comes to real life scenarios, I couldn't find any advantage of neutrosophic logic over Intuitionistic fuzzy logic.
Even in some cases, intuitionistic  fuzzy logic is seems more logical than neutrosophic logic. Just like the following situations in neutrosophic...
(T, F, I) : (1,0,1), (1,1,0), (1,1,1), (0,0,0), (0,1,1)
seems to be not possible in real life scenario.
Whereas, There is no chance of getting such scenarios in case of Intuitionistic fuzzy logic.
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Neutrosophic theory is more flexible and useful as compared to all fuzzy-like and intui fuzzy-like theories. Respected Prof. Dr. Florentin Smarandache has provided a vivid details to prove it with strong arguments in his above qouted papers. No doubt, Excellent work done by him
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In the study of Duality theory, Nonlinear programming problem, Dual space etc,( particularly on fuzzy system also) we generally see a duality gap appears and this gap varies differently according to the selection of feasible region. So, it is trouble some to get best approximation of the solution of the problem. However, in linear programming problem no duality gap exists .
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My problem was a part of fuzzy system. I think you never heard about fuzzy system/ rough system and hence you do not have primary knowledge about fuzzy sets. So you need to read Zadeh (1965)' fuzzy sets. I gave a research link in support of my answer.
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In fuzzy system, we generally try to measure the qualitative difference of a certain object/ subject. In Physics/ Chemistry discipline there are specific formula to answer the question. But, my point is to get an alternative formula to do the same job via fuzzy system in Applied Mathematics discipline/ soft computing discipline. To tackle with such question the following subtopic may be considered.
Fuzzy logic and Fuzzy set, Degree of fuzziness, Learning experiences, Human perception, Time series analysis
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In fact , I am looking a concise formula to get the age of a rock etc.. My recent work might help others to develop the idea. Please see the following link.
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I am working on Power system modles in MATLAB with some adaptive controllers. The simulation run for different time duration like 8,10, and 15 sec. Now i need to get the computational time taken by the computer to solve the iteration behind theses simulations. I found tic and toc command but need more detailed explanation to use it. Thanks
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% For Simulink model
tic, sim('Simmulink_model_Name'), toc
% It is strongly recommended that you run the model at least min once before
% this test because it compiled before start.
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I need the program that it contains the triangular functionplease....
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I have prepared one two DOF semi active fuzzy control system with Bouc-Wen model. But Fuzzy system is not working its very slow.
What mistake I am doing or what is wrong with my model.
The model, fis file, and two reference paper are attached with this. What's wrong with the model not clear.
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You shoul review if the dinamical systems is so fast for the answer of your controller
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I am working on the Delayed Singular T-S fuzzy systems. I have a question, how to select the matrix "E" for the simulation. Mean its compulsory its values is non-unity or we can put the value unity?
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Dear Muhammad Shamrooz Aslam,
Initially those values are unity, during the simulation we can modify them, however we must take into account certain eligibility requirements.
For more details and information about this subject, i suggest you to see links and attached file on topic.
-Fuzzy filtering for nonlinear singular systems with time-varying delay
-Delay-dependent robust H∞ filter for TS fuzzy time-delay systems with ...
-Robust Adaptive Sliding Mode Observer Design for T-S Fuzzy ...
-Robust Fault Estimation for a Class of T-S Fuzzy Singular Systems ...
Best regards
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Dear all,
I am trying to design an FRBS using Matlab fuzzy logic toolbox. The fuzzy system will be used to predict player's type based on inputs (gameplay data) and a set of rules defined by experts.
I have 6 inputs and 4 outputs (types of players). The given rules do not concern all inputs (specific inputs are used for each player type).
Is it imperative to include all inputs and outputs in a rule? Also is there a min/max of rules that an FRBS should include?
Thank you for your help.
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As far as I know, it is not necessary to have all the inputs and outputs in a rule. For example, in your system a rule can have only 2 inputs which are along with at least one output. This can be applied in the Matlab fuzzy logic toolbox as well.
Hope it could help you.
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Hi
i'm having a hard time working with Fuzzy toolbox in matlab, i have made a fis, i have added my desired membership functions for input and outputs. Now i want to generate fuzzy rules based on my Data set for input/output. I have 1000 input data and their 1000 output data. what should i do?
this is my code
%% Fuzzy Inference System Definition
MyFuzzySystem=newfis('Amin');
MyFuzzySystem=addvar(MyFuzzySystem,'input','theta',[-40 40]);
MyFuzzySystem=addvar(MyFuzzySystem,'output','x',[0 20]);
MyFuzzySystem=addvar(MyFuzzySystem,'output','y',[0 10]);
%% Adding MFs to the theta input
MyFuzzySystem=addmf(MyFuzzySystem,'input',1,'','trapmf',[-40 -40 -39.2 -38.4]); %A1
for i=2:99
MyFuzzySystem=addmf(MyFuzzySystem,'input',1,'','trimf',[0.8*i-40.8 0.8*i-40 0.8*i-39.2]); %%A2-A99
end
MyFuzzySystem=addmf(MyFuzzySystem,'input',1,'','trapmf',[38.4 39.2 40 40]); %A100
%mfedit(MyFuzzySystem)
%plotmf(MyFuzzySystem,'input',1);
%% Adding MFs to the x output
for i=1:101
MyFuzzySystem=addmf(MyFuzzySystem,'output',1,'','trimf',[0.2*(i-2) 0.2*(i-1) 0.2*(i)]); %%B1-B101
end
%% Adding MFs to the y output
for i=1:101
MyFuzzySystem=addmf(MyFuzzySystem,'output',2,'','trimf',[0.1*(i-2) 0.1*(i-1) 0.1*(i)]); %%C1-C101
end
%mfedit(MyFuzzySystem)
%% Generating Input-Output Data
%%% Generating theta
phi=rand(100,1)*2*pi;
omega=rand(100,1)*50;
theta=zeros(1,1000);
alpha=zeros(100,1000);
for i=1:100
for t=1:1:1000
alpha(i,t)=(((40/sqrt(2))*(sin(omega(i,1)*(t/100)+phi(i,1))+cos(omega(i,1)*(t/100)+phi(i,1)))));
end
end
for k=1:1000
sum_alpha=0;
for w=1:100
sum_alpha=sum_alpha+alpha(w,k);
end
theta(1,k)=sum_alpha/100;
end
subplot(2,2,1);
t=1:1000;
y=(40/11)*theta;
theta_degree=theta*(pi/180);
plot(t/100,y);
xlabel('t');
ylabel('theta(t)');
xlim=[0,10];
ylim=[-40,40];
%%% Calculating phi
b=10;
phi_out(1,1)=45;
for i=1:999
phi_out(1,i+1)=phi_out(1,i)-asin((2*sin(theta_degree(1,i)))/b);
end
subplot(2,2,2);
t=1:1000;
plot(t/100,phi_out);
xlabel('t');
ylabel('phi(t)');
%%% Calculating x(t), y(t)
x_out(1,1)=0;
y_out(1,1)=0;
for i=1:999
x_out(1,i+1)=x_out(1,i)+cos(phi_out(1,i)+theta_degree(1,i))+sin(theta_degree(1,i)).*sin(phi_out(1,i));
y_out(1,i+1)=y_out(1,i)+sin(phi_out(1,i)+theta_degree(1,i))-sin(theta_degree(1,i)).*cos(phi_out(1,i));
end
subplot(2,2,3);
plot(x_out,y_out)
xlabel('x');
ylabel('y');
InputOutputData=[theta' x_out' y_out'];
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Dear Professor,
This link may be useful for you
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How to optimize Model predictive controller using machine learning ? e.g. using Neural Network or fuzzy systems
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Dear Muhammad Asad,
I suggest you to see links and attached files in topic.
-Simplifying Model Predictive Control algorithms via Machine Learning ...
-Speeding up Model-Predictive-Control with Machine Learning
-Model Predictive Control implementation on neural networks using ...
-Fast Model Predictive Control Using Online Optimization
-Machine Learning for Identification and Optimal Control of ... - Deep Blue
Best regards
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Hi! I have a system that loosely looks like this-
$\dot{x}_{1}=f_{1}(x_{1},x_{2},x_{3},x_{4})$,
$\dot{x}_{2}=f_{2}(x_{1},x_{2},x_{3},x_{4})$,
$\dot{x}_{3}=x_{4}$,
$\dot{x}_{4}=f_{4}(x_{1},x_{2},x_{3},x_{4})+bu_{1}$,
$y=x_{3}$,
I am designing a direct fuzzy adaptive controller to control the state x3. I wish to know what should be inputs to the fuzzy system that will approximate the ideal controller? Is it going to be all the states i.e $x_{1},x_{2},x_{3},x_{4}$ or $e,\dot{e}$? And finally what kind of adaptive law will ensure that the error is driven to zero. In my real system, I have got 9 states, and the state that I am interested in controlling has a relative degree of two. So, Shall I take all the states as input to my adaptive fuzzy controller? If I choose that, then will it not be exhorbitantly computationally expensive- considering the fact that there are 3 MFs per input-- resulting in $3^{9}$ rules? Kindly provide your inputs. Thanks in advance.
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Question #1:
One possibility is due to poor approximation. Have you really compared the output of the approximated function with the output of the actual function? If the approximation error is large or deviating from zero, there could be various reasons.
Question #2:
Another possibility is that the performance of the baseline control (nonlinear state feedback) is poor, slow, or sluggish. Have you really compared the results of the adaptive control with the results of the baseline control with known functions f1 & f2?
Question #3:
Have you really checked if the residual is sufficiently compensated by robustifying term in the adaptive control? Please check the V' signal, where V' is the time derivative of Lyapunov function.
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Right from the fuzzy number  developed by Zadeh (1965), new series of uncertain number are developed by researchers like grey number (Deng 1989), rough number (Zhai et al. 2007), Type-2 fuzzy number (Mendel & John 2002),  neutrosophic numbers (Smarandache 2003), Z- number (Zadeh 2011), D-number (Deng 2012), shadowed fuzzy set (Pedrycz 1998). 
Recently, in the year 2015-2017, are there any methods developed.
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I will upload the file on researchgate shortly,
B.R.
Khaled
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To develop research about modeling the path of the planets by fuzzy systems and artificial neural networks, what methods can be useful?
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Read about 'Fuzzy motion control'.
Read the paper available at: http://mech-ing.com/journal/papers/6.pdf
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I need a mathematical equation of the form z= f(x, y) where x's domain is (0,1), y's domain is (0,4), and z must be [0 , 1]. Are there any methodology.
To be more accurate, x is the weight of a fuzzy system, y is the output of this fuzzy system, and z is the final weighted output of this fuzzy system, which will be entered in another process.
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@ Shaker,
0<x<1
0<y<4
0<z<1
Assume that
z=f(x,y)=ax+by, just a plane.
We need to find a and b such that
0<ax+by<1....(1)
0<x<1.....(2)
0<y<4.....(3)
a>0,b>0....(4)
The fourth condition guarantees monotonicity of f(x,y):
((∂f)/(∂x))=a>0,((∂f)/(∂y))=b>0,
Now, using (2) and (3):
0<ax<a
0<by<4b
then, by addition:
0<ax+by<a+4b
We choose a+4b=1
(((1-a)/4))>0,hence, 0<a<1,
Therefore, any
z=f(x,y)=ax+(((1-a)/4))y , 0<a<1.( family of planes),
satisfies your request.
Example: choose a=(1/3), z=f(x,y)=(1/3)x+(1/6)y,
defined over R={(x,y),0<x<1,0<y<4}.
satisfies all required conditions:
For:
(1) 0<x<1,then 0<(1/3)x<(1/3)
(2) 0<y<4,then 0<(1/6)y<(2/3)
by addition: 0<(1/3)x+(1/6)y<1,that is 0<z<1.
Also: If x<x₁ and y<y₁,then (1/3)x<(1/3)x₁ and (1/6)y<(1/6)y₁
implies (1/3)x+(1/6)y<(1/3)x₁+(1/6)y₁,hence f(x,y)<f(x₁,y₁).
P.S. Peter 's answer accepted for this new range.
Just consider a= (1/2).
You can choose other forms for f(x,y) and apply the four conditions to reach a new equation for f.
Best regards
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I have a fuzzy system with multiple vague parameters represented as fuzzy numbers. I have to simulate the system performance. I am thinking of randomly generating membership grades for these parameters (individually) and find the performance of the system. If I randomly pick a membership grade and find the alpha cut, can it be another fuzzy number ? If it can be treated as another fuzzy number, what will the membership function of it look like?
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Dear Srijith,
I suggest you to see links and attached files in subject.
-chapter - 3 - Shodhganga
- an alpha -cut operation in a transportation problem using ... - Wireilla
wireilla.com/papers/ijfls/V7N1/7117ijfls03.pdf -A Generalization of Trapezoidal Fuzzy Numbers Based on ... - MDPI
- Fuzzy Sets and Fuzzy Logic - Brian T. Luke, Ph.D.
- Fuzzy Logic
Best regards
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For instance with three variables and three membership function, 27 rules can produced, but the problem is when you have more than five variables all with three membership functions
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A problem requires more than 2000 rules which are difficult even to decide by the experts. So, can we simply use an Orthogonal Array?
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Try to correlate inputs to reduce number of input features which ultimately reduce fuzzy rules as well.
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- Could you please point me out to some successful Medical sciences applications using partial differential equations?
- Preferably, involving heat, reaction-diffusion, Poisson, or Wave equation.
- If possible in fuzzy environment.
Best regards
Sarmad.
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Dear Professor, In mathematical modelling for drug delivery we are using PDE.
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What is the Necessary and sufficient conditions for using the Fuzzy systems and when we cant use this theory?
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Dear Gandhi,
The advantages of Fuzzy is so clear for all. What I need is that when we cant use this method, its limitations and its weaknesses
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How to implement Interval typre2 Fuzzy system in Matlab Simulation.
How to add Matlab toolbox?
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How to implement interval type2 fuzzy system in Matlab Simulation?
Is there is any Type2 fuzzy system in Matlab?
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I am unsure what he wants exactly. The M-files needed for IT2FL simulation are provided by Prof. Jerry Mendel (link is given in his previous Question thread) and Dr. Dong-rui Wu.
But I think he is probably looking for some GUI toolboxes for creating IT2FIS like the "Interval Type-2 Fuzzy Logic Toolbox" that was proprietarily developed by Dr. Juan R. Castro, Prof. Oscar Castillo and Dr. Luis G. Martínez. The "IT2FL Toolbox" does not come with standard MATLAB installation. The following image is an excerpt from the article. 
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This type of algorithm (Takagi-Sugeno fuzzy)  is talent to deal with MIMO plants that possess lag time, big inertia and uncertainty and can be deemed as one of the most important components of intelligent buildings
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Dear Raad Z. Homod,
I suggest for you look at link, attach files and publication in topics.
-comparative study of fuzzy control, neural network control ... - CiteSeerX
-ANFIS: Adaptive Neuro-Fuzzy Inference System- A ... - Semantic Scholar
Best regards
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which defuzzification method is more suitable for triangular fuzzy numbers considering their shape, height, relative location and spread?
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Dear Khubaib;
I have not researched on this question directly, but I have an indirect answer with an application.
I have been developing a prediction or projection system.
Global Grid Prediction Systems
In some modules, I will have fuzzy models.
In this first publications, I already have triangle fuzzy members (same shape) and I have several defuzzification methods by Fuzzy Logic Toolbox on Scilab.
May be my system research can give an idea and give a clue to answer to your question.
Please find my paper and data files.
G2EDPS's First Module & Its First Extension Modules
Please look at core modules "defuzzifier, best core model defuzzifier selection".
It has 10 extension modules. The 1st core module works with "type 1 Mamdani like Fuzzy Inference System (FIS) with 7 triangle membership functions and 49 rules is designed for 2 input and 1 output variables for a 100 year forecasting period".
1st Module: GGED-SS-C-T1MFIS7TMF-2VPGATA-100YPP-2015
You can study all data files and get some idea for your question only on this system design case of my problem.
Have a nice day
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I must write Sugeno type fuzzy controller with .m script. How can I write without using fuzzy toolbox? Where can I find an example about it?
Thanks... 
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Hi Dr. Öztürk,
You can certainly find some examples related to Fuzzy Logic Systems in the links given below. However, we are unsure of the real reasons you want to build a Sugeno-type fuzzy controller with the m-script. If the output of the m-scripted fuzzy inference system (FIS) is the same as the output of the FIS built using the Fuzzy Logic Toolbox™ GUI tool, then we don't see any motivation for doing so. 
If you want to build a FIS using Custom Membership Functions, other than using the standard functions (triangular, trapezoidal, bell, gaussian, etc) in the toolbox, open the 4th link. 
Perhaps you should try building a simple Sugeno FIS with the Fuzzy Logic Toolbox™ first, unless you want to build an Adaptive Fuzzy Controller, or a Genetic Algorithm optimized Fuzzy Controller, where the shapes of the input membership functions, output singleton locations and the IF-THEN rules are time-varying.
Good luck!
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How large or How small the values of scale factors can be set to assure that the fuzzy logic control performance will not be affected?
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You may refer to the below paper for optimal tuning of scaling factors by doing correlation between inputs and outputs of the fuzzy controller.
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I have a project to develop the application of fuzzy logic / fuzzy set theory to pictures made by patients and in psychotherapy more generally such as recovery and diagnosis.
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Dear Ralph,
I suggest to you links and attached files in topics.
- Introduction to Information Systems, Third Canadian Edition
- Fundamentals of the Fuzzy Logic-Based Generalized Theory of Decisions
- Fuzzy Logic and Enriching Over the Category [0,1] | The n-Category ...
- Foundations of Fuzzy Logic and Soft Computing: 12th International ...
Best regards
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By providing dependent variable and independent variables in fuzzy, How get the solution using fuzzy logic ?
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I want to create a membership function for the probability distribution (generated from statistical data) of the remaining fatigue life. Can anybody guide me on how to do so? I have found few papers on internet but most of these seem to confuse me rather than helping me. It would be great if somebody could guide me in the aforementioned matter. Thanks.
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Thanks a lot Dr. Mauris.
Best Regards,
Arvind Keprate
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Dear researchers,
Please help me out to learn about the fuzzy system from the scratch.
Please guide me with the steps and resources to follow .
Thanking you,
With regards,
Bhaskar Ghosh
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Thank you very much madam for your valuable guidance.
Thanks a lot.
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I m working on use of fuzzy logic in water quality indezing...
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Please check this book: 
T.J. Ross, Fuzzy Logic with Engineering Applications, 3ed, John Wiley & Sons, 2010”
Also the following Q&A in RG:
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I would like to implement type 2 fuzzy controller system on FPGA . Which FPGA module is best to implement for real time Type 2 Fuzzy Logic System for Control System Applications?
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Virtex-7 or Stratix-10.
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I want to compare proposed measure of directed divergence with some existing measure,a research paper states that since it depict the minimization of degree of difference, directed divergence is better. Why? Refer attached file
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Sir
I have already referred all the papers. But I am not satisfied(/ unable to understand) by the reason of comparison "depict the minimization of the degree of difference"
Regards
Pratiksha
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If I am designing a fuzzy Logic system and one of the input variables is with two levels:
Low:  having the range ( 0-2)
High: having the range (3-5)
If I am designing two membership functions to represent the two levels of the variable using a trapezoidal type, are the bellow values correct to form the trapezoidal:
Low: [ 0 0 1 2 ]
High: [ 1 3 5 5 ]
If not, how can I consider the overlap area from the above mentioned ranges? 
Thanks,
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is the variable integer all or not it can be decimal this imprtant main
each trapezoidal MF. have 4-triples [a,b,c,d]
where a ;LB, b;Lower mode ;c upper mode and d;UB.
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I want to use fuzzy DEA and I haven't found any solver handled this kind of problem, that's why I have written my own program. How can I learn to easily write my DEA program to MATLAB or AMPL?
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Is ur problem solved..
I have a similar problem..help needed.
Thank you.
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Suppose the two traingular fuzzy numbers A=(a1,b1,c1) and B=(a2, b2, c2). The subtraction operator "(-)" can be implemented by the following formula: A(-)B=(a1-a2, b1-b2, c1-c2). There may occur some dilemmas if (b1-b2)>(c1-c2) or (a1-a2)>(b1-b2). So are there any improvements can be explored to deal with this matter? Or are there some specific distance concepts can be used to reflect the subtraction operation?
Thanks very much for your attention and advice. 
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hi Zhou,
first check if area you substracting smaller than substractor. from there you can decide is result positive or negative and continue with substraction in safe way A=(abs(a-a1), abs(b-b1),abs(c-c1))
hope i helped
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i am working on fault detection of a suspension system using fuzzy. problem is i have to convert my model (differential equations)  into space space form. but in which form i can convert it ? need any paper or stuff that can help me understand how i can do it all. i want to implement multiple fuzzy models for fault detection.
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dearest noman
hope tis info could help
arie
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The system is nonlinear described by a set of 8 ODEs (8 states). Two discontinuous functions (jump discontinuity) are present in the first state equation. Can any one suggest the method to design a TS fuzzy model for such system?
dx1/dt = -x1.x3 + k12.x2 + EGP(1 - x5) - F - Fr + u1
dx2/dt = x1.x3 - k12.x2 - x2.x4
dx3/dt = -ka1.x3 + kb1.x6
dx4/dt = -ka1.x4 + kb1.x6
dx5/dt = -ka1.x5 + kb1.x6
dx6/dt = -ke.x6 + ki.x7
dx7/dt = -ki.x7 + ki.x8
dx8/dt = -ki.x8 + u2
states: [x1 x2 x3 x4 x5 x6 x7 x8]
parameters: [k12 EGP ka1 ka2 ka3 kb1 kb2 kb3 ki ke]
dis-continuous functions: [1] Fr = 0.003(x1-9), when x1>=9
                                              Fr = 0, [otherwise]
                                         [2] F = 0.97 , when x1>=4.5
                                              F = 0.97.x1/4.5  [otherwise]
Q/ How to take the discontinuous functions as premise variables of fuzzy model? 
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Dear Anirudh,
One researcher who has worked in this field and has achieved convincing results of K. Mehran’s. Here files attached on this researcher and some other researcher.
Best regards
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How to get the values of parameters of pimf from dataset?
Like pimf(x, [a b c d]) or another pimf(x, C, lambda), C is centre and lambda>0 is the scaling factor. How can I calculate the value of lambda?
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In the pimf syntex "y = pimf(x,[a b c d])" y is the output, x is the input, and a, b, c, d values are taken from the process operating range, is nothing but the universe of discourse of fuzzy logic (x axis or input).  Say for example, need to design a temperature control for a water tank means, the operating range is 30-90 degree Celsius. This operating range ie universe of discourse can be split into three to seven equal or unequal intervals with different MF labels.
this x axis may have overlapping or not, based on your application you can select all these.example y = pimf(x,[30 36 39 42]), y = pimf(x,[38 46 50 67 ]), y = pimf(x,[55 67 73 90])
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I would be grateful if you could send me the download link of it, because I could not find it via internet while I really need it. There is interval type2 fuzzy toolbox but I could not find Generalized fuzzy toolbox.
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Dear Vitalii Pertsevyi
Thanks for your response
The first attachment does not support Generalized type2 fuzzy system. While the second attachment supports this fuzzy system, it does not have simulink block to have outputs for control aims. Do you know how to have outputs of this toolbox(difuzzificated output) in matlab?
I appreciate your time and response
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i want to create two types of chromosomes based on different criteria. The first type is based on job length,the CPU speed of the resources,and the RAM size of the resources. The second type is based on the job length and the bandwith of the resources.These criteria are the input parameters for the fuzzy system.
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Thanks Mr. Carvalho and Mr mlakic, Can iget one example (with structure)of first or second type of chromosome.
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I have Input and output data set and going for modelling. I am getting negative values of output from ANFIS model but in training as well as testing input there is no negative value. Tell me how to solve this problem.
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Hi Rohit Sharma,
You can use the normalize data module to transform a dataset so that the columns of the data set are on a common scale.
For example, the input dataset can contain columns with very different values, which can cause problems when you combine the values as features for modeling. By transforming the values so that they retain their distribution and their general reporting, but respecting a common scale, you can usually get better results when modeling.
You can apply standardization to a single or multiple columns in the same data set.
You can also record the steps of normalization that you set in this module as a transformation that can be applied to other datasets.
you can use Microsoft Azur to normalize the data, here is the link.
Good Luck
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I am new to Fuzzy logic. I created membership functions with some rules by using matlab Fuzzy Logic Toolbox. Now i want to train this mamdani fuzzy model Can any body help ? 
you can see Rule view. 
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consultez vous  ce document vous "Introduction à la logique floue en Utilisant MATLAB"
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Identification of societal problems which are related to fuzzy dynamical systems and suitable techniques for solving them. 
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Fuzzy logic can be used to effectively model and solve societal problems. One thing that has made fuzzy logic popular is its ability to tackle problems that are complex and their mathematical models are intractable and imprecise. In this case, societal challenges such as transportation planning in large cities, urban planning, socioeconomic challenges and spreading processes such as AIDS, HIV, diseases have been successful modelled and controlled via application of fuzzy logic. Some references such as these could be of help:
Fuzzy Applications in Industrial Engineering by Cengiz  Kahraman
Application of fuzzy logic in transport planning by A. Sarkha, G. Sahoo and G.C. Sahoo, IJSC Journal, 3(2):1-21
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I want to determine the fuzzy intervals in a medical fuzzy system but physicians who consult to me do not have any view about fuzzy decisions . They say me "according our medical references , anything is crisp and based on discrete values" . I disappointed from their helps and now want to determine this fuzzy MFs based on clinical guidelines and aome experiences in medicine. Is there a machine learning or wizard or default and simple and basic method to determine these parameters ?  I want a scientific approach if exists ?!
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A fuzzy membership function is a range to represent a condition which could be as simple as the fever is 'low', 'medium' or high or the pain is 'severe' , 'medium' etc...
You need to read several papers on the problem which you wish to address in order to check if you can get this range from the available literature. If not, you need to 
consult several medical Experts to identify and optimize this range and develop an Expert system. Fuzzy rules can be framed by consulting several Experts. This can be done in case when the information is linguistic and/or ambiguous.  You can determine the appropriate intervals in fuzzy membership functions based on the range you acquire and develop membership functions which represent this range/intervals. At an initial step you can use the 'fuzzy' tool in MATLAB and develop a Fuzzy Inference System. 
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In the event of borrowing the concept of fuzzy soft set into ontology so as to reason with the uncertain concepts of a domain, I discover fuzzy soft set is best used in making comparison among instances (objects) and then the optimal decision could be reached using the score values of those objects. But what happens when am only concern about the truthfulness of a particular object in the domain, must I also have to make comparison with other objects in that domain? Also how best can I handle the binary relationships that exist between the object of concern and other objects in the domain
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I have applied fuzzy soft sets for decision making in an imprecise environment and
have found it to be an effective technique.
Following paper elaborates on this approach:
Your Queries:
Q) Can fuzzy soft set be used without the comparison table?
A comparison table used in Fuzzy soft sets is required for element/parameter wise comparison of objects. Here by parameter, I mean the attributes which describe the
objects under comparison. The row-sum and column sum of objects is further used for ranking of the objects compared.  In most  of the decision making problems, after construction of comparison table the next step is computation of score followed by decision. So a comparison table is very much essential in decision making problems.  
Q) But what happens when am only concern about the truthfulness of a particular object in the domain, must I also have to make comparison with other objects in that domain?
By Truthfulness of a particular object in the domain do you mean you are only concerned with full/partial membership in the fuzzy sets? This can be achieved 
with regular fuzzy sets as well.
Q) Also how best can I handle the binary relationships that exist between the object of concern and other objects in the domain?
This can be done with a comparison table. 
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can any one provide me any material for understanding or code of Optimal Completion Strategy in Fuzzy k Nearest Neighbour
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Mohan Chandra Pradhan Sir and Oluwarotimi Williams Samuel Sir,
            Thank you for your suggestions, I will go through these papers. Can you provide me any material of Optimal Completion strategy used in FCM. How the distance is calculated between samples.
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Dear all,
I am working with an ANFIS (adaptive neuro-fuzzy) model (genfis1) using grid partitioning.  I would like to know the time complexity in terms of Big O of an ANFIS. I am also wondering how can we decide a complexity of a multi-layered perceptron (MLP) neural network?
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 the complexity is occurrence due to the big structure which used  such as the rule and membership function. so the time is to take much to get optimal model  
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As the title,How can I train some zero-order TSK fuzzy systems with the same antecedents and same input MFs? Obviously,these zero-order TSK fuzzsy systems have different consequent parameters.
I hold the idea that it is impossibile to obtain different zero-order TSK fuzzy systems  with the same antecedent and input MFs.
Are there some solutions?thank you!!!
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The Sugeno Fuzzy model (also known as the TSK fuzzy model) was proposed by Takagi, Sugeno, and Kang in an effort to develop a systematic approach to generating fuzzy rules from a given input-output dataset. A typical fuzzy rule in a Sugeno fuzzy model has the form:
where A and B are fuzzy sets in the antecedent, while z=f(x,y) is a crisp function in the consequent. Usually f(x, y) is a polynomial in the input variables x and y, but it can be any function as long as it can appropriately describe the output of the model within the fuzzy region specified by the antecedent of the rule. When f(x, y) is a first-order polynomial, the resulting fuzzy inference system is called a first-order Sugeno fuzzy model, which was originally proposed in [1, 2]. When f is a constant, we then have a zero-order Sugeno fuzzy model, which can be viewed either as a special case of the Mamdani Fuzzy inference system, in which each rule’s consequent is specified by a fuzzy singleton (or a pre-defuzzified consequent), or a special case of the Tsukamoto fuzzy model, in which each rule’s consequent is specified by an MF of a step function centre at the constant. Moreover, a zero-order Sugeno fuzzy model is functionally equivalent to a radial basis function network under certain minor constraints, as discussed in Chapter 12 in “Neuro-fuzzy and soft computing”.
The output of a zero-order Sugeno model is a smooth function of its input variables as long as the neighbouring MFs in the antecedent have enough overlap. In other words, the overlap of MFs in the consequent of a Mamdani model does not have a decisive effect on the smoothness; it is the overlap of the antecedent MFs that determines the smoothness of the resulting input-output behaviour.
Figure 1: 1st order Sugeno Fuzzy Model
Figure 1 shows the fuzzy reasoning procedure for a first-order Sugeno fuzzy model. Since each rule has a crisp output, the overall output is obtained via weighted average, thus avoiding the time-consuming process of defuzzification required in a Mamdani model. In practice, the weighted average operator is sometimes replaced with the weighted sum operator (that is, z=w1z1 + w2z2 in Figure 1) to reduce computation further, especially in the training of a fuzzy inference system. However, this simplification could lead to the loss of MF linguistic meanings unless the sum of firing strengths (that is, ∑iwi ) is close to unity. Since the only fuzzy part of a Sugeno model is in its antecedent, it is easy to demonstrate the distinction between a set of fuzzy rules and nonfuzzy ones.
Example 1: Fuzzy and nonfuzzy rule set – a comparison
An example of a single-input Sugeno fuzzy model can be expressed as:
If “small”, “medium”, and “large” are nonfuzzy sets with membership functions shown in Figure 2(a), then the overall input-output curve is piecewise linear, as shown in Figure 2(b). On the other hand, if we have smooth membership functions instead, the overall input-output curve become a smoother one, as shown in Figure 2(d).
Figure 2: Comparison between fuzzy and nonfuzzy rules: (a) Antecedent MFs and (b) input-output curve for nonfuzzy rules; (c) Antecedent MFs and (d) input-output curve for fuzzy rules.
Sometimes a simple Sugeno fuzzy model can generate complex behaviour. The following is an example of a two-input system.
Example 2: Two-input single-output Sugeno fuzzy model
An example of a two-input single-output Sugeno fuzzy model with four rules can be expressed as:
Figure 3(a) plots the membership functions of input X and Y, and Figure 3(b) is the resulting input-output surface. The surface is complex, but it is till obvious that the surface is composed of four planes, each of which is specified by output equation of a fuzzy rule.
Figure 3: Two-input single-output Sugeno fuzzy model: (a) antecedent and consequent MFs; (b) overall input-output surface.
Unlike the Mamdani fuzzy model, the Sugeno fuzzy model cannot follow the compositional rule of inference strictly in its fuzzy reasoning mechanism. This poses some difficulties when the inputs to a Sugeno fuzzy model are fuzzy. Specifically, we can still employ the matching of fuzzy sets, as shown in the antecedent part of Figure 1, to find the firing strength of each rule. However, the resulting overall output via either weighted average or weighted sum is always crisp; this is counterintuitive since a fuzzy model should be able to propagate the fuzziness from inputs to outputs in an appropriate manner.
Without the time-consuming and mathematically intractable defuzzification operation, the Sugeno fuzzy model is by far the most popular candidate for sample-data-based fuzzy modelling.
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In the fuzzy system,once we fix the input variables and corresponding to MFs, are the rules of the fuzzy system been fixed?For example ,threre are 2 input variables and corresponding to 4 MFs in each input. So how many rules in total, 8 or 16? And I have some findings in a paper of ANFIS presented in the picture? I want to know why is that? Thanks a lot!!!
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Initially you should consider 16 rules. But the main issue is: How many MF's do we need to represent each input variable ?? If you have data, a clustering procedure should be applied in this case in order to determine a suitable number of cluster related to each input. Each cluster can be represented by a MF.
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i referred some books and journals they dealing with only two para meters, kindly clarify my doubt .
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You can use a fuzzylite software. It is a free and open-source fuzzy logic control library programmed in C++. It is on http://www.fuzzylite.com/ 
The next way is to use specialized software LFLC 2000 (Linguistic Fuzzy Logic Controller) which is based on deep results obtained in formal theory of fuzzy logic. It makes possible to deduce conclusions on the basis of imprecise description of the given situation using fuzzy IF-THEN rules. 
In the LFLC you can deducing dependent variable based on more than two input variables. You can find a demo version where it is possible to do some tests on
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Hi
I am using a Sugeno fuzzy system to represent a controller for a non linear system. The input of the system is a current feedback measurement across the load (RLC load) and the output to the system is a biphasic DC voltage.
One of my colleague ask if I can show proof that the system is stable under the fuzzy controller. 
Is there exist a simple proof for this?
Thank you
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Hi Phi Vo,
When you move from the LTI (Linear Time Invariant) world to the Nonstationary or Nonlinear world, even very experienced developers suddenly "discover" that experience, good ideas and intuition are not enough and some Math, even some pretty heavy Math, might have to be used. 
Take a very simple system, which works well with a gain of 5. You test it and see that actually it could work for any constant gain from 1 to 10. You test it and test it again and it works. So, you decide that you want to fit the right gain to the right situation. It seems to make sense letting the gain vary arbitrarily within the "admissible" stability region. You try it with some gain schedule and it works. You try again with another gain schedule and again it works. Some great names in Control, such as Aizerman and Kalman, actually conjected that it must work. So, you let it work and... it may work but then, it may not only not perform, but may actually blow up. Why? Just because no one has ever showed otherwise for the general nonstationary gain or system. Poles-zeros and their implications on stability are only valid for LTI systems. There is no proof of stability for any method with the general nonlinear controller or system and you would have to make the proof for the specific system you work with.
At some point in time I also thought I could “prove” that the conjectures were right. In retrospect, it forced me to learn so much about positive realness, passivity, etc., which can guarantee stability with nonstationary systems and/or controllers, that I call this the happiest mistake of my long Control career. 
Fuzzy logic could just be a good control idea, so fuzzy systems “work,” yet the proof of stability requires you to learn some Math, so not much could be added if you would rather not. You will have to just try to demonstrate performance and hope that your customers accept this as “proof.”
Anyway, a good book is
Li-Xin Wang
A Course in Fuzzy Systems and Control
Prentice Hall PTR, 1997
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I finished my M.Sc. in Chalmers Unvesity in Sweden and have two ISI indexed publication. I have a good knowledge of decision making. My last paper about Decision Making accepted in on of springer journals.
Note that the current paper which I want to co-auther it is half ready.
I am looking for somebody with PhD degree or higher who can comment on it and be a second author.
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Decision support systems could be employed in various areas of studies and different sectors. What is exactly your area of study and the focused sector? 
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I want to measure the quality of a fuzzy clustering algorithms, and I need a reliable measure to do this.
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Validity measures proposed for clustering algorithms fall broadly into three classes. The first type is based on calculating properties of the resulting clusters, such as compactness, separation and roundness. This approach is called internal validation because it does not require additional information about the data. A second approach is based on comparisons of partitions generated by the same algorithm with different parameters or subsets of the data. This is called relative validation and also does not require additional information. The third approach, called external validation, compares the partition generated by the clustering algorithm to the true partition of the data. External validation corresponds to a kind of error measurement, either directly or indirectly.
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I designed  a controller to the cable-driven robot, and get a group of parameter Q,r and ᵨ  based on  cut-and-try method. The original parameter Q,r and p taken from a paper on IEEE transaction on fuzzy system. I try to find the best parameter Q,r and p for our controller although the cut-and-try method does works in Riccati-like equation(1).
PA + ATP – 2/rPBBTP + I/ᵨ2 PBBTP=0 (1)
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A  classical useful book with ideas on this question constrained to the linear time-invariant  case is:
Schultz and Melsa " State functions and linear control systems", McGraw 1967.
Paying  attention to chapters 9 and 8 , specifically to example 9.2 and to the indications there on previous related materrial iwithin the book.
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Kindly suggest me some related resources.