# Fuzzy Logic Nonlinear Systems Computer Science Essay

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The nonlinear systems that are difficult or impossible to model mathematically are usually monitored by fuzzy logic. It is a system of logic and based on set theory and continuous variables are used in FL. Also Boolean logic is the reverse or complement of FL and discrete variables are used in it. Fuzzy logic is a methodology for problem solving or in other words " problem solving control system methodology".

Its implementation can be performed in hardware or software or by combining both. Conclusion that are based on vague, imprecise, missing input information are simply provided by fuzzy logic. It can mimic much faster, the decision making by a person which is an important approach to control problem.

An article by zadeh [1] describes that the application of fuzzy logic that have been applied to many areas or fields, for example fuzzy logic has played an important role in the field of medicine. Over the last 20 years applications of FL have become widely used. They are used in control, automobiles, household appliances and decision making systems. These applications also spread in medicine field.

Fuzzy logic uses different vocabulary in itself, i.e fuzzification, defuzzification, membership function, linguistic variables, domain, rules etc.

In Boolean algebra or Boolean logic crisp sets are used, which has only two values 0 and 1, but in fuzzy logic sets have infinite logic values between 0 and 1, in Boolean logic completely inclusive, exclusive membership is used, but in FL completely inclusive, exclusive or between these two membership is used.

A word domain uses in fuzzy sets which is the range of values in which fuzzy membership defines (domain is the part of universe of discourse; it is the complete range of given values). Different types of fuzzy sets like triangular shaped etc, shows a central value which is called as a fuzzy number. Fuzzy sets are different from others that gives variables of its sets degree of membership. The base of FS is the MF (membership function). MF is defined as a region which provides a relation between a domain value and its membership degree.

Some variables are used in FS and in fuzzy rules are called Linguistic variables. Lets take an example to define linguistic variable , for example in the rule if temperature is high then speed is fast, both high and fast are linguistic variable.

Fuzzification is defined as it is the procedure to find a value of a number in a fuzzy set which is actually the membership value. Basically rule-base model only works after the values are fuzzyfing. Rule defines the fuzzy relationship among the input values. Defuzzification is the process which is used to convert output of fuzzy set into a single value.

## 1.2. Fuzzy Rule based System

FBR stands for "Fuzzy rule base". The collection of rules is called a rule-base and mostly rules are in the style like IF-THEN. Basically rule has two sides, Firstly IF side and secondly THEN side. The first side is called condition (antecedent) and second side is called as conclusion (consequent). Inputs may be in the form of linguistic and also numeric. We call fuzzy because fuzzy set is used in condition and conclusion and knowledge is expressed in the form of IF-THEN statement so calling "Rule". And then in the end completely "Rule-base" because making inference on the basis of rules. Generally a rule base fuzzy system is a fuzzy expert system. Some of the main feature of the rule based fuzzy system is as follow.

Fuzzy inference engine uses and apply these rules.

Rules uses here to set output values.

Variables and their related fuzzy sets uses to find output.

When rules are executed after that inference engine give output value.

Fig.1.1. shows fuzzy rule based system[18]

There are three major types of rule format.

Mamdani

Takagi-sugeno-kang(TSK)

Tsukamoto

In my problem or thesis mamdani type is used. The general style of mamdani type is.

If [x1 is P1] & [x2 is P2] then [y is Q]

This type is sometimes called min-max inference technique. The use of mamdani method is to give linguistic variable process state for the controlling of rules and to linguistic variables as inputs.

## 1.3. Fuzzy Inference Engine

Inference engine like its name does inference and find result from inputs and rule base. FBR and inference engine consist of three main parts.

Assignment of membership

Connection between antecedent and consequent

Selection of inference

Firstly assign the membership functions to antecedent and consequent which is of different shapes. Like triangular, trapezoidal etc.

2ndly assign connection between the antecedent and consequent. There are two types of connection.

## &

IF-THEN

Both are used in mamdani inference method. The rule-base has various rules, these rules have to be "aggregated" into a single rule, basically aggregation connects various rules. Aggregation is a procedure to join the output fuzzy sets in a rule. Mostly 'maximum' and 'minimum' are used for aggregation. The IE parallel drive all the described rules then defuzzification process produces the final output result.

## 1.4. Fuzzy Logic Control System

Fuzzy logic control systems are used to handle difficult processes on the bases of human knowledge. FLC systems and expert systems have the same ground, but expert system can not handle the difficult process where as the FLCS are used for the ambiguous process. The old control methods are mostly have physical model so these are mostly time consuming and need a strong theoretical background and mostly have human operator to operate. But FLC controller uses linguistic rules that shows the strategy of the of the user.

The basic advantage of this method that it does not require the model[2]. Knowledge based systems in which fuzzy logic controllers are explained with the help of IF-THEN rules, that are based on professionals knowledge about system controllers, performance etc and established. Such kind of control system are fuzzy logic control systems. Designer's experience and information are the factors upon which the input-output intervals and membership functions depends. The reason for designing and application of FLCS is to handle the ambiguous and unclear and difficult processes which are not easily handled by old techniques of the control systems. Also the fuzzy expert system is a system in which fuzzy rules are used with MF to find the conclusion or result. Now-a-days most uses of the fuzzy logic are through FES.

Fig.1.2. shows structure of an expert system[17]

Fig.1.3. shows the block diagram of fuzzy controller[17].

## 1.5. Fuzzy Diagnostic system

Predefined patterns and the behaviour of a process are mostly controlled by Diagnostic systems. The problems controlled by such systems involve suggestions for a certain treatment after identification. Diagnostic systems are in the form of an expert system based on rules. Sure patterns are explained by set of rules which is called as rule based expert system. Evaluation of rules is done after the collection of observed data. Identification of pattern and suggestion of problem linked with that pattern is given when the rules are logically satisfied. Implication of certain treatment is performed by each one of specific problem. Normally computation of human expert is performed by diagnostic system instead of its replacement. So the conclusive decision is finally made by human diagnostic expert to search the reason and give the prescription.

FL has been used in diagnostics for cancer and diabetes [3]. Turku University Hospital have made a software known as DIAGAID that uses FL [4]. Results from the research studies in Finland [5, 6, 7] and data from international publications [8] used in this thesis.

## 1.6. Cerebrospinal fluid (CSF)

CSF is a fluid present in nervous system (nervous blood) of the human body. The main function of cerebrospinal fluid is the brain and spinal cord fluid; influx of hormones etc. the puncture or abnormality of CSF include; spinal cord disorder, hemorrhage, tumors and many more.

## 1.6.1. Blood and types in CSF

We can define blood as it is like a tissue of the liquid form. It has different types

Red blood cells

Lymphocytes

Neutrophils

Eosinophils

Fig.1.4. shows the blood types[19].

Blood basically does two types of functions

Circulate through the body; food particals, oxygen, harmones etc.

Defensive system of the body.

## 1.6.1.1 Red blood cells

It is the very numerous type in the blood. This type is ues for the transport of CO2 and O2.

Fig.1.5. shows red blood cells[19]

## 1.6.1.2 Lymphocytes

The quantity of these cells in the blood is much less than RBS. These are the type of white blood cells and used in the defensive and immune system of the body. Lymphocytes are in the bone marrow.

Fig.1.6. shows lymphocytes[19].

## 1.6.1.3 Neutrophils

These are also white blood cells. The fig shows a neutrophil cell surrounded by RBS. Neutrophils are present in the bone marrow and blood percentage wise.

Fig.1.7. shows neutrophils[19].

## 1.6.1.4 Eosinophils

These cells are the type of white blood cells and use in the immune system of the body. These are present in blood, bone marrow and in tissues.

## 1.6.1.5 Protein

Protein enters the CSF through blood also protein transfer from brain to CSF.

## 1.7. Dissertation Overview

This thesis proposed diagnostic system using fuzzy logic control system and its design and simulation. Thesis proposed a diagnosis of the haemorhage and brain tumor disease infact show the probability of the disease. I make a simulation by using fuzzy logic that shows the probability of the disease to occur and normal result probability. Haemorhage and tumor occur by the abnormal increase or decrease of blood cells in the cerebrospinal fluid. I take data range of the blood cells include red blood cells, lymphocytes, protein, neutrophils, eosinophils. These cells use as an input parameter for the fuzzy logic system. Cells make input which is to be fuzzified. Then make rules and on the basis of these rules fuzzy rules base gives the fuzzified output. The output describes which disease is probable and the chances of the normality by the change in the input parameters that are blood cells. Then I use the fuzzy surface that shows the graphical relationship between the input parameters and output. At a time one graph shows the relationship between any two inputs with any one output.

## 1.8. Dissertation Organization

This proposed thesis has four chapters. First chapter describes the introduction of the fuzzy logic, fuzzy control, and fuzzy diagnostic system. Also the introduction of the proposed problem fuzzy logic medical diagnosis control system and the introduction of the variable or inputs used in this thesis.

Second chapter describes the literature survey of the international research papers.

Third chapter describes the simulation and design of the fuzzy logic medical diagnosis control system.

Fourth chapter describes the result and discussion of the design model and simulated results.