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Printed: 23, March 2015

Whenever we consider the good reputation for Fuzzy Logic, we discover the first person because of its development was Buddha. He resided in India within 500 BC and founded a faith known as Buddhism. His philosophy took it’s origin from the idea the world is stuffed with contradictions, that nearly everything contains a number of its opposite, or quite simply, that things could be a and never-A simultaneously. Ideas can easily see a obvious link between Buddha’s philosophy and modern fuzzy logic.

About two centuries later, the Greek scholar Aristotle developed binary logic. In unlike Buddha, Aristotle believed that the planet was comprised of opposites, for instance male versus female, hot versus cold, dry versus wet, active versus passive.

Everything needs to be A or otherwise-A, it cannot be both.

Aristotle’s binary logic grew to become the bottom of science it had been demonstrated using logic, and it was recognized as scientifically correct. Like many more, Russell attempted to lessen math to logic. As he discovered his paradox while working, she got scared themself. It did, however, provide him the recognition to be among the fathers of fuzzy logic.

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In 1965 Lotfi Zadeh at UC Berkeley suggested a logic system that supported infinite value logic. Zadeh suggested that the element may have a membership function that describes its membership of the set. For instance, the expression mA(x) may be the membership purpose of x inside a.

Zadeh’s logic was known as Fuzzy set theory that has demonstrated just a little unfortunate because some took fuzzy to mean imprecise or inaccurate.

He’d the concept that should you could tell an aura-conditioner to operate just a little faster if this will get hotter, or similar problems, it might be a lot more efficient than getting to provide a guide for every temperature.

## What’s FUZZY LOGIC?

The term FUZZY essentially means: imprecise, not obvious, vague or inexact

Couple of definitions of fuzzy logic:

## A kind of reasoning, produced from fuzzy set theory, whereby a truth value don’t have to be exactly zero (false) a treadmill (true), but instead could be zero, one, or any value among

Fuzzy Logic was created by Lotfi Zadeh, a professor in the College of California at Berkley like a better way of sorting and handling data.

It mimics human control logic and it is now being applied in the realm of buying and selling systems.

A sub-discipline of mathematics accustomed to evaluate subjective linguistic concepts, for example vibrant, dark, far, quite close, most typically, nearly impossible, etc.

A technique accustomed to model linguistic expressions which have nonbinary truth- values. It’s been combined with PID algorithms in process control, especially where process relationships are nonlinear.

A method utilized by a specialist system to cope with imprecise data by the probability the input details are correct.

Fuzzy logic is made for situations where details are inexact and traditional digital on/off decisions aren’t possible. It divides data into vague groups for example hot, medium and cold.

## The Fundamental Concept of Fuzzy Sets

Fuzzy sets are functions that map something, which can be part of set, to some number which lies between zero and something, therefore indicating its actual amount of membership

A diploma of zero implies that the worth is away from the set, along with a amount of one implies that the worth is totally associated with the set.

## Characteristic Function:

Conventionally we are able to specify a collection C by its characteristic function, Char C(x).

If U may be the universal set form which values of C are taken, only then do we can represent C as

This is actually the representation for any crisp or non-fuzzy set. To have an ordinary set C, the characteristic function is from the form

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Char C(x): U à

But also for a Fuzzy set A we’ve

Char F(x): U à [,1]

That’s, for any fuzzy set the characteristic function assumes all values between and 1

## and not simply the discrete values or 1.

## For any fuzzy set the characteristic function is frequently known as the membership function and denoted by mF(x)

## A good example:

When we use conventional method we are able to say that an individual is TALL if his height is 7 ft and one is NOT TALL with height 5 ft. This is often symbolized the individual is either TALL or NOT TALL in Boolean Logic 1 or , 1 for TALL and for NOT TALL

## To exhibit the connection or amount of precision, we are able to use FUZZY SETS also:

If S may be the group of everybody within the World, a diploma of membership is owned by each individual in set S to obtain the subset TALL.

The membership function is dependant on the individual’s height.

TALL(x) = , if Height(x) 5′

(Height(x) – 5′ )/ 2′ if 5’= Height(x) = 7

1, if height(x) 7 ft

Boolean logic versus Fuzzy Logic

## Boolean Logic

## Fuzzy Logic

Boolean or two-valued logic is traditional logic with all of statements either being true or false.

Fuzzy or multi-valued logic is really a variation of traditional logic by which there are lots of (sometimes infinitely many) possible truth values for any statement. True is recognized as comparable to a truth worth of 1, false is really a truth worth of , and also the real figures between 1 and are intermediate values.

Here’s a good example: Suppose you want to illustrate the group of adults utilizing a binary set, we’d obtain a graph such as the one around the right. Within this picture the assumption is a thief turns into a grown-up with their 18th birthday. It’s that each individual is either adult or non-adult, within the graph 1 or .

Whenever we graph the fuzzy group of adults, we obtain something similar to the image around the left. Within this there lies a gentle process between being adult and non-adult. Again we are able to argue or disagree over this saying exactly how the bend ought to be attracted. Someone might state that a 13 years old is totally non-adult or that the 19 years old needs to be counted within the group of adult. But we are able to make certain that fuzzy curve from the group of adults is nearer to the reality then your binary curve naturally we all can agree there can’t obtain a specific date when individuals become adults. It isn’t like we go to sleep eventually growing up and awaken the following being an adult. Becoming an adult is really a gradual process and gradual processes could be better described using fuzzy sets where you can find no discrete values.

## Couple of MORE Types Of FUZZINESS And It Is USAGE

For instance, should you ask an issue inside a school class, Who’s female?, all of the women will set up their hands up and all sorts of boys could keep them lower. We are able to obtain a obvious answer, since everybody is either female or perhaps is a non-female.

Let’s say exactly the same children are requested an issue like, Who likes school? Some kids may set up their hands completely (they certainly like school) yet others might maintain their hands lower (they hate school). The majority of the kids however will take their hands up and go lower again a couple of occasions by leaving it somewhere in the centre. Maybe that they like school generally, but there are several bad reasons for it they don’t like for example examinations, or they really can’t stand school generally, but may it’s fun so within an all they’re confused and really should be demonstrated in middle way.

If these answers are symbolized with binary logic, they should be reduced to every lead to the extremes of either loving school or hating school A or otherwise-A. Ideas require a different of logic to notice the solutions precisely and precisely we want a logic in which the kids can both like school and never like school simultaneously. For your we use fuzzy logic.

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An individual characteristic for example healthy.

The classification of patients as depressed.

The bifurcation of certain objects as small or large.

The distinguition of individuals by age for example old.

A guide for driving for example if the obstacle is close, then brake immediately.

## FUZZY OPERATIONS

## STEPS OF IMPLEMENTATION OF FUZZY LOGIC

Fuzzification – to transform number data (for e.g. $24.50 ) in tangible-world domain to fuzzy-figures in fuzzy domain

Aggregation (rule firing) – computation of fuzzy figures (which lie between . and 1. ) i.e. in fuzzy domain

Defuzzification – convert the acquired fuzzy number to the number data within the real-world domain (e.g. 150.34% as a whole profitability).

## WHY To Make Use Of FUZZY LOGIC?

## Fuzzy logic advantages:

Mimics and translates human making decisions to deal with vague, uncertain and imprecise concepts

Rapid and faster computation because of intrinsic parallel processing nature

Ability to cope with imprecise or imperfect and unsure information

Resolving conflicts by collaboration and propogation

Improved understanding and knowledge representation and uncertainty reasoning

Modeling of complex and non-straight line problems

Natural language processing in addition to programming capacity

Computers don’t reason as brains do. A persons brain can reason with vague assertions or claims which involve uncertainties or value judgments: The environment is awesome, or That speed is fast or She’s youthful. Unlike computers, humans have good sense that permits them to reason inside a world where situations are only partly true. Fuzzy logic is really a branch of machine intelligence that can help computers paint grey, commonsense images of an uncertain world.

## Fuzzy logic limitations:

Highly abstract and heuristic concept

Necessity of experts for rule discovery (data relationships) i.e using fuzzy computation

Insufficient self-organizing self-tuning mechanisms of Neural Nets

Though fuzzy Systems are utilized world-wide in a variety of applications, still it remains questionable among statisticians preferring Bayesian logic or two-valued theory.

Applying FUZZY

## You will find numerous applications for fuzzy logic. Actually, some declare that fuzzy logic may be the encompassing theory over all kinds of logic. These couple of products described here are more prevalent applications which may encounter in everyday existence.

## Bus Time Tables

How precisely perform the schedules of bus timings predict the particular travel time or even the actual arrival duration of public transit?

Bus schedules are formulated on information that doesn’t remain constant. With this fuzzy logic ought to be used since it is impossible to provide a precise answer regarding once the bus is going to be in a certain stop. Many unforeseen occurrences can happen. There might be accidents, abnormal traffic backups, or even the bus could break lower. An observant scheduler would take each one of these options into consideration, and can include these questions formula for working the approximate schedule. It’s that formula which imposes the fuzziness using fuzzy logic.

## Predicting genetic traits

Genetic traits or characteristics really are a fuzzy situation in excess of one good reason. There’s the truth that many traits can not be linked one gene. So only specific mixtures of genes can create confirmed trait. Next, the dominant and recessive genes which are frequently highlighted with Punnet squares are takes hold fuzzy logic. The quality of membership in individuals sets is measured by the appearance of an inherited trait. In obvious installments of dominant and recessive genes, the potential levels within the sets are very strict. Take, for example, the color of eyes. Two brown-eyed parents produce three blue-eyed children. Sounds impossible, right? Brown is dominant, so each parent should have the recessive gene within them. Their membership within the blue eye set should be small, but it’s there. So their kids have the possibility for top membership within the blue eye set as it is a recesive one. to ensure that trait really comes through. Based on the Punnet square, 25% of the children must have blue eyes, using the other 75% must have brown. But in cases like this, 100% of the children possess the recessive color. Was the wife being disloyal with this nice, blue-eyed salesperson? Most likely not. It is simply fuzzy logic at the office.

## Temperature control (heating/cooling)

The primary objective in temperature control would be to keep your room in the same temperature consistently. Well, that appears pretty easy, right? But exactly how much will a room need to awesome off prior to the heat takes over again? There has to be some standard, therefore the heat (or ac) is not inside a constant condition of turning off and on i.e. in conventional type of 1’s and 0’s. Within lies the fuzzy logic. The set is dependent upon exactly what the temperatures are really set to. Membership for the reason that set weakens because the 70 degrees differs from the set temperature. Once membership weakens to some certain point, temperature control takes over to obtain the room to the high temperature it ought to be.

## Auto-Concentrate on a video camera

So how exactly does your camera know what to pay attention to?

Auto-focus cameras are a good revolution for individuals who spent years battling with old-fashioned cameras. These cameras in some way determine instantly, according to multitudes of inputs, what is supposed to function as the primary object from the photo. It uses fuzzy logic to create these assumptions. Possibly the conventional is to pay attention to the item nearest to the middle of the viewer. Maybe it concentrates on the item nearest towards the camera. It’s not an exact science, and cameras err periodically. This margin of error is suitable for that average camera owner, whose primary usage is perfect for snapshots. However, the old-fashioned and earlier used manual focus cameras are liked by best photographers. For just about any errors in individuals photos can’t be related to an analog glitch. The choice making in focusing a handbook camera is fuzzy too, but it’s not controlled with a machine.

## Medical diagnoses

The number of of what types of signs and symptoms will yield an analysis? How frequently are doctors by mistake?

There lies a summary of signs and symptoms for any horrible ailment that say for those who have a minimum of 5 of those signs and symptoms, you’re in danger. It’s a hypochondriac’s haven. Now you ask ,, how can doctors undergo that listing of signs and symptoms to some diagnosis? Fuzzy logic. There’s no guaranteed system to achieve an analysis. If there have been, we wouldn’t learn about installments of medical misdiagnosis. Diagnosing are only able to be some extent inside the fuzzy set.

## Predicting travel time

This is particularly hard for driving, since there are many traffic situations that may occur because of slow lower travel.

Just like bus timetabling, predicting ETA’s (believed duration of arrival) is a superb exercise in fuzzy logic. A significant player in predicting travel time. Weather, traffic, construction, accidents really should be added in in to the fuzzy equation to provide a real estimate.

## Antilock Braking Mechanism

The purpose of an ABS would be to monitor the braking mechanism around the vehicle and release the brakes right before the wheels lock. A pc is involved with figuring out when the optimum time to get this done is. Two primary factors which go into figuring out this would be the speed from the vehicle once the brakes are applied, and just how fast the brakes are depressed. Usually, the occasions you would like the ABS to actually work are when you are driving fast and slam around the brakes. There’s, obviously, a margin for error. It’s the job from the ABS to become smart enough never to permit the error go beyond the point once the wheels will lock. (Quite simply, it does not permit the membership within the set to get too weak.)

## Fuzzy Machines

Fuzzy Washing Macine

## REFRENCES

Fuzzy Sets and Fuzzy Logic theory and applications, George J.Klir, Bo Yuan

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Printed: 23, March 2015

Abstract- This paper presents a fuzzy logic controller to have an isolated signalized intersection. The controller controls traffic light timings and phase sequence to make sure smooth flow of traffic with minimal waiting some time and period of queues. Usually, fuzzy traffic controllers are enhanced to maximise traffic flows /minimize traffic waiting time under typical traffic conditions. Consequentially, these aren’t the perfect traffic controllers under exceptional traffic cases for example roadblocks and road accidents. We apply Condition-space equations to formulate the typical waiting time vehicles in traffic network at fixed time control. Results reveal that the performance from the suggested traffic controller at conventional model is much better those of conventional fuzzy traffic controllers under normal and abnormal traffic conditions.

Keywords- signalized intersection condition-space equations traffic light timing fuzzy controller abnormality conditions

## Introduction

Traffic signal control continues to be probably the most active research areas in intelligent transportation systems (ITS), because such control directly affects the efficiency of urban transportation systems. For a long time many investigators have conducted research into optimal signal control algorithms. Webster[1] gave equations for that optimal cycle length and also the eco-friendly phase time assignment, what are foundation of fixed-time control that has been broadly used. Akcelik[2,3] modified Webster’s theory for that over-saturated scenario inside a new signal timing formula known as ARRB. These techniques succeed with low calculational costs when traffic the weather is in line with historic records, but cannot react to real-time variations. With the introduction of a number of affordable sensors and computer and communication technologies, many advanced methods happen to be designed to adjust signal timings based on real-time traffic data. For example, vehicle actuated control, which extends eco-friendly signals based on the detected headway instantly, is a such method. Numerous adaptive traffic control systems happen to be deployed around the globe, for example SCOOT[4], SCATS[5], OPAC[6], and RHODES[7]. Recently, artificial intelligence techniques happen to be introduced into signal control using fuzzy logic controllers[8] and genetic algorithms (GA)[9]. Scalping strategies have various qualities and different effectiveness in field applications.

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Transportation systems are complex dynamic systems which are difficult to be modeled exactly. Because of this, many current methods don’t have good theoretical bases. However, with no model description, the interior qualities from the transportation system can’t be identified to judge existing algorithms and also to recognize potential issues and improve them. Sen and Mind[10] suggested an over-all formulation to model signal controls as discrete-time optimal control problems. Additionally they noticed that the issue can, in principle, be solved while using dynamic programming (DP) method once the performance index is separable within the DP sense, which this option would be not virtually achievable because of the curse of dimensionality. Within this paper, condition-space equations are utilized to formulate the signal control problem for any single intersection inside a simplified mathematical model, be responsible for designing better signal controllers [12].

## The modeling of single intersections

## Condition – Space Equations

The queue length is a vital variable that describes the traffic condition of the intersection. The queue evolves as

where’s the index from the traffic streams may be the index from the discretized time times. in unit of quantity of vehicles, may be the queue entire i -th stream in the start of the n -th time interval is the amount of vehicles that join the i -th queue within the n -th time interval is the amount of vehicles that leave the i -th queue within the n -th time interval and, that takes (for stop) or 1 (for go), may be the signal condition from the i -th stream within the n -th time interval. and therefore are normally distributed random signals.

A 2 Phases Signalized Intersection that employs for demonstrating single intersections is Fig. 1

## Leg 4

## Leg 2

## Leg 1

## Leg 3

Two Phase Signalized Intersection shape

In Fixed-time control and Fuzzy intelligent control model, the control variables was considered in follows. For phase 1 intersection implies that traffic light is eco-friendly in lane 2 and 4 which is red in lane one and three. Therefore. the vehicles will go in lane 2 and 4 plus they shoud stay in lane one and three. however, for phase 2 intersection implies that traffic light is eco-friendly in lane one and three which is red in lane 2 and 4. Therefore. the vehicles will go in lane one and three plus they shoud stay in lane 2 and 4.

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Integrating the size of queue regarding time yields the typical vehicles waiting duration of the queue. Let T denote the size of the discretized time interval. If Its short enough, the vehicles arrivals may be treatable to be uniform in each and every time interval. Hence, integrating Eq. (1) yields

where’s the typical vehicle-wise waiting duration of the i -th queue right from the start from the period towards the start of the n -th time interval.

Equations (1) and (2) would be the condition-space equations describing the dynamic evolution from the traffic condition in a single intersection. The waiting some time and the amount of vehicles are popular performance indices for signal controls. The waiting time can be used because the performance index. Therefore, the optimization objective is

To facilitate the formulation, the condition-space equations and also the optimization objective could be re-written in matrix form as

where would be the condition variables and therefore are the control variables. The different coefficient matrices and vectors are [12]:

## fuzzy logic controller

## Fuzzy Logic

The introduction of fuzzy logic goes back to 1973 [14]. Presenting an idea he known as approximate reasoning, Zadeh effectively demonstrated that vague logical statements let the formation of algorithms that may use vague data to derive vague inferences. Fuzzy logic assists you to compute with words, which helps complex analysis reflecting a persons attitude. Each fuzzy logic system could be split into three elements fuzzification, fuzzy inference and defuzzification [15,16,17,18].

Input data are most frequently crisp values. Fuzzification maps crisp figures into fuzzy sets. The fuzzifier decides the related membership grades (or levels of membership) in the crisp inputs. The resulting fuzzy values will be joined in to the fuzzy inference engine. Fuzzy inference is dependant on a fuzzy rule base containing some IfThen fuzzy rules.

The very fact following If is really a premise or antecedent and also the fact following Then is really a consequent. A fuzzy inference system could be composed in excess of one rule with every rule composed in excess of one premise variable. During defuzzification, one value is selected for that output variable. A generally used defuzzification technique for continuous membership functions may be the centroid method (center of area) [13,15]

## Methodology

Signal control is essentially a procedure for allocating eco-friendly time among conflicting movements. Alternatively, signal control is really a process for figuring out whether in order to extend or terminate the present eco-friendly phase. The suggested fuzzy logic controller (FLC) works in the same manner but it’s considerably not the same as actuated control. Actuated control extends eco-friendly time according to extra time interval, an optimum eco-friendly some time and the vehicular actuations about them approach. No study of the circumstances on conflicting movements with no optimization is active in the actuated control process [13].

The suggested fuzzy logic controller determines whether or not to extend or terminate the present eco-friendly phase with different group of fuzzy rules. The fuzzy rules compare traffic conditions using the current eco-friendly phase and traffic conditions using the next candidate eco-friendly phase. The group of control parameters is:

= may be the total vehicle-wise waiting duration of the i -th queue right from the start from the period towards the start of the n -th time interval.

= is the amount of vehicles that join the i -th queue within the n -th time interval.

= may be the signal condition from the i -th stream within the n -th time interval.

The fuzzy logic controller determines whether or not to extend or terminate the present eco-friendly phase following a minimum eco-friendly the years have been displayed. When the eco-friendly time is extended, then your fuzzy logic controller will settle if to increase the eco-friendly following a time interval. The interval can vary from .one to ten sec. with respect to the controller processor speed. When the fuzzy logic controller determines to terminate the present phase, then your signal will visit the next phase. Otherwise, the present phase is going to be extended and also the fuzzy logic controller can make the following decision after and so on before the maximum eco-friendly time is arrived at [13].

The choice making process is dependant on some fuzzy rules which considers the traffic conditions using the current and then phases. The overall format from the fuzzy rules is really as follows:

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Where and therefore are linguistic variables for is split into four fuzzy sets: Low(L), Medium(M) and High(H). is split into three fuzzy sets: Low(L), Medium(M) and High(H). is split into two fuzzy sets: STOP and GO.

The amount of fuzzy rules relies upon the mixtures of fuzzy sets for. and. Within this paper the amount of fuzzy rules is 81 fuzzy rules.

The parameters. as well as for are characterised by fuzzy figures as proven in Fig. 2-7. Trapezoidal fuzzy figures are utilized within this study.

The input data (traffic conditions) are first fuzzified while using suggested fuzzy sets for ,and. Then your fuzzified input data are joined in to the fuzzy inference system which consists of some fuzzy rules. The max-min composition method [15,18,19] is used to make inferences and also the centroid technique is requested defuzzification [13]. The membership grades for GO and prevent are compared. The main one using the greatest membership grade is selected because the control action .

## simulation results

The simulation is transported out using MATLAB 7.4 and also the Fuzzy Logic Toolbox. The Fuzzy logic toolbox is helpful to construct rapidly the needed rules and changes are often made. This considerably cuts down on the development duration of the simulation model. The novel fuzzy controller that may optimally control traffic flows under both normal and exceptional traffic conditions. The Qualifying criterion of optimization would be the decrement period of queues and also the average of waiting time vehicles in intersection. the outcomes of simulation of model was mentioned within the each of open and shut loop models. In simulation. is sampling some time and the cycle duration of traffic light is 100 seconds. The simulator operates 1000 seconds using the following assumptions:

1. A four arm intersection and every arm has three lanes.

2. The appearance of vehicles is independent on every lane.

The inter-arrival of vehicles can also be independent and normal distribution can be used to create arrivals.

This leads to inter-arrival of vehicles is 5 seconds.

3. Pedestrian crossing is recognized as.

4. Sensors are put in a certain distant in the intersection, the utmost vehicle that may be detected queuing is 30 vehicles.

5. Maximum eco-friendly time is 40 seconds and also the minimum eco-friendly time is 5 seconds.

The amount of vehicles that leave the i -th queue within the n -th time interval is tailored by equation

so that saturation flow rates are

for. The parameter is larger equal fifty. ( ). The parameter is between and 1, so that it’s variations are based on follows table (TABLE I). The traffic informations was recorded every 5 seconds and it was utilized in the simulations. The and variables are usually distributed random signals within this model.

The outcomes of simulation of classic model for Fixed time control and Fuzzy intelligent control were shown in follows .

The positioning of traffic by variations of

## Fixed-Time Control

The traffic lights of Leg1 and Leg3 in Fig. 1 were considered eco-friendly in first 40 seconds and red in second a minute. However ,The traffic lights of Leg2 and Leg4 in Fig. 1 were considered red in first 40 seconds and eco-friendly in second a minute. The aim of simulation may be the decrement of waiting time vehicles and the size of queue. The classic type of Two Phase Signalized Intersection was created in Fig. 8 without controller. The creation of classic model was shown in Fig. 9 on intersection in fixed time control. Time of simulation is 1000 second.

The classic type of Two Phase Signalized Intersection

The summation of number vehicles in Queues on intersection were shown in each and every 5 seconds in Fig. 9.

The amount of vehicles in Four Queues of Intersection without controller

## Fuzzy Intelligent Control

The creation of controller may be the charge of variables (). This charge of variables for that Leg1 and Leg3 of intersection were shown in Fig. 10. also, The summation of number vehicles in Queues on intersection were shown in each and every 5 seconds in Fig. 11. Time of simulation is 1000 seconds.

The Charge of Variables of Leg1 and Leg3

The amount of vehicles in Four Queues of Intersection with Fuzzy controller

## Conclusion

The classic type of urban traffic network was symbolized for any single intersection. The aim was calculating the size of queue and also the average waiting time vehicles in almost any lane because the condition of variables. However, for demonstrating the proportion of improvement traffic, a brand new fuzzy signal controller was created. The controller was tested using simulink program on Matlab 7.4. The outcomes of simulation and also the number of improvement reveal that the intelligent fuzzy of controller cuts down on the average waiting time vehicles in almost any lane of intersection when compared with Fixed-time control (TABLE II). The techniques of other for designin of fuzzy controller and control in complicated intersections and nonisolated intersections in urban traffic network and analysis into heuristic ways of solving developed optimal control problem in line with the condition-space equations must be carried out in the long run.

the compare of results average waiting amount of time in lanes of classical model

## Average Waiting Time (second)