Wednesday, June 08, 2005

Fuzzy Logic and its Practical use in Mass Transit Systems

Fuzzy Logic and its Practical use in Mass Transit Systems


Problem Statement

In recent years it fuzzy logic has become more and more prolific. Chances are that if you have bought any appliances from a washer and dryer to a coffee machine that it probably uses fuzzy logic in its day to day functions. Home appliances indicate the prolific use of fuzzy logic but I am surprised to read that fuzzy logic stable enough and trusted enough to operate highly critical machinery in a complex and ever changing environment – in particular recent mass transit systems such as the Maglev trains in Japan and Germany. The city of Sendai in Japan has its fuzzy control of subway since 1988, which is a good case study for this type of project. My paper will concentrate on why fuzzy logic is used in these types of systems (namely in Sendai), what problems needed to be solves in implementing fuzzy logic, and if the 16 years of fuzzy logic implementation in Sendia is seen as a breakthrough for Fuzzy Logic or perhaps illustrating flaws in fuzzy logic.


To make this report as clear as possible, let me define two terms that I will refer to throughout this paper:

Fuzzy Logic: Fuzzy logic is a superset of Boolean logic dealing with the concept of partial truth. Whereas classical logic holds that everything can be expressed in binary terms (0 or 1, black or white, yes or no), fuzzy logic replaces Boolean truth values with degrees of truth which are very similar to probabilities, except they need not add up to 100%. This allows for values between 0 and 1, shades of gray, and maybe; it allows partial membership in a set. It is related to fuzzy sets and possibility theory. It was introduced in 1965 by Dr. Lotfi Zadeh of Berkeley.

Magnetic Levitation Train (Maglev) - A magnetic levitation train or maglev is a train-like vehicle that is suspended in the air above the track, and propelled forward using the repulsive and attractive forces of magnetism. Because of the lack of physical contact between the track and the vehicle, the only friction is that between the carriages and the air. Consequently maglev trains can travel at very high speeds with reasonable energy consumption and noise levels (systems have been proposed that operate at up to 650 kilometers/hour (404 miles/hour), which is far faster than is practical with conventional rail transport). Whilst the very high maximum speeds make maglev trains potential competitors to airliners on many routes, the costs of constructing the tracks are still high.

Definitions attainted at Wikipedia:

Maglev trains are not used in Sendia but they will be talked about in conjunction with traditional rail systems. Much of the early work was identified and set forth by Lotfi A. Zadeh, Ph.D., University of California, Berkeley. He described fuzzy logic as follows,

As the complexity of a system increases, it becomes more difficult and eventually impossible to make a precise statement about its behavior, eventually arriving at a point of complexity where the fuzzy logic method born in humans is the only way to get at the problem.”

This is an arguable point since very complex systems have been designed without the use of fuzzy logic. In particular I wanted to find material that talking about the pros and cons of fuzzy logic. For the most part this has been possible, but specific instances involving the Sendai Subway have been elusive. For the most part I will be relying on facts distributed about the Sendai project.

Origins of the Fuzzy Controller

Fuzzy Logic was first implemented in England in 1973 at the University of London. A professor and student were trying to stabilize the speed of a small steam engine the student had built. They had good equipment for the time but they had problems with the engine control. Engine speed would either overshoot the target speed or arrive at the target speed after a series of oscillations, or the speed control would be too sluggish, taking too long for the speed to arrive at the desired setting.

This experiment describes a common engineering problem and this is the heart of the fuzzy logic application – the machine was essentially not doing its job well because its understanding of its environment was poor. E. Mamdani, the project lead, had read of a control method proposed by Dr. Lotfi Zadeh, head of the electrical engineering department at the University of California at Berkeley, in the United States. Dr. Zadeh is the originator of the unorthodox designation ‘fuzzy logic’. Fuzzy logic was used Professor Mamdani’s engine controller and thus the first fuzzy controller was born. The controller worked very well and the speed of the engine reached it target in a third of the time with no oscillations in acceleration – simply a smooth movement from start to finish.

This fuzzy control would go on to serve in many practical applications include the ones used in the Sendai subway. In 1988 Hitachi turned over control of a subway in Sendai, Japan, to a fuzzy system. This is perhaps the most visible application of fuzzy logic, the Sendai Subway System of Japan, and it includes such devices as smart transmissions, braking systems, and camcorder focusing systems. Fuzzy logic is also used in planning traffic and predicting customer usage of subway facilities. Since then, Japanese companies have used fuzzy logic to direct hundreds of household appliances and electronics products. The Ministry of International Trade and Industry estimates that in 2002 Japan produced about $3 billion worth of fuzzy products. U.S. and European companies still lag far behind. Although the main focus of the paper is on the success of Sendai, I will talk a bit about the over all application of fuzzy logic as well.

Fuzzy Logistics

Fuzzy logic is controversial. It is widely accepted within the engineering and computer science communities but generally rejected by mathematicians and statisticians. Critics argue that it is unscientific by the standards of Karl Popper, since set membership values are not empirically verifiable. So is Fuzzy Logic fit for every day use when human lives are affected?

A good example is mass transit systems such as the Maglev and subway trains in Japan and Germany that widely use Fuzzy Logic. The city of Sendai in Japan has had fuzzy controls in it’s subway since 1988, and this will be an ideal case study for the practical use of Fuzzy Logic since it has been implemented for 16 years. My paper will concentrate on why fuzzy logic is used in Sendai, what problems needed to be solves in implementing fuzzy logic, and if the 16 years of fuzzy logic implementation in Sendai is seen as a breakthrough or perhaps illustrating flaws in fuzzy logic.

It is important to understand the strong and weak point of fuzzy logic to give an accurate assessment of the Sendai project. I think the most important aspect about fuzzy logic is that it is very tolerant on Imprecise Data. It can take vague information and give a reasonable suggestion for a response, much in the same way that people do. It is also conceptually easy to understand because it is based on linguistic terms. For example, if the weather is warm, wear cool clothing. Warm and cool a terms that we are familiar with, but is vague for a machine to understand. Fuzzy logic also is good with expert and common sense knowledge. It is good as universal approximation and fuzzy logic can model abstract non-linear functions.

Conventional approaches may be formally verified to work, where as fuzzy logic can not be empirically verified. This makes some scientist weary of fuzzy logic. Other methods are more direct and crisp precise models may be more efficient for certain task because they are very direct in how they move data around and make choices. Lastly fuzzy logic is not a cure all. It is not good for many tasks and it is an arguable point that fuzzy logic is not worth using at all. However it does seem to be a complementary choice for machine speed control, such as for the Sendai subway.

Fuzzy logic is used in many different fields. Fuzzy mathematics is used in many ways. Some techniques from fuzzy mathematics include fuzzy relation equations, group decision-making, abstract algebra, clustering methods, belief functions, fuzzy measures, evidence theory, sugero-integrals, abduction, automata theory, genetic algebras, and hyper graphs. The medical field is known for using many of these methods.

Fuzzy Expert systems can potentially be used in any expert system that would benefit from a non-Boolean set of functions and rules.  These include Medical Diagnosis, Stock Market Analysis, Mineral Prospecting, Weather Forecasting, and Politics. Fuzzy logic applications are used in many every day devices from toasters to coffee machines.  Interesting examples I have found include the battle AI for Lord of the Rings, , Noise Detection on Compact Disks, Air Control in Soft Drink Production, and of course Mass Transit Systems.
We should ask ourselves what the primary goal is of a fuzzy logic in the Sendai system.  The goal is fairly simple – to create a more efficient and cost effective and safe subway.  It is said that you can do far more with a simple fuzzy logic BASIC or C++ program in a personal computer running in conjunction with a low cost input/output controller than with a whole array of expensive, conventional, programmable logic controllers.  While this may be true one necessarily better than the other.
I found it interesting that some claim fuzzy logic can effectively go faster, smoother, and stop at exactly the right place in less time for a mass transit system such as a Maglev train and the Sendai subway.  Claims were made that trains could be stopped in exactly the right place, which was not possible with conventional controllers. I am skeptical since older trains in the USA and England can be seen to routinely stop very smoothly and crisply, with less than an inch of position error. This is because the track-side door had to align with the door of the train, within less than an inch of tolerance. Even the PRT at WVU has accurate stopping mechanisms (I have found no material that states the PRT runs with Fuzzy Logic). These transit systems could stop perfectly and consistently and these systems are decades old, some say far outdated. Although they do seem to stop at the right place, but only by slowing to a crawl and then creeping up the last few inches.   Once again we come across oscillations in acceleration and deceleration and this is wasted seconds. The PRT seems to slow within three meters of its target and stops within about two feet of its target before inching along.

Non-fuzzy engine speed should either overshoot the target speed or arrive at the target speed after a series of oscillations, or the speed control would be too sluggish, taking too long for the speed to arrive at the desired setting. When Fuzzy Logic is applied, you can achieve a sense of no-motion from start to stop. A fuzzy variable becomes a linguistic variable when we modify it with descriptive words, such as somewhat fast, very high, real slow. Speed is a fuzzy variable. Accelerator setting is a fuzzy variable. Examples of linguistic variables are: somewhat fast speed, very high speed, real slow speed, excessively high accelerator setting, accelerator setting about right, and so forth.

For the older trains, fuzzy logic had not been invented when they started running so I doubt Fuzzy logic has upgraded most of these systems. Part of the problem is that I have not actually have been able to ride a fuzzy logic train (to my knowledge) so I have nothing to compare the conventional experience with. A ‘smooth ride’ for example, it is a very ambiguous term, and a smooth ride is not necessarily our target goal. Efficiency and less energy consumption is our target goal. I have read a good deal of material that is contradictory on the subject. Some say fuzzy logic is clearly more efficient, some say that normal methods function identically, and surprisingly I have read arguments that traditional controllers are more refined to their task an perform better.

Fuzzy Logic in the Sendai Subway

One of the most successful fuzzy logic implementations is the control of subway in Sendai, Japan. The fuzzy system controls acceleration, deceleration, and breaking of the train. Since its introduction, it is said that it not only reduces energy consumption by 10%, but the passengers hardly notice now when the train is changing its velocity. In the past neither conventional, nor human control could have achieved such performance. The ten percent claim may be in dispute but the acceleration gradient is not. There is no doubt that the change in velocity is much better than a standard controller can produce, but the efficient claim is disputable.

The Sendai Subway is slightly over 9 miles and uses an overhead wire with 1067 mm gauge and 1500V DC. The trains operate every four to six minutes depending on the cycle of the trains, the time of day, and the dictations of the fuzzy logic traffic. The line has 17 stations, and most are underground. The line contains some curves but the majority of it is in a straight line. The price for the line varies from 200 Yen to 350 Yen, where roughly one dollar is 102 Yen. The prices are comparable to the United States subways such as the Blue Line Metro.

The Sendai Subway was first in operation in 1987. It uses fuzzy logic to accelerate and brake. Only a conductor is needed to ensure safety during operation. The centroid method for use with motion control is used, developed by Hitachi and further expands on the fuzzy logic control method I described above.

The Sendai Subway has two operation modes, train speed regulation control and train stopping control. These operate on two separate but communication fuzzy logic controllers and take a number of calculations into account. These include acceleration to a target speed with velocity oscillation. Maintaining target speed (coasting), and stopping at the correct location with velocity control for a no motion feel. Other factors taken into account are safety, energy consumption, traceability, and passenger comfort.

The Sendai subway has three main areas for subway control and maintenance.

The Administrative Center

There are two departments: the Operations Department which takes care of operations and maintenance, and the Electrical Department which supplies electric power and evaluates the equipment for disaster prevention. They cooperate with each other to maintain safe and efficient operation of the subways.

Train Maintenance Warehouse

Used for Inspection and Maintenance of the Trains. Subway cars are inspected every three days and examined by automatic inspecting devices every three months. They are also overhauled in the factory every three years and six years for two different types of inspections.

Car Base
Subway cars are kept in the safe and good-running condition at the Car Base in Tomizawa. The
Administrative Center, the factory, the train maintenance shed and an automatic car washing machine are all located there.

A second line is planned as an east-west line (Tozai Line): 13.9 km, 13 stations, all underground, and linear motor technology as in Tokyo's O-Edo Line. Construction starting in 2004 for completion in 2016.


I would like to point out a few facts from two similar subways systems. The Blue Line in LA and the Sendai subways system.

Blue Line Facts & figures

  • Length: 22 miles(21.5 miles surface/elevated, 0.5 subway)
  • Groundbreaking: October, 1987
  • Opening: July 14, 1990
  • Cost: $877 Million
  • Ridership 63,000 daily avg (as of 7/00)

Sendai Facts & figures

  • Length: 15 km
  • Groundbreaking: October, 1986
  • Opening: July 14, 1987
  • Cost: $472 Million
  • Ridership 165,000/day (as of 2001)

The future Sendai rail addition is said to cost in the neighborhood of 285 billion yen.

As you can see these two subways are built in similar periods and when correlating the figures they are relatively similar in construction and costs. Note that the blue line is traditional non-fuzzy controllers where as the Sendai subway uses fuzzy logic controllers. Note that the Japanese and USA per-capita income is in less than a 25% deviation.

The Sendia Operational costs per passenger are $0.61 while Los Angeles is around $0.29. This is about double in Sendai what the costs are in LA. The costs do vary in other subway systems however. The skyrail systems in the dollars or even tens of dollars in operational costs per passenger. This is mainly because of the new technology and the high cost on construction. Other rails have a cost as low as $0.15 per passenger, namely in Tokyo/Eidan, although these are known as ‘light rail transit’ and this typically operates in a variety of alignments, including streets, but is capable of operating in trains, and usually includes well-defined passenger stations or transit stops, perhaps with prepaid or other more specialized types of fare collection.

Delineating the Pros and Cons

Sendai is thought of as a success story for fuzzy logic so it is a good example to work with. With this in mind, the other factors in Sendai are comparable to subways build in the same time frame, such as the Blue Line LA rail mentioned above. As the data points out, the operational and maintain ace costs are roughly double for the fuzzy logic system than for the LA Blue Line system. This data is based on per passenger per mile traveled, and both rails are fairly similar with the exception of geography.

Fuzzy Logic may be in everyday use including micro controllers and expert systems, but those are not in particular concern. What is of concern is the efficiency of the Sendai project and no evidence of exceptional efficiency is presented nor have I found any conclusive evidence. Oddly enough I have read about significant savings in energy but I have yet to read exactly where these saving are from. From what I have seen, the time travel is roughly the same, the passenger load is the same, and the distance traveled is a constant. If this is true, then where are the savings? One reference I did read is the idea of coasting when acceleration is not needed. Although this may not be applicable in conventional controllers it seems unlikely as a source of significant savings.

Although the material I reviewed used Sendai in their examples, they are lacking some of specific details of the Sendai subway – specifically how well it is running today. What I did get was a bit of philosophical arguments and I can see the occasional loss of objectivity in the material I have reviewed. If you are pro or con fuzzy logic, it does not matter. This paper is only concerned with the bottom line, and that is I see no significant savings. If anything the Sendai costs are significantly higher than those run by the conventional subway in LA. If you include per person income then the costs are roughly 23% more to operate and maintain the subway. There may be other factors than fuzzy logic naturally – but these are countless and can be swayed one way or the other depending on the argument. The bottom line is Sendai costs more than the Blue Line.

Maglev trains, which do use fuzzy logic as well, have an enormous cost per passenger compared to Sendai. This can be as much as ten times the conventional costs. This likely has nothing to do with fuzzy logic however and is due to the new technological costs and the scope of those projects in the Germany and Japan. The Maglev trains would have probably been a better example to use for a fuzzy logic paper since the data of energy consumption is readily available and a little engineering work can give us some idea on how much energy is being spent if a conventional engineering method was used in its stead.


The use of fuzzy logic is an interesting and useful method for solving AI problems in today’s machinery. In the instance of Sendai, it seems to be in its infancy and it proves that Fuzzy Logic can and does work on a daily basis. While the operational and maintenance costs of the Sendai system are more, fuzzy logic is likely not a direct factor in this. With this same frame of mind, I did not see any conclusive evidence that Fuzzy Logic contributed to any energy savings either. Some of the documentation I have said that this was indeed the case but I have yet to read any data that backs up these claims.

From a wider perspective Fuzzy Logic itself can be seen as a success. Any working operational model should be deemed a success and this is particularly true of fuzzy logic since it solves its problem by very abstract means with application beyond machinery control. Fuzzy logic allows for human like prediction and it likely will have an impact in robotics, market and weather predictions, AI and other fields of study. It is also true that fuzzy logic does indeed provide a better riding experience on the maglev and Sendai rails because of the sense of no motion. If this uses a little or less energy may be irrelevant but a more comfortable ride has other effects that may be more subtle. For example, if the ride is less prone to velocity adjustments that passengers feel, some safety equipment may be irrelevant. It may possible to serve food and other delicate activities that were not possible before. Movement sensitive devices such as networking and computer equipment maybe more reasonable as well. This is in addition to the creature comforts that we as people enjoy.

I have the feeling that future fuzzy logic application may be subtle things and not necessarily any earth shattering all-inclusive methods to solve problems. Fuzzy logic will become another tool to be used in a repertoire of utilities to be used by future engineers. While entire trains and complex systems may not be entirely run with fuzzy logic, it should be very useful for specific tasks. In particular tasks that involve a low amount of precise data or work that needs predictions in a human-like method of solving problems. Fuzzy logic will not replace all conventional machine controllers any time soon however. Likely there will be a need for both with emphasis on the conventional types of controllers.


The Logic of Fuzziness, Nazim Soylemezogolu, (

Fuzzy Logic: The revolutionary computer technology that is changing our world
by Dan Mcneill
Publisher: Simon & Schuster; Reprint edition (April 14, 1994)

Fuzzy Logic with Engineering Applications
by Tim Ross Publisher: John Wiley & Sons; 2 edition (August 20, 2004)

The Importance of Being Fuzzy
by Arturo Sangalli Publisher: Princeton University Press; (November 2, 1998)

The Fuzzy Systems Handbook: A Practitioner's Guide to Building, Using, & Maintaining Fuzzy Systems by Earl Cox Publisher: Morgan Kaufmann Publishers; 2nd Bk&Cdr edition (January 15, 1999)

Fuzzy Future by Bart Kosko (1999). The Fuzzy Future. From Society and Science to Heaven in a Chip. Harmony Books. New York

Fuzzy Logic for just ‘Plain Folks’

by Thomas Sowell

Monorail Operational Costs data -

Blue Line Metro home site -

Report by:

Samuel E Kisko of West Virginia University


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