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Fuzzy Logic and Controls

David J. Nowacki, MBA

Course Outline

The only way a computer can process information like a human is for the control systems to incorporate fuzzy logic into its decision making activities.  This course will review the creation of fuzzy logic (1960’s) and lay the foundation for how fuzzy logic comes about and how fuzzy sets help to create better control decisions and control systems.  Defined in the course is the idea of crisp data versus fuzzy data, fuzzy data sets and how one can “defuzzify” data to create clear (crisp) decisions.  As an example, picture a driver entering a medium-busy interstate highway.  The course will introduce the idea that this driver does make life and death decisions without ever knowing ‘true data’ such as how fast they may be going, how far away other drivers might be or how fast anyone else is traveling.  It is this “human processing” of information which we explore through the world of “fuzzy logic”.

This course includes a multiple-choice quiz at the end, which is designed to enhance the understanding of course materials.

Learning Objective

At the conclusion of this course, the student will:

Intended Audience

This course is a basic introduction of the world of “fuzzy” logic and is intended for architects, engineers and contractors.

Benefit for Attendee

Attendee of this course will be able to understand why many parts of the world are embracing control systems based on “fuzzy logic” and, accordingly, why there is a biasness away from this subject in our domestic markets.  This negative biasness is a direct result of the word “fuzzy” as its context domestically is thought to be less than prudent while the word translated into other languages means almost the opposite.

Course Introduction

Human beings have the ability to take in and evaluate all sorts of information from the physical world and mentally analyze, average and summarize all this input data into an optimum course of action.   All living things do this, but humans do it more and do it better and have become the dominant species of the planet.
Computers, on the other hand, operate on a binary true or false basis. Unfortunately our world is not binary. The world we live in is full of ambiguities.  The way a computer operates and how our world functions appear to be odds if we try to have computers mimic worldly events.   "The temperature is pretty warm" cannot be evaluated as strictly true or false.  We accept that this statement has certain ambiguities.   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.    

Thus, the mathematical theory of fuzzy logic was developed. The theory of fuzzy logic states that rather than a statement being true or false, each statement has a certain confidence level. For example let us say a confidence value of 0.000 meant false and a confidence value 1.000 meant true, then the statement "this room is warm" might have a confidence value of .700 at 80 degrees. The idea of fuzzy logic has had a profound impact in many areas including decision making software in the control arena. Specifically, there are applications where “fuzziness” is utilized when human lives are at stake.

If you think about it, much of the information you take in is not very precisely defined, such as evaluation of the behavior of a vehicle entering from a side street and the likelihood of the vehicle pulling in front of you.   This is called fuzzy input.   However, some of your "input" is reasonably precise and non-fuzzy such as your speedometer reading.  A human processing of all this information is not very precisely definable.   This is called fuzzy processing.   Fuzzy logic theorists would call it using fuzzy algorithms (algorithm is another word for procedure or program, as in a computer program).

Fuzzy logic is the way the human brain works, and we can mimic this in machines so they will perform somewhat like humans, not to be confused with Artificial Intelligence, where the so far unattainable goal is for machines to perform EXACTLY like humans.  

About Course Author

Professor David J. Nowacki is an adjunct professor teaching graduate finance courses at Texas A&M University-Commerce and through the Mechanical Engineering Department at Southern Methodist University (SMU), Dallas, Texas.  Mr. Nowacki has 20 years experience in the investment-banking arena having worked for Wall Street firms in New York City, San Francisco, Houston and Dallas.  His specialty is fixed income securities and derivatives including hedge strategies.  Mr. Nowacki also consults on merger and acquisitions, strategic planning and the venture capital arena.

Course Content

The course content is contained in the following PDF file:

Fuzzy Logic and Controls

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Course Summary

The idea of fuzzy sets and analysis is not a new item as it was developed in the 1960’s. Since that time, many applications have been commercialized in the control and systems arenas.  Fuzzy logic allows the ability to utilize crisp data in such a way that data points can be associated with different fuzzy sets.  Then, these sets themselves can be analyzed to create some outcome….with that outcome being a crisp decision.

Creating fuzzy sets allows for characteristics to a factor rather than mere numbers.  All the while, these characteristics can be assigned set participation numbers.  A quick example with both descriptive ‘sets’ and outcomes is:

  1. Different characteristics of players
    • Strength: strong, medium, weak
    • Aggressiveness: meek, medium, nasty
  2. Outcomes
    • If meek and attacked, run away fast
    • If medium and attacked, run away slowly
    • If nasty and strong and attacked, attack back
  3. Control of a vehicle
    • Should slow down when close to car in front
    • Should speed up when far behind car in front

The major result in applying fuzzy logic to control systems is that this approach provides smoother transitions.   There are no a sharp boundaries in the application stage even though a fuzzy might have such boundaries.  That is to say, if data points are increasing and nearing an end point of one fuzzy set, that same data point can be a member of another fuzzy set near that fuzzy set’s midpoint.  It might be that this second fuzzy set now controls the outcome of the system.

Classical set theory requires an object or data point to be either in or not in the set.  Likewise, controls based on this logic would have binary decisions….one or off.  Fuzzy set allow for data to be described as not completely in or out of a given set – somebody 6” is 80% tall.  In other words, fuzzy set theory allows for an object to be in a set by matter of degree:

    1.  1.0 => in the set
    2.  0.0 => not in the set
    3.  0.0 < object < 1.0 => partially in the set

The idea of fuzzy logic applied to software, computers, controllers and many other applications should not be a deterrent in using such products in the market.  Most applications of fuzzy logic are first adopted and adapted overseas with users in North Americas coming later to the game.   The intent of this presentation is to introduce the “fuzzy” concept so that engineer-managers can have a little comfort on the subject. 


Once you finish studying the above course content, you need to take a quiz to obtain the PDH credits.

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DISCLAIMER: The materials contained in the online course are not intended as a representation or warranty on the part of PDH Center or any other person/organization named herein. The materials are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered architect and/or professional engineer/surveyor. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.