Fuzzy LogicBY: ASHLEY REYNOLDS

Where Fuzzy Logic Falls in the Field of Mathematics

Mathematics

Mathematical Logic and Foundations

Fuzzy Logic

Computer Science

Logic in Artificial Intelligence

Reasoning Under Uncertainty

Information and Communication, Circuits

Fuzzy Sets and Logic

Boolean Logic

The logic that we have learned about so far falls in the classification of Boolean logic. In Boolean logic all values are reduced to either “True” or “False”

An example of this can be seen by looking back to Discrete.

Truth Tables

Fuzzy Logic

The term Fuzzy Logic was introduced in 1965 by Lotfi Zadeh who was working on the problem of a computer understanding natural language.

Natural language is not easily translated into completely true or completely false.

Fuzzy Logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact.

Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false

Example

“Fuzzy logic includes 0 and 1 as extreme cases of truth (or "the state of matters" or "fact") but also includes the various states of truth in between so that, for example, the result of a comparison between two things could be not "tall" or "short" but ".38 of tallness”(Rouse)

Another example is asking people to identify a color. You will receive answers of varying degree.

What’s the Problem

The main “problem” that is trying to be solved is in the application of fuzzy logic to the real world.

Fuzzy logic has been used in many areas of the real world to improve the everyday life of a population

The first notable application was on the high-speed train in Sendai, in which fuzzy logic was able to improve the economy, comfort, and precision of the ride. It has also been used in recognition of hand written symbols in Sony pocket computers.

Example of an application

A temperature measurement for anti-lock breaks might have several separate membership functions defining particular temperature ranges needed to control the brakes properly.

Each function maps the same temperature value to a truth value in the 0 to 1 range.

These truth values can then be used to determine how the brakes should be controlled.

Example Continued

The meanings of the expressions cold, warm, and hot are represented by functions mapping a temperature scale.

A point on that scale has three "truth values"—one for each of the three functions. The vertical line in the image represents a particular temperature that the three arrows (truth values) gauge.

Since the red arrow points to zero, this temperature may be interpreted as "not hot". The orange arrow (pointing at 0.2) may describe it as "slightly warm" and the blue arrow (pointing at 0.8) "fairly cold".

Extra

Fuzzy logic usually uses IF-THEN rules, or constructs.

Rules are usually expressed in the form:IF variable IS property THEN action

There is no "ELSE" – all of the rules are evaluated, because the value might be “true" and “false" at the same time to different degrees.

The AND, OR, and NOT operators of Boolean logic exist in fuzzy logic, usually defined as the minimum, maximum, and complement; when they are defined this way, they are called the Zadeh operators.

Example

IF temperature IS very cold THEN stop fan

IF temperature IS cold THEN turn down fan

IF temperature IS normal THEN maintain level

IF temperature IS hot THEN speed up fan

For example, a simple temperature regulator that uses a fan might look like this:

Review

Fuzzy Logic is a type of logic that recognizes more than simple true and false values.

Prepositions can be represented with degrees of truthfulness and falsehood.

This is a lot more representative of how our brains work.

Resources

Rouse, Margaret. “Fuzzy Logic”. Whatis.com. July 2006. Web. 25 September, 2013. http://whatis.techtarget.com/definition/fuzzy-logic

“Fuzzy Logic Introduction”. Fuzzy Logic and Its Uses. Web. 25 September, 2013. http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol2/jp6/article2.html

Kaehler, Stephen. “Fuzzy Logic – An Introduction” seattlerobotics.org. June 1995. Web. 25 September 2013. http://www.seattlerobotics.org/encoder/mar98/fuz/fl_part1.html#INTRODUCTION

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=10&ved=0CHQQFjAJ&url=http%3A%2F%2Fpayam.malakut.org%2Farchives%2FFuzzy_logic.doc&ei=1XhJUrzcJenk4AO4j4HoDw&usg=AFQjCNEm24XDh03KHs2LDqli68x-Xv0Ckg&sig2=4vsuxq1dypbtG8wgRowCqA

http://blog.peltarion.com/2006/10/25/fuzzy-math-part-1-the-theory/