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Don Baechtel

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Introduction to Fuzzy Logic in Artificial Intelligence
Don Baechtel
• Architect and Principal Systems Engineer

• 33 years experience in Robotics and Industrial Automation

• Expert in Process Control, Motion Control, PID Control

• Real Time Systems and Industrial Communications

• Graphical Programming and Domain Specific Languages

• Experience in Fuzzy Logic and Evolutionary Algorithms

• Microsoft .Net Technologies

• Cloud Computing and Web Oriented Applications

• 8 U.S. Patents

• Member NE-Ohio-Artificial-Intelligence-Group

What Is Fuzzy Logic ?
• Form of multi-valued logic (algebra) derived from fuzzy set theory.

• Designed to deal with reasoning that is approximate rather than accurate.

• Consequence of the 1965 proposal of fuzzy set theory by Lotfi Zadeh.

• In contrast with "crisp logic", where binary sets have binary logic,

fuzzy logic variables may have a truth value that ranges between 0 and 1.

• Is not constrained to the two truth values of classic propositional logic.

• Can include linguistic variables, like: high, low, hot, cold, and very.

Has been applied to many fields, from control theory to artificial intelligence

Fuzzy Logic

Membership Functions
• Membership Functions are subranges of a continuous variable.

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

• Membership functions can take any shape as long as sum at any point = 100%.

• A “crisp” temperature reading converted to n-tuple {80% cold, 20% warm, 0% hot}.

• May be described as “fairly cold, slightly warm and not hot”.

• Membership Function definitions can be adaptively tuned.

Fuzzy Set Theory
• Fuzzy Set Theory defines fuzzy operators on fuzzy sets.

• Fuzzy Logic usually uses IF-THEN rules, or constructs that are equivalent,

such as fuzzy associative matrices.

• 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 temperature

might be both "cold" and “warm" 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.

• So for the fuzzy variables x and y:

NOT x = (1 - truth(x))

x AND y = minimum(truth(x), truth(y))

x OR y = maximum(truth(x), truth(y))

• There are also operators, more linguistic in nature, called hedges that can be applied.

These are generally adverbs such as "very", or "somewhat", which modify

the meaning of a set.

• Multiple overlapping rules provide a “consensus” type output.

Example Fuzzy Ruleset
A simple Fuzzy temperature regulator that uses a fan might look like this:

IF temperature IS very cold THEN stop fan.

IF temperature IS cold THEN turn down fan.

IF temperature IS comfortable THEN maintain fan speed.

IF temperature IS hot THEN speed up fan.

Fuzzy Ruleset Evaluation
Notice how each rule provides a result as a truth value of a particular membership function for the output variable. In centroid defuzzification the values are OR'd, that is, the maximum value is used and values are not added, and the results are then combined using a centroid calculation. The result or answer(s) provided by the Fuzzy Logic ruleset is a combination or consensus of all of the rules taken together and then frequently converted to a “crisp” value using one of the defuzzification techniques

Fuzzy Defuzzification Methods
• AI (adaptive integration) DOI 10.1109/ICMNN.1994.593726

• BADD (basic defuzzification distributions)

• CDD (constraint decision defuzzification)

• COA (center of area)

• COG (center of gravity)

• ECOA (extended center of area)

• EQM (extended quality method)

• FCD (fuzzy clustering defuzzification)

• FM (fuzzy mean)

• FOM (first of maximum)

• GLSD (generalized level set defuzzification)

• ICOG (indexed center of gravity)

• IV (influence value) DOI 10.1109/FUZZY.1996.552647

• LOM (last of maximum)

• MeOM (mean of maxima)

• MOM (middle of maximum)

• QM (quality method)

• RCOM (random choice of maximum)

• SLIDE (semi-linear defuzzification)

• WFM (weighted fuzzy mean)

Fuzzy Applications
• Fuzzy Control Systems

• Expert Systems

• Fuzzy Databases

• Fuzzy Search Engines

• Fuzzy Data Mining

• Fuzzy Enhanced Programming Languages

• Sensor Data Fusion

Redundant Systems

Artificial Neural Networks
The original inspiration for the term Artificial Neural Network came from examination of central nervous systems and their neurons, axons, dendrites and synapses which constitute the processing elements of biological neural networks investigated by neuroscience. In an artificial neural network simple artificial nodes, called variously "neurons", "neurodes", "processing elements" (PEs) or "units", are connected together to form a network of nodes mimicking the biological neural networks — hence the term "artificial neural network".

Because neuroscience is still full of questions and because there are many levels of abstraction and many ways to take inspiration from the brain, there is no single formal definition of what an artificial neural network is. Most would agree that it involves a network of simple processing elements which can exhibit complex global behavior determined by the connections between the processing elements and element parameters. While an artificial neural network does not have to be adaptive per se, its practical use comes with algorithms designed to alter the strength (weights) of the connections in the network to produce a desired signal flow.

These networks are also similar to the biological neural networks in the sense that functions are performed collectively and in parallel by the units, rather than there being a clear delineation of subtasks to which various units are assigned (see also connectionism). Currently, the term Artificial Neural Network (ANN) tends to refer mostly to neural network models employed in statistics, cognitive psychology and artificial intelligence. Neural network models designed with emulation of the central nervous system (CNS) in mind are a subject of theoretical neuroscience and computational neuroscience.

In modern software implementations of artificial neural networks, the approach inspired by biology has been largely abandoned for a more practical approach based on statistics and signal processing. In some of these systems, neural networks or parts of neural networks (such as artificial neurons) are used as components in larger systems that combine both adaptive and non-adaptive elements. While the more general approach of such adaptive systems is more suitable for real-world problem solving, it has far less to do with the traditional artificial intelligence connectionist models. What they do have in common, however, is the principle of non-linear, distributed, parallel and local processing and adaptation.

Differences:

Fuzzy Logic vs. Neural Networks