Artificial Intelligence for Games

Lecture 5

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Minor Games Programming

Artificial Intelligence for Games

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Theory: Short introduction to Fuzzy Logic

Jan Verhoevenj.verhoeven@windesheim.nl

Theory: Fuzzy Logic,(see study book: chapter 10)

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Crisp and Fuzzy Sets with Operators Fuzzy Rules Fuzzy Inference Procedure

Coding a Fuzzy Logic Module Fuzzy Logic Classes in Raven The Combs Method

Fuzzy Logic:how to make perfect cheese on toast:

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1. Cut two slices of bread medium thick.2. Turn the heat on the griddle on high.3. Grill the slices on one side until golden

brown.4. Turn the slices over and add a generous

helping of cheese.5. Replace and grill until the top of the cheese

is slightly brown.6. Remove, sprinkle on a small amount of

black pepper, and eat.

intermezzo

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What is medium thick ?

1 cm?

And what about 0,999 cm?

Discrete intervals are sometimes to rigid.

Fuzzy Logic

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Fuzzy logic, invented by a man named Lotfi Zadeh in the mid-sixties, enables a computer to reason about linguistic terms and rules in a way similar to humans

Fuzzy rule-based inference

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Crisp Sets,an object belongs to a set or it doesn’t

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Crisp Sets,a graphical way of showing your IQ

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Dumb = {70, 71, 72, … 89} Average = {90, 91, 92, … 109} Clever = {110, 111, 112, … 129}

Fuzzy Sets

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Dumb = {60, 61, …, 100} Average = {80, 81, … 120} Clever = {100, 101, … 140}

Defining Fuzzy Boundaries with Membership Functions

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DOM (degree of membership)

fuzzy set, Membership value, DOM

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The dotted line shows the IQ of 115, which is a member of two sets:m(115) = { Average/0.25, Clever/0.75 }

Another example:m(80) = {Dumb/1.0, Average/0.0} = {Dumb/1.0}

Note:0.25 = membership degree (DOM)

Exercise Time -1-

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Student X owns a IQ of 110 What are his degrees of membership in Dumb,

Average and Clever?

Figure 10.6: The set of people who are Average AND Clever

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Figure 10.7: The set of people who are Average OR Clever

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Figure 10.8: The complement of Clever

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Exercise Time -2-:Draw Fuzzy Sets

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1. The fuzzy set A = NOT (Average OR Dumb)2. The fuzzy set: B = (Average AND Clever) OR

(NOT Dumb)

Exercise Time -3-

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1. What is DOM of student X with an IQ of 110 in fuzzy set A?

2. And in fuzzy set B?

3. Which IQ belongs to a DOM value of 0.5 in fuzzy set A?

4. And in fuzzy set B?

Hedges

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Hedges are unary operators that can be employed to modify the meaning of a fuzzy set. Two commonly used hedges are VERY and FAIRLY

Fuzzy Modifiers

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Possible fuzzy definitionsvery(a) = a2

extremely(a) = a3

moreorless(a) = a1/2

slightly(a) = a1/3

exactly(a) = a+

always(a) = a0

Example: DOM(90) in fuzzy set: Very(Dumb) is (0.5) 2

Fuzzy Linguistic Variables (or FLV)

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A fuzzy linguistic variable (or FLV) is the composition of one or more fuzzy sets to represent a concept or domain qualitatively.

Given our earlier example, the sets Dumb, Average, and Clever are members of the fuzzy linguistic variable IQ.

This can be written in set notation as:

IQ ={Dumb, Average, Clever}

Designing FLV’s

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There are a couple of important guidelines to adhere to when designing FLVs. They are:

For any vertical line (representing an input value) drawn through the FLV, the sum of the DOMs in each of the fuzzy sets it intersects with should be approximately 1. This ensures a smooth transition between values over the FLV's fuzzy manifold (the combined shape of all membership sets).

For any vertical line drawn through the FLV, it should only intersect with two or fewer fuzzy sets.

Badly designed FLV’s:

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Fuzzy Rules

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Fuzzy rules are comprised of an antecedent and a consequent in the form:

IF antecedent THEN consequent

The antecedent represents a condition and the consequent describes the consequence if that condition is satisfied. This type of rule is familiar to all programmers.

Fuzzy Rules Examples

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IF Target_isFarRight THEN Turn_QuicklyToRight

IF VERY(Enemy_BadlyInjured) THEN Behavior_Aggressive

IF Target_isFarAway AND Allegiance_isEnemy THEN Shields_OnLowPower

IF MOREORLESS(Coffee_Break_Time) AND EXTREMELY(Sleepy) THEN Take_A_Cup

Fuzzy Inference

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This is where we present the system with some values to see which rules fire and to what degree. Fuzzy inference follows these steps:

1. For each rule,a) For each antecedent, calculate the degree of

membership of the input data.b) Calculate the rule's inferred conclusion based upon the

values determined in 1a.2. Combine all the inferred conclusions into a single

conclusion (a fuzzy set).3. For crisp values, the conclusion from 2 must be

defuzzified.

Fuzzy rule-based inference

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An Example:Weapon Selection in RAVEN

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Steps:1. Designing FLVs for Weapon Selection2. Designing the Rule Set for Weapon Selection3. Fuzzy Inference

To keep the example simple, we'll say the desirability of selecting a particular weapon from the inventory is dependent on two factors: the distance to the target and the amount of ammo

Example Raven:FLV Desirability (consequent)

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Example Raven:antecedent: Distance to Target

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Example Raven:Designing the Ammo Status FLV (for each weapon type)

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Example Raven:Designing the Rule Set for Weapon Selection -1-

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To cover all the possibilities, a rule must be created for each possible combination of antecedent sets.

The FLVs Ammo Status and Distance to Target each contain three member sets, so to cover every combination nine rules must be defined.

The rules must be defined by an expert user!

Example Raven:Designing the Rule Set for Weapon Selection -2-

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Rule 1. IF Target_Far AND Ammo_Loads THEN Desirable Rule 2. IF Target_Far AND Ammo_Okay THEN Undesirable Rule 3. IF Target_Far AND Ammo_Low THEN Undesirable Rule 4. IF Target_Medium AND Ammo_Loads THEN

VeryDesirable Rule 5. IF Target_Medium AND Ammo_Okay THEN

VeryDesirable Rule 6. IF Target_Medium AND Ammo_Low THEN Desirable Rule 7. IF Target_Close AND Ammo_Loads THEN Undesirable Rule 8. IF Target_Close AND Ammo_Okay THEN Undesirable Rule 9. IF Target_Close AND Ammo_Low THEN Undesirable

Example Raven:Fuzzy Inference

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Let's now work through these steps using some of the rules we've created for weapon selection and some crisp input values.

Let's say the target is at a distance of 200 pixels and the amount of ammo remaining is 8 rockets.

One rule at a time then…

Example Raven:Fuzzy Inference, Rule One

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IF Target_Far AND Ammo_Loads THEN Desirable

Example Raven:Fuzzy Inference, Rule Two

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IF Target_Far AND Ammo_Okay THEN Undesirable

Example Raven:Fuzzy Inference, Rule Three

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IF Target_Far AND Ammo_Low THEN Undesirable

EXERCISE TIME

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Fuzzy Inference, Rule 5:

IF Target_Medium AND Ammo_Okay THEN VeryDesirable

Draw and compute the inferred conclusion for VeryDesirable

Example Raven: Rules one to nine in fuzzy associative matrix (FAM)

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Inferred conclusions

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Undesirable 0.33 (maximum value of 0.33 and 0.2)

Desirable 0.2 Very Desirable 0.67

The inferred results of processing the rule set for weapon selection

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Combining the conclusions

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Defuzzification

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Now that we have a composite fuzzy set representing the inferred conclusion of all the rules in the rule base, it's time to turn the process around and convert this output set into a single crisp value. This is achieved by a process called defuzzification.

Many techniques are possible (see study book): Mean of Maximum (MOM) Centroid Average of Maxima (MaxAv)

Example Raven:Defuzzification

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Mean of Maximum (MOM) 83

Centroid 62

Average of Maxima (MaxAv) 60.625

Example Raven:Selection

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If this whole process is repeated for each weapon type a bot is carrying, it's a simple matter to select the one with the highest desirability score to be the weapon the bot should use given its current situation.

Homework

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Homework Study Chapter 10 Fuzzy Logic, pages 415 to 437.

Practice (next TUESDAY)

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Program a fuzzy (console) application in C++.

You must use the FuzzyModule Class (and others) of Buckland, see study book pages 437 to 452. The sources will be on Blackboard.

For an example see weapon selection code in Raven.

TIP: Use your study book during next practice!