Erdem

We are surprisingly flexible in processing information in the real world. The real world is up and down, constantly moving and changing, and full of surprises. In other words, fuzzy.

Fuzzy techniques let you successfully handle real world situations. The real world? -Parking a car! -Standing on the doorway -Genes coding the proteins -Drugs acting on genes -Fuzzy pharmacology -Fuzzinnes in Drug Design.......etc...

Fuzzy logic is a type of mathematics and programming that more accurately represents how the human brain categorizes objects, evaluates conditions, and processes decisions. The human brain, consisting of more 100 billions of neurons, realizes intelligent information processing based on exact and commonsense reasoning. Scientists have been trying to implement human intelligence in computers in various ways. Fuzzy logic is a powerful problem-solving methodology with a lot of applications in embedded control and information processing.

Fuzzy provides a remarkably simple way to draw definite conclusions from vague, ambiguous or imprecise information. In a sense, fuzzy logic resembles human decision making with its ability to work from approximate data and find precise solutions.

Fuzzy Logic was initiated in 1965 by Lotfi A. Zadeh , professor for computer science at the University of California in Berkeley.

İt resembles human reasoning in its use of approximate information and uncertainty to generate decisions. It was specifically designed to mathematically represent uncertainty and vagueness and provide formalized tools for dealing with the imprecision intrinsic to many problems.

Soul is defined by Aristotle as the perfect expression or realization of a natural body.

300 years B.C., the Greek philosopher, Aristotle came up with binary logic(0,1), which is now the principle foundation of Mathematics.

Two centuries before Aristotle, Buddha, had the belief which contradicted the black-and-white world of worlds, which went beyond the bivalent cocoon (Yin-Yeng) and see the world as it is, filled with contradictions, with things and not things.

Conventional (Boolean) logic states that a glass can be full or not full of water. However, suppose one were to fill the glass only halfway. Then the glass can be half-full and half-not-full. Clearly, this disprove's Aristotle's law of bivalence. This concept of certain degree or multivalence is the fundamental concept which propelled Lofti Zader

The essential characteristics of fuzzy logic founded by Lotfi Zadeh are as follows; In fuzzy logic, exact reasoning is viewed as a limiting case of approximate reasoning. In fuzzy logic everything is a matter of degree. Any logical system can be fuzzified In fuzzy logic, knowledge is interpreted as a collection of elastic or, equivalently , fuzzy constraint on a collection of variables Inference is viewed as a process of propagation of elastic constraints.

Fuzzy logic is a superset of conventional (Boolean) logic that has been extended to handle the concept of partial truth- truth values between "completely true" and "completely false". As its name suggests, it is the logic underlying modes of reasoning which are approximate rather than exact.

Basically, Fuzzy Logic (FL) is a multivalued logic, that allows intermediate values to be defined between conventional evaluations like true/false yes/no, high/low active/inactive

Crisp sets handle only 0 and 1. Fuzzy sets handle all values between 0 and 1. Characteristics of fuzziness: •Word based, not number based. For instance, hot; not 45°C. • Nonlinear changeable. • Analog (ambiguous), not digital (0/1).

What’s the process of parallel parking a car?

you’ve just performed a series of fuzzy operations.

you’ve just performed a series of fuzzy operations

Peter is in a house the kitchen and the dining room Peter is s either "in the kitchen" or "not in the kitchen”

What about when Peter stands in the doorway? partially in the kitchen (Quantifying this partial state yields a fuzzy set membership) With only his little toe in the dining room, we might say Peter is 99% "in the kitchen" and 1% "in the dining room"

Fuzzy sets are based on vague definitions of sets, not randomness.

Fuzzy is Not Probability In probability you deal with frequencies of events. When you throw a pair of dice, the probability of getting a 2 is 1 in 36. You will get one of the values. In fuzzy you deal with degrees. When you fill a glass ¾ full, is it full or not? Yes to 0.75 degree.

Degrees of truth are often confused with probabilities, although they are conceptually distinct, because fuzzy truth represents membership in vaguely defined sets, not likelihood of some event or condition.

Fuzzy Modeling - The use of “linguistic variables” in place of or in addition to numerical variables. - The characterization of simple relations between variables by “conditional fuzzy statement”. - The characterization of complex relations by “fuzzy algorithms”.

IF e(t) is N IF e(t) is SN IF e(t) is Z IF e(t) is SP IF e(t) is P

THEN THEN THEN THEN THEN

σ = σ1 σ = σ2 σ = σ3 σ = σ4 σ = σ5

N, SN, Z, SP, P are linguistic variables

IF substitution IS very inactive THEN change pattern IF substitution IS inactive THEN try to adjust pattern IF substitution IS promising THEN maintain level AND change other parameters IF substitution IS active THEN stop

Fuzzy Modeling

(1) Fuzzification; (2) Inference (or reasoning); and (3) Defuzzification

Fuzzification is the first step in the computation of a fuzzy system and it must be performed for each input variable. It is a process of mapping the crisp numbers into fuzzy domain using the membership functions of linguistic variables to compute each term’s degree of validity at a specific operation point of the process.

“Intensity of Biological Activity”= 100 - high-degree of validity= 0.8; - medium-degree of validity= 0.4; and - low-degree of validity= 0.2.

Inference is the process of obtaining the outputs of a fuzzy system. The output of a fuzzy algorithm is a fuzzy subset, which is not the crisp number required. The process of retranslating a fuzzy output into a crisp value is termed defuzzification, in which, a defuzzification algorithm (defuzifier) selects a best crisp value to be the output of the fuzzy system. - mean of maximum - the center of area

Goal of Expert Systems - To make expertise available for decision making - To accelerate decision making

• Expert systems

- Rule-based expert systems - Fuzzy rule-based expert systems - Machine learning expert systems

• Case studies

- Car parking - Molecular descriptors

Rule-Based Expert Systems • Human mental process is too complex to be presented as an algorithm • However, most experts are capable to express their knowledge in the form of rules for problem solving IF THEN

the ‘molecular descriptor ’ is well-defined for biological activity the process is on

IF THEN



• Multiple antecedents using AND, OR • Antecedent is in the form of ‘Linguistic object’ Operator Value

IF logP > 4 AND pKa > 1 THEN ............

• Types of rule-based Expert Systems Relation

Recommendation

Directive

Heuristic

Strategy

IF ‘the fuel tank’ is empty THEN the car is dead IF ‘the season’ is autumn AND ‘the sky’ is cloudy THEN the advice is taking umbrella IF ‘the car’ is dead AND ‘the fuel tank’ is empty THEN the action is refuel the car

IF ‘the spill’ is liquid AND ‘the spill pH’ < 6 THEN the spill material is acetic acid IF ‘the car’ is dead THEN the action is checking fuel tank; step 1 complete IF ‘step 1’ is complete AND ‘the fuel tank’ is full THEN the action is checking battery step 2 complete

Basic Structure

Inference Chain

Fuzzy Expert Systems

Basic Fuzzy Operations

• Membership function µ(.)

µ (a AND b) = min [µ(a), µ(b)] µ (a OR b) = max [µ(a), µ(b)]

Fuzzification & Defuzzification in Rule-Based Systems

Biological Activity N3: Large negative N2: Medium negative N1: Small negative Z: Zero P1: Small positive P2: Medium positive P3: Large positive. Rule1: IF logP is low AND BindE is weak THEN BA is P3 Rule1: IF logP is low AND BindE is low THEN BA is P2 Rule1: IF logP is low AND BindE is ok THEN BA is Z Rule1: IF logP is low AND BindE is strong THEN BA is N2

"Fuzzy logic is a generalization of standard logic, in which a concept can possess a degree of truth anywhere between 0.0 and 1.0. Standard logic applies only to concepts that are completely true (having degree of truth 1.0), or completely false (having degree of truth 0.0). Fuzzy logic is supposed to be used for reasoning about inherently vague concepts, such as 'tallness.' For example, we might say that ‘Peter is tall,' with degree of truth of 0.9. MEMBERSHIP FUNCTIONS In Computer Programming, fuzzy logic allows for set membership values between and including 0 and 1, shades of gray as well as black and white, and in its linguistic form, imprecise concepts like "slightly", "quite" and "very". Specifically, it allows partial membership in a set. It is related to fuzzy sets and possibility theory.

The membership function of a fuzzy set A is defined by A, A : X ------> [0, 1]. Let Y(t) ( t = ......, 0, 1, 2, .......) , a subset of R' , be the universe discourse on which fuzzy sets fi (t) (i = 1, 2, ........) are defined and F(t) is a collection of f1 (t) , f2 (t), ....... Then F(t) is called a Fuzzy Time Series defined on Y(t) (t = ...., 0, 1, 2, ......)

Gaussian

Triangular

Trapezoidal

S-shaped

G(u:m,σ)=exp[-{(u-m)/√2σ}2 ]

Λ(u:α,β,γ) = 0 = (u-α)/ (β-α) =( α - u)/( β-α) =0 f(x, a, b, c, d) = 0 = (x - a) / (b - a) =1 =(d - x) / (d - c)

u<α α<=u<=β β<=u<=γ u>γ when x < a and x > d when a <= x <= b when b <= x <= c when c <= x <= d

S(u:α,β,γ)=0 =2[(u-α)/(γ-α)]2 =1-2[(u-γ)/(γ-α)]2 =1

u<α αγ

Fuzzy logic models, called fuzzy inference systems, consist of a number of conditional “if-then" rules. For the designer who understands the system, these rules are easy to write, and as many rules as necessary can be supplied to describe the system adequately (although typically only a moderate number of rules are needed).

fuzzy logic : The fuzzy membership value μ is used for the relationship between the term or object in question where 0<μ<1, and μ corresponds to a fuzzy membership relation such as “strongly”, “partially”, “somewhat”, ” slightly”

In the language of fuzzy sets, degrees of membership vary. This figure represents functions µA , which express the degree of membership of elements x in the set A. µA is a set of ordered pairs in which the first element of the ordered pair is from the set x of temperatures and the second element is degree of membership. A is cold (blue), mild (green), or hot (red); 0 represents nonmembership, 1 represents complete membership, and values in between represent intermediate degrees of membership.

Three basic operations apply to fuzzy sets:

negation, intersection, union. To negate a fuzzy set, simply subtract the membership value in the fuzzy set from 1. For example, the membership value in “cold” at 5 °C is 1. With negation, the membership value at 5 °C becomes 0. The intersection of two sets is the minimum of the two membership values at each point on the x axis. The fuzzy set “cold” has a membership value of 0.7 corresponding to x = 14 °C, and the fuzzy set “mild” has a membership value of 0.3 corresponding to x = 14 °C. The intersection has a membership value of 0.3 at x = 14 °C. The union of two sets is the maximum of the two membership values at each point on the x axis. In Figure, the union of the sets “cold” and “mild” at x = 14 °C has a membership value of 0.7. In mathematical terms:

Negation: µnot A(x) = 1 – µA(x) Intersection: µA∩B (x) = Min [ µA(x), µB (x) ] Union: µA∩B (x) = Max [ µA(x), µB (x) ]

5

9 7

{A: 5, 7, 9}

5

7

6 9

{ A ∪ B: 5, 6, 7, 8, 9, 11} UNION

9

11

{B: 6, 8, 9, 11}

5

11 8

6

8

7

9

6 8

11

{ A ∩ B: 9} INTERSECTION

Membership value

The Fuzzy Process:

Low

Medium

High

Lipophilicity

An AnAssumed Assumed Fuzzy FuzzyExpert ExpertSystem Systemto tostudy studyfor forDrug DrugDesign Design

• Problem statement - Biological Activity Forecasting using some molecular descriptors

• Strategy: Fuzzy rule-based system IF (lipophilicity is optimal AND relative binding energy is medium) THEN (biological activity is quite poor)

An AnAssumed Assumed Fuzzy FuzzyExpert ExpertSystem Systemto tostudy studyfor forDrug DrugDesign Design

Membership value

X1 = Lipophilicity

X1 (Knot)

An AnAssumed Assumed Fuzzy FuzzyExpert ExpertSystem Systemto tostudy studyfor forDrug DrugDesign Design

X2 = Relative Binding Energy Membership value

1,2 1 0,8 Low Medium High

0,6 0,4 0,2

X2 (au)

0 70

75

80

85

90

95

100

An AnAssumed Assumed Fuzzy FuzzyExpert ExpertSystem Systemto tostudy studyfor forDrug DrugDesign Design

Y = Biological Activity Membership value

1,2 1 0,8

Poor Quite poor Quite good Good

0,6 0,4 0,2

Y (Level)

0 0

1

2

3

4

5

6

7

An AnAssumed Assumed Fuzzy FuzzyExpert ExpertSystem Systemto tostudy studyfor forDrug DrugDesign Design

R1: R2: R3: R4: R5: R6:

IF (logP is rather low AND BindE is low) THEN (BA is quite good) IF (logP is low AND BindE is low) THEN (BA is quite good) IF (logP is rather low AND BindE is med) THEN (BA is quite poor) IF (logP is light AND BindE is med) THEN (iBA is quite poor) IF (logP is rather low AND BindE is high) THEN (BA is quite poor) IF (logP is low AND BindE is high) THEN (BA is quite poor)

The process is similar to the mentioned fuzzy rule-based systems

(a) First, the observed concentration range for a parameter in an area, such as concentration of required biological activity normalized to a convex fuzzy interval. (b) Next, experts determine what concentrations constitute “very good”, “good”, “fair”, and “poor”. values that all experts assign get a membership value of 1, and values that no experts assign get a membership value of 0. (c) Finally, a degree of match (DM) operator is used to determine the overlap (shaded area) between (a) and (b). Here, the DM between the observed concentration range and the fuzzy set “very good” is shown.

Advantages of Fuzzy Logic for System Control • • • •

• • • • • •

Fewer values, rules, and decisions are required. More observed variables can be evaluated. Linguistic, not numerical, variables are used, making it similar to the way humans think. It relates output to input, without having to understand all the variables, permitting the design of a system that may be more accurate and stable than one with a conventional control system. Simplicity allows the solution of perviously unsolved problems. Rapid prototyping is possible because a system designer doesn’t have to know everything about the system before starting work. They’re cheaper to make than conventional systems because they’re easier to design. They have increased robustness. They simplify knowledge acquisition and representation. A few rules encompass great complexity.

Expert Systems - Rule-based (inc. Fuzzy) - Machine learning Mainly used for forecasting, problem solving, decision making

Machine Learning Experts • Most of learning machines can be used in expert systems - Artificial neural network (ANN) - Support vector machines (SVM) - Decision tree (DT)

2007/1 AI - TU

42

Artificial Neural Networks

x : Input vector y : Output value h : Number of hidden layer wi : Weight value vi : Weight vector that is multiplied with input f(x) : Activation function(transfer function) α : constant

Integration of Fuzzy Logic with Neural Network

The integration of the techniques of fuzzy systems and NNs suggests the novel idea of transforming the burden of designing fuzzy systems to the training and learning of the NNs. The NNs provide learning ability to the fuzzy systems, whereas the fuzzy systems offer NNs a structure framework with high level IF-THEN rule thinking and reasoning. The neural fuzzy system, one form of integration of fuzzy systems and NNs, is a fuzzy system that uses a learning algorithm derived from or inspired by NN theory to determine its parameters (fuzzy memberships and fuzzy rules) by processing data. In order words, neural fuzzy systems aim at providing fuzzy systems with automatic tuning method of NNs, but without altering their functionality. In a neural fuzzy system, the NN helps the fuzzy system to elicit membership functions, map fuzzy sets to fuzzy rules, and implement defuzzification.

Neuro-Fuzzy Modeling The process of construction a neural fuzzy system is called “neuro-fuzzy modeling”. It consists of the design of a fuzzy system and a NN that equips the fuzzy system with learning capability. Generally, the commonly used fuzzy systems are rulebased fuzzy system, and the NNs used are mainly multi layer feedforward networks with the back-propagation learning algorithm.

Fuzzy inference networks, Fuzzy aggregation networks, Neural network-driven fuzzy reasoning, fuzzy modeling networks, ANFIS (adaptive neuro-fuzzy inference system), Fuzzy associative memory systems.

Fuzzy Logic Software * Matlab * Aptronix (www.aptronix.com) * Mathworks (www.mathworks.com) * FuzzyTech (www.fuzzytech.com)

REFERENCES 1. LOTFI A. ZADEH, Is there a need for fuzzy logic? Information Sciences, 178, 2751-2779 (2008). 2. THOMAS E. MCKONE UNIV ERSIT Y OF CALIFORNI A, BERKELEY, LAWRENCE BERK ELEY NATIONAL LABOR ATORY Can Fuzzy LOGIC Bring Complex Environmental Problems into Focus? Environmental Science & Technology, 42A-47A (2005). 3.

MARCUS C. HEMMER EXPERT SYSTEMS IN CHEMISTRY CRC PRESS, TAYLOR & FRANCIS GROUP, NEW YORK, 2008.

4.

F. MARTIN McNEILL, ELLEN THRO FUZZY LOGIC – A PRACTICAL APPROACH ACADEMIC PRESS Inc., 1994

5.

S. N. SIVANANDAM, S. SUMATHI and S. N. DEEPA Introduction to Fuzzy Logic using MATLAB SPRINGER, BERLIN, 2007