Fuzzy Logic

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FUZZY LOGICManagement Mathematics Assoc. Prof. Dr. Gl Polat TATAR

Ekin ERAY Emre GKYT1

Content Introduction History of Aristo Logic and Fuzzy logic Stages of fuzzy modeling An Academic example Conclusion References

ITU Graduate School of Science Engineering & Technology Construction Management

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ARSTO LOGIC

FUZZY LOGIC

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Triangle Type Fuzzy Functions

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Trapeze Type Fuzzy FunctionsA(x)

1

a1

a2

a3

a4

x

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ITU Graduate School of Science Engineering & Technology Construction Management

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Assingment of Membership Degree Intuition Logic Experience

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How to Create a Fuzzy Functions? Discuss with people who know about the subject and than make an arrangement Trial and error Use the data directly and make arrangement.

ITU Graduate School of Science Engineering & Technology Construction Management

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Fuzzy Set Operations AUB(x) = maks {A(x) , B(x)} AB(x) = min {A(x) , B(x)}

ITU Graduate School of Science Engineering & Technology Construction Management

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Stages of Fuzzy Modeling

ITU Graduate School of Science Engineering & Technology Construction Management

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Rule Base AND OR A B = min (A, B) A B = maks (A, B)

ITU Graduate School of Science Engineering & Technology Construction Management

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Example The users of the heating system wants Less fuel consumption Easy to use Inexpensive More warranty period

ITU Graduate School of Science Engineering & Technology Construction Management

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There is; 5 different company (A-E) 4 different consumer needs

ITU Graduate School of Science Engineering & Technology Construction Management

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1st need: FUEL Company A: Fuel consumption is good Company B: Fuel concumption is high Company C: Fuel consumption is low Company D: Fuel consumption is normal Company E: Fuel consumption is good

ITU Graduate School of Science Engineering & Technology Construction Management

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2nd need: USAGE Company A: Usage is quite hard Company B: Usage is quite easy Company C: Usage is easy Company D: Usage is easier Company E: Usage is hard

ITU Graduate School of Science Engineering & Technology Construction Management

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3th need: WARRANTY Company A: 7 years. Company B: 8 years. Company C: 5 years. Company D: 6 years. Company E: 8 years

G 0,7 / a 0,8 / b 0,5 / c 0,6 / d 0,8 / e

ITU Graduate School of Science Engineering & Technology Construction Management

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4th need: COST(x)

Company A: 40 Company B: 50 Company C: 60 Company D: 20 Company E: 45

M M M M M

1,0

0,8

0,80,6 0,5 0,5 5 0,4

xc b e a d

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Intersections of all sets.

G 0,7 / a 0,8 / b 0,5 / c 0,6 / d 0,8 / e

We should choose the max mambership value from this set. Best heating system company is D.ITU Graduate School of Science Engineering & Technology Construction Management Fuzzy Logic 18

Most Common Defuzzification Process Maximum membership method The center of gravity method Weighted average method Avarage maximum membership method.

ITU Graduate School of Science Engineering & Technology Construction Management

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Mamdani Type Fuzzy Inference System All inputs and outputs are fuzzy functions. can easily create compatible with human behavior

ITU Graduate School of Science Engineering & Technology Construction Management

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Most comman defuzzification system for this model is the center of gravity method

ITU Graduate School of Science Engineering & Technology Construction Management

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Sugeno Type Fuzzy Inference System Duductive part (THEN) of the system is a simple mathematical function of the premise part. It can be a constant or a linear function. IF x=A AND y=B THEN z=f(x,y)=px+qy+r

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ADVANTAGES Easy to compute Works well with the other techniques suitable for mathematical analysis

DISADVANTAGES Not compatible with human behavior

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A Fuzzy Logic Implementation

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Thesis Modeling Bid Mark-up of International Construction Projects with Fuzzy LogicGen, A., 2012 Uluslararas naat Projelerinde Katk Paynn Bulank Mantk ile Modellenmesi, T Yap letmesi.

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Goal of the Thesis The goal of the survey is determining importance levels of factors that affects amount of bid mark-up.

The other goal is to create a fuzzy logic model to estimate amount of bid mark-up in the light of the obtained datas.

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Amount of Bid Mark-up Bid mark-up is a component of bidding price which is prepared by construction companies in bidding period.

Amount of bid mark-up. Gen, A., (2012)

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Factor Titles 61 factors which is contained with the literature survey are divided into 5 titles. 1-Factors associated with the employer 2-Factors associated with the project 3-Factors associated with the firm 4-Factors associated with the bidding period and the contract 5-Factors associated with the economical milieu and the riskITU Graduate School of Science Engineering & Technology Construction Management Fuzzy Logic 30

Survey 16 firms with 39 different project participated to survey. The questionnaire which is generally answered by bidding department managers, is provided a reliable database.

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Ranking The factors that affects amount of bid markup, ranked on an importance scale from 1 to 5 by the company representatives. 1: very low 2: low 3: medium 4: high 5: very highITU Graduate School of Science Engineering & Technology Construction Management Fuzzy Logic 32

Fuzzy Logic Modeling As complexity rises, precise statements lose meaning and meaningful statements lose precision Lotfi Zadeh

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Fuzzy Logic Modeling Fuzzy logic modeling doesnt need any acceptation contrary to statistical and stochastic processes. This is the most important advantage of fuzzy logic modeling. In order to create this kind of model, the logical relations between input and output datas should be exposed.ITU Graduate School of Science Engineering & Technology Construction Management Fuzzy Logic 34

Method of Working 5 input data for the fuzzy logic model (Employer Factor, Project Factor, Firm Factor, Bidding Period and Contract Factors, Economical Milieu and Risk Factors) and an output data (Total estimated amount of bid mark-up which is estimated as a percentage of construction cost).ITU Graduate School of Science Engineering & Technology Construction Management Fuzzy Logic 35

Method of Working Mamdani type of fuzzy logic modeling method is used because of easily creating and its compatibility with the human behaviour and senses. MATLAB package program was used for creation of the model.

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Method of Working

Mamdani type of fuzzy logic model. Gen, A., (2012)37

ITU Graduate School of Science Engineering & Technology Construction Management

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Method of Working Fuzzification - First of all, fuzzification of input and output datas is required in order to create a fuzzy logic model. - The fuzzification comprises the process of tra