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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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.
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Fuzzy Set Operations AUB(x) = maks {A(x) , B(x)} AB(x) = min {A(x) , B(x)}
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Stages of Fuzzy Modeling
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Rule Base AND OR A B = min (A, B) A B = maks (A, B)
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Example The users of the heating system wants Less fuel consumption Easy to use Inexpensive More warranty period
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There is; 5 different company (AE) 4 different consumer needs
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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
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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
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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
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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.
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Mamdani Type Fuzzy Inference System All inputs and outputs are fuzzy functions. can easily create compatible with human behavior
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Most comman defuzzification system for this model is the center of gravity method
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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 Markup 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 markup.
The other goal is to create a fuzzy logic model to estimate amount of bid markup in the light of the obtained datas.
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Amount of Bid Markup Bid markup is a component of bidding price which is prepared by construction companies in bidding period.
Amount of bid markup. Gen, A., (2012)
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Factor Titles 61 factors which is contained with the literature survey are divided into 5 titles. 1Factors associated with the employer 2Factors associated with the project 3Factors associated with the firm 4Factors associated with the bidding period and the contract 5Factors 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 markup 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