Basic Decision Theory

GIS Asia Link 2 : Course of Rehabilitation and Monitoring Degraded Forest in Southeast Asia

Material Discussion AHP and Land Zoning decision Muhamad Buce Saleh Tatang Tiryana

• Basic Decision Theory • Basic Theory of AHP • Case Study on Land use planning in Puncak Bogor

Department of Forest Management Faculty of Forestry IPB

Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana


Decision urgencies… urgencies…. • For human’s life:

Material 1:

Basic Decision Theory


– Facing the problems: • Gap between the real and hopes

– Generally the problems are complicated, – The resources always limited for solving the problems, – Then decision should be made – even if we do nothing is a decision


Ways of explaining reality

Sea Snow Phenomenon




MODEL Limitation Characters of MODEL: 1. Generality 2. Precision 3. Reliable In general a model only fulfilled 2 among 3 characters model above



Decision urgencies …(2)

Decision urgencies…(3) • Decision are not easy, because of:

– How to chose the best school for our children? – How to chose our vehicles? Which one I have to chose …??? – etc?

– The problems are really complicated – The limitation of human’s brain – Non-linear utilities: Rating sale

• Examples:

Cost of promotion (Rp)

– Most of the criteria are contradictive or conflicting • For example: we want a good car but cheap …????

– Measurement technique are difficult: • We should combine the data with difference scale • No scale for qualitative factors Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana


How to implement decision? • Stages of decision (Herbert Simon, 1960): Intelligence

Are there any problems?

Design

Are there any solution?

Choice

Implementation Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana

A common use in decision • Usually decision made by method: BOGSAT (a Bunch of Old Guys/Gals Sitting Around Talking) Procedural stages: • Collecting the data/information, • Analyzing the data/information, • Discussing • Take a Decision

Which Alternative solution to chose?

Are the choices effective? Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana


A common use in decision…(2)

Decision theories development – other subjects:

• weaknesses of BOGSAT: – Dominated by only a few people – Ignore the cognitive limitation: • BOGSAT have to discussed many thing in one time (e.g. problem, alternatives, goal, criteria, etc), • Though human brain have a limited capacity (up to 7 items)

– There is a satisfying principles, only concern with the alternatives which proposed – aspiration of the group: • Limited to find more information for evaluate other alternatives

Sumber: Forman & Selly (2002) Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana


• Value System: a belief that used in natural resources management with or without consciousness – Efficiency – Precautionary – Equity • Preference: a knowledge, experiences, etc – Time Preference – Risk Preference • Information: data or information that we have – Quantitative/qualitative – Type of data: nominal, ordinal, cardinal, ratio2 Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana

Decision Situation (ADAPTED FROM EPA, 2000; STERN & FINEBERG, 1996; KØ KØRNØ RNØV & THISSEN, 2000).


Decision Framework

Foundation of a decision

Compatibility with/usability of decision principles in DAFs: – weak but not impossible; + possible but not central; * essential essential feature of DAF (Sub--national); L=Local (community); M = Micro (Family, Level of application: G = Global; I=Inter/SupraI=Inter/Supra-national; N=National; R = Regional/Sectoral (Sub firm, farm); X = All Typical domain of application: D=Direct intervention; I=Indirect I=Indirect influence; B=Both Uncertainty treatment: Rigor: * high; + good; – moderate/low Form: St=Model structure; SA=Sensitivity analysis; Sc=Scenarios Sc=Scenarios Source: Joseph Alcamo [et al.]. 2003.


History of Decision Theory



Data as source of decision

Measurement Techniques in Decision • • • • • • • •

Ranking Rating Pairwise comparison Utility theory Probability Theory Posterior/Subjective probability (Bayesian) DempsterDempster-Shafer Fuzzy


60

Ordinal

Number not always as it is - seen …!

Mathematical Operation

Scale Nominal Ordinal

Nominal

• Human weight

6 5 1

3

: 7000

• What operation should be done with number…!!!

Ratio Interval

2

Total

Measurement Scale…(2)

• What kind of analysis?

9

• Human Population : 5000 • Animal Population : 750 • Area : 1250


Measurement Scale

• Number of runner

• Decision based on data/information, • But, be careful on data….!!!

• Ranking winner

• Performance rating on scale 0 - 10


Decision Method

Interval

Ratio

+/-

No

No

Yes

Yes

x/:

No

No

Yes

Yes

Mathematical Function

-

-

Y=aX+b

Y=aX


MADM method classification

• Popular Decision Method PK : “Multi-criteria decision making (MCDM)” – Consisted of 2 groups: • MODM (multi-objective decision making): – Decision space is continue – Alternatives choices based on several objectives that are conflicting • MADM (multi-attibute decision making): – Decision space is discrete (alternatives is limited and have determined before) – Alternatives choices based on attributes (criteria) which are conflicting for a certain goal Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana


©Yoon & Hwang (1995)


Characteristics of MADM – Alternatives: • Several action that will be prioritized • Number of action limited

– Multi Attribute (goals, criteria): • Used for evaluating the alternatives • Each problem has specific attribute:

Characteristic of MADM…(2) – Weight for attributes: • Relative Important level for each attributes • Can be determined directly or using a certain method (example: pairwise comparison AHP)

– Decision Matrix: • column represent attributes • row represent alternatives

– Examples when we chose the car: price, comfort ability, safety, etc.

– Measurement scale are different. Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana


How to conduct MADM ? • 3 stages : 1) Determined the relevant criteria and alternatives 2) Used numerical scale for relative important level of criteria and alternatives 3) Calculated and Analysis the numerical values to determined priority/ranking of alternatives


AHP? • Introduced and developed by Dr. Thomas L. Saaty at early 1970 period • One of MCDA methods which explained a complicated problem through a simple way as follow: – Structurized the problem into hierarchical form – Put a numerical value to determined important level for one element compare with other element – Synthesizing to get priority of alternatives solution


Material 2:

Basic Theory of AHP


Basic concept AHP • Decomposition : put the problem into hierarchical form • Priority determination through pairwise comparison • Priority Synthesizing • Evaluate inconsistency



Why AHP?

AHP Procedure

• Helpful in organizing the elements of problem into a hierarchy form: – Fit with human natural thinking to analyzed a complex problem

• Determination of important level conducted carefully: – Pairwise comparison more intuitive

• Integration of qualitative and quantitative data: – qualitative: judgment, preference – quantitative: measurement result (e.g. price, cost, etc) Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana

1. Problem definition 2. Organized elements of problem into hierarchy 3. Assessment the criteria and alternatives 4. Determined the relative priority 5. Evaluated consistency index 6. Synthesis the alternatives priority Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana

1. Problem definition • Problem:

2. Hierarchy framing • Basic Structure AHP:

– Gap between the recent condition (what is) and the expectation (what should be)

Goal Goal

Goal Goal

• Problem Identification: – What goal/objectives should be achieved? – What criteria and sub-criteria which are suitable? – What are alternatives solution?


Criteria Criteria

K1 K1

K2 K2

K3 K3

K4 K4

Alternatives Alternatives

A1 A1 A2 A2

A1 A1 A2 A2

A1 A1 A2 A2

A1 A1 A2 A2

A3 A3

A3 A3

A3 A3

A3 A3


2. Hierarchy framing …(2)

2. Hierarchy framing …(3) Generally there are 2 models of AHP:

• Structure expanded:

1. Relative measurement model:

Goal

Goal

Scenario

Actor

Criteria & Sub-criteria

Criteria & Sub-criteria

• • •

Alternatives Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana

Alternatives

If alternative solution has known exactly (maximum 9 alternative), then Alternatives can be compared one to others directly Example: choice 3 alternative cars

2. Absolute measurement model: • • •

If alternative solution has not known well or might be the number is too many Alternatives rated by a certain standard Example: - rating model for student selection




3. Criteria and Alternative assessment

• Example of relative model: The Thebest bestcar carfor forfamily family

Goal Goal

Price Price

Criteria Criteria

Alternative Alternative

Prestige Prestige

Toyota Toyota Kijang Kijang

BMW BMW

Multiuse Multiuse

Suzuki Suzuki Karimun Karimun


• Conducted for each hierarchy level to determined the relative important value between one and other element • Pairwise comparison used: – Data (measurement results), or generally used – Scale 1-9



2. Hierarchy framing …(6) • Struktur hierarki PHTL LEI: model rating

• Example absolute model:

Pengelolaan Hutan Tanaman Lestari (PHTL)

TUJUAN

The Thebest bestcar carfor forfamily family

Goal Goal

Prestige Prestige

Multiuse Multiuse KRITERIA

Intensity IntensityScale Scale

Cheap Cheap Expens Expens

Low Low

Medium Medium High High

Less Less

More More

Kelestarian Sumberdaya

Kelestarian Hasil Hutan

Kelestarian Usaha

Kelestarian Kualitas Lahan dan Air

Kelestarian Keanekaragaman Hayati

Kelestarian Akses & Kontrol Komuniti

Kelestarian Integrasi Sosial dan Budaya

Pm-K

MH

Pn-K

Pg-K

Alternative Alternative (all (alltype typeand andtrade trademark markin inmarket) market)

KP

PK

KL

KS

PO

PSDM

MK MH PK

MKeu

INDIKATOR INDIKATOR

Pm-K Pn-K Pg-K KP KL KS PO PSDM MKeu

NILAI (SKALA INTENSITAS) NILAI (SKALA INTENSITAS)


3. Criteria and Alternative assessment …(2)

Value 1 3 5 7 9 2,4,6,8

Statement Criteria/alternative A and B equally important A little more important than B A clearly more important than B A very clearly more important than B A absolutely more important than B If feel hesitated between two close values

Reciprocal value (1/3, 1/5,…) used if B more important than A


Kelestarian Hubungan Tenaga Kerja

Keterangan :

MK

PROSES

SUB-PROSES

Alternative Alternative

Kelestarian Fungsi Sosial Ekonomi dan Budaya

Kelestarian Fungsi Ekologi/Lingkungan

Kelestarian Fungsi Produksi

PRINSIP

Price Price

Criteria Criteria

: Manajemen Kawasan : Manajemen Hutan : Penataan Kelembagaan : Pemantapan Kawasan : Penataan Kawasan : Pengamanan Kawasan : Kelola Produksi : Kelola Lingkungan : Kelola Sosial : Penataan Organisasi : Peningkatan Sumberdaya Manusia : Manajemen Keuangan


3. Criteria and Alternative assessment …(3) • Assessment results put on pairwise comparison matrix (PCM) • Example PCM (1): criteria level – “Which criteria is more important and how much important?” Criteria

Price

Multiuse

Prestige

1

3

4

Multiuse

1/3

1

2

Prestige

1/4

1/2

1

Price



Interruption… Interruption…!!!

3. Criteria and Alternative assessment …(4) • Example PCM (2): alternative level – “From prestige aspect, which car more important and how much important?” Prestige

BMW

Kijang

Karimun

BMW Kijang Karimun

1 1/3 1/7

3 1 1/5

7 5 1

If only determined the weight, why we should use pairwise comparison? I think easier to determined directly such as for example: 0,4??

But why 0,4? Why not 0,45? Then here in AHP, when determined the weight not careless…!!!

”it is better to be approximately right than precisely wrong”

• If n element, then the total number of comparison: n(n-1)/2 Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana


3. Criteria and Alternative assessment…(5) • How if assessment conducted by group? – Better if group made a consensus: • Discussion and argues should be done before coming with one value

– Value based on consensus used in PCM OK, we deal with that price is 3 time more important than prestige..!!!


4. Priority determination • Each element (criteria, alternative) in hierarchy has relative weight: – To show priority/important relatively

• Weight get from PCM: – Calculate eigen value (eigenvector)


3. Criteria and Alternative assessment …(6)

• How if there is no consensus among the group? – Used mean geometric from individual assessment: – Example: x = n x1.x2....xn A=2B A=3B

A=7B

A=5B

Mean-geo: A = 3,8B

x = 4 (2).(3).(5).(7) = 3,8


4. Priority determination …(2) • Calculation methods (eigen value): – According to Saaty: power method – Procedure: • Squared the matrix • Calculate sum of number for each row, then normalized (divided by total sum) • Iterated until we get the deviation value between two iteration is very small (not change in 4 decimal)



4. Priority determination …(3) • Example weight: Criteria Price

• Iteration 1:

Price

Multiuse

Prestige

1

3

4

Multiuse

1/3

1

2

Prestige

1/4

1/2

1

PCM

3 4  1  0,33 1 2    0, 25 0,5 1 

• Iteration -1: – Squared PCM: 1,000 3,000 4,000 1,000 3,000 4,000 3,000 8,000 14,000 0,333 1,000 2,000 x 0,333 1,000 2,000 = 1,167 3,000 5,333        0,250 0,500 1,000 0,250 0,500 1,000 0,667 1,750 3,000  Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana

4. Priority determination …(5) • Iteration-2: – Again squared the matrix from iteration -1:

 3,0000 8,0000 14,0000  3,0000 8,0000 14,0000  1,1667 3,0000 5,3333  x  1,1667 3,0000 5,3333      0,6667 1,7500 3, 0000  0,6667 1,7500 3, 0000   27,6667 72,5000 126,6667 = 10,5556 27,6667 48,3333   6,0417 15,8333 27,6667 


4. Priority determination …(7) • Now, calculate deviation between eigen value from iteration-1 and iteration-2: 0, 6263 − 0, 6250 = 0, 0013 0, 2380 − 0, 2385 = −0, 0005 0,1357 − 0,1365 = −0, 0008 – Deviation not large until 4 decimal


4. Priority determination …(4) – Summed value of each row and normalized: Sum row

3,0000 8,0000 14,0000 1,1667 3,0000 5,3333    0,6667 1,7500 3,0000 

normalized

25,0000 9,5000 5,4167

25,0000/39,9167 = 0,6263 9,5000/39,9167 = 0,2380 5,4167/39,9167 = 0,1357

Sum: 39,9167

– So, eigen value from iteration -1: • 0,6263, 0,2380, 0,1357


4. Priority determination …(6) • Iteration-2 : – Summed the value for each row and normalized: 27.6667 72.5000 126.6667 10.5556 27.6667 48.3333     6.0417 15.8333 27.6667 

Sum row

normalized

226.8334 86,5556 49,5417

226,8334/362,9307 = 0,6250 86,5556/362,9307 = 0,2385 49,5417/362,9307 = 0,1365

Sum : 362,9307

– So, eigen value from iteration -2: • 0,6250, 0,2385, 0,1365


4. Priority determination …(8) • If iteration-3 continued, we will get the eigen value not change in 4 decimal: – So, eigen value for criteria level:

 0,6250   Harga   0, 2385 ⇒ Serbaguna       0,1365   Prestise  – That means the most important criteria is price, follow by multiuse then prestige



4. Priority determination …(9) Not of course…, Just used the software…!!!

Stop…stop..!!! Should we calculated so complicated like this…???

5. Consistency evaluation • Are pairwise comparison conducted consistently? Consistent: •A = 2B, B = 3C A = 6C •Price > Multiuse, Multiuse > Prestige Price > Prestige

Inconsistent: • A = 2B, B = 3C A = 4C • Price > Multiuse, Multiuse > Prestige Price < Prestige

• Consistency will guaranteed the weight validity Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana


5. Consistency evaluation …(2) • Inconsistency might be happen when: – Wrong entry data – Information not enough – Less concentration – Facts are really not always consistent: • Team A outmatch Team B, and Team B outmatch Team C, but • May be Team C outmatch Team A

5. Consistency evaluation …(3) • AHP tolerate inconsistency: – Measure by consistency index (CI) dan ratio consistency (CR): CR =

CI RI

– Random value (RI):

– Good Consistency : CR ≤ 0,1 Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana


5. Consistency evaluation …(4) • Example consistency evaluation: – Is the assessment consistent? Criteria

Price

Multiuse

Prestig e

1

3

4

Multiuse

1/3

1

2

Prestige

1/4

1/2

1

Price

PCM

3 4  1  0, 33 1 2    0, 25 0, 5 1 

– From the calculation we have eigen value (priority vector): 0, 6250 Price 0,2385 Multiuse 0,1365 Prestige Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana

5. Consistency evaluation …(5) Next Procedure: • Calculate weighted sum vector : multiply matrix with eigen value (priority vector)

3 4   0, 6250   1 1,8865   0, 33 1 2  x  0, 2385  =  0,7178         0,4120   0, 25 0, 5 1   0,1365  • Divide the weight sum vector with priority vector:

1,8865   0, 6250 3, 0184 0,7178 :  0, 2385 = 3, 0096        3, 0183 0,4120  0,1365  Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana


5. Consistency evaluation …(6) Next Procedure: • Calculate maximum eigen value :

λmax

5. Consistency evaluation …(7) Next Procedure: • Calculate consistency ratio (CR):

(3,0184)+(3,0096)+(3,0183) = =3,0154 3

CR =

• Calculate consistency index (CI):

CI =

λmax − n n −1

3, 0154 − 3 = = 0, 0077 3 −1


5. Consistency evaluation …(8) Once more… feel dizzy? Just used the software…!!!

CI 0, 0077 = = 0, 0132 RI 0,58

(Note: RI value for n=3 we get from table)

– Conclusion: assessment of the criteria level was consistent because CR value < 0,1 Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana

6. Synthesis Alternative Priority • For example we get relative priority as follow: Chose Ideal Car Chose Ideal Car

Price Price (0,625) (0,625)

Multiuse Multiuse (0,238) (0,238)

Prestige Prestige (0,136) (0,136)

1. 1. Karimun Karimun(0,648) (0,648) 1. 1. Kijang Kijang(0,625) (0,625) 2. 2. 2. Kijang Kijang(0,230) (0,230) 2. Karimun Karimun(0,238) (0,238) 3. 3. 3. BMW BMW(0,122) (0,122) 3. BMW BMW(0,136) (0,136)

1. 1. BMW BMW(0,649) (0,649) 2. 2. Kijang Kijang(0,279) (0,279) 3. 3. Karimun Karimun(0,072) (0,072)

So, which is car we have to chose…??? Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana


6. Synthesis Alternative Priority …(2) • If we want to get total priority for alternatives, we have to synthesis: – Combine all relative priority vector – One of the method is weighted summation, compromise method, etc

6. Synthesis Alternative Priority …(3) • Example synthesis: Weight

Criteria

Alternative Priority

Price (0,625)

Multiuse (0,238)

Prestige (0,136)

BMW

0,122

0,136

0,649

0,197

Kijang

0,230

0,625

0,279

0,333

Karimun

0,648

0,238

0,072

0,470

Alternative

Calculation: For BMW: (0,122).(0,625) + (0,136).(0.238) + (0,649).(0.136) = 0,197 Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana



6. Synthesis Alternative Priority …(4) • After all, then: – Total Priority level is: Karimun > Kijang > BMW

Material 3:

Oh I have to chose just Karimun …!!!

Case Study: Implementation on Land use Planning in Puncak Area, Bogor



Thank you bu Syar, pa Hadi and pa Lilik …!

Province Jawa Barat

Pulau Jawa

PENERAPAN MULTI CRITERIA DECISION MAKING (MCDM) DAN GEOGRAPHICAL INFORMATION SYSTEM (GIS) PADA EVALUASI PERUNTUKAN LAHAN

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(Studi Kasus: DAS Ciliwung Hulu, Kab. Bogor, Jawa Barat)

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By: SYARTINILIA Supervisor : Ir. Hadi Susilo Arifin, MS., Ph. D. Dr. Ir. Lilik Budi Prasetyo, M.Sc

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Ground truth point

GPS track 2002

Sungai C illiwung

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DAS Ciliwung Hulu, Kabupaten Bogor, Jawa Barat



Land use

Protected Area Criteria

Slope (%)

Elevation

>40%

>2000 m

Soil

Litosol, slope > 15%

Regosol, slope > 15%

River bank

Important Catchment Area

High Land creep area

100 m both side of river

Source : - Ketentuan teknis kawasan lindung dalam RTRW Bopunjur (Bappeda, 2000) dengan berpedoman pada Keppres No.32 tahun 1990 tentang Pengelolaan Kawasan Lindung dan SK Gubernur Jawa Barat No. 413.21/SK.222-HUK/91 tentang Kriteria Lokasi dan Standar Teknis Penataan Ruang di Kawasan Puncak. Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana

Criteria Elevation) Drainage

Rice field

<3 3-8 9-15 16-25 >25

300300-700 700-1000 1000-1500 1500-2000 >2000

slow Medium-Good Fast

Dry land agriculture

<3 3-8 9-15 16-25 >25

300-700 700-1000 1000-1500 1500-2000 >2000

Medium-Good Fast Slow

Estate/ plantation

<8 8-15 16-25 >25

1000-1500 1500-2000 >2000

Medium-Good Fast Slow

Settlement

<10 10-15 16-20 >20

300-700 700-1000 1000-1500 1500-2000 >2000

Good Medium Fast Slow

Land suitability for Protected Area

Slope

3 Kilometers


Land cover Forest Tea estate Shrubs Dry agriculture Rice field Settlement Forest Tea estate Shrubs Dry agriculture Rice field Settlement Forest Tea estate Shrubs Dry agriculture Rice field Settlement Forest Tea estate Shrubs Dry agriculture Rice field Settlement

Land suitability for Build up and Cultivation Area


DRY LAND AGRICULTURE AREA

CULTIVATION AREA • Weight and intensity scale: AHP

Kesesuaian lahan untuk pertanian lahan kering

Land suitability for rice field Level 2 : Bobot

Level 2: Weight

Slope (%)

Elevation (m)

Drainage

<3

300-700

Slow

Level 3: Value

Penggunaan/pe nutupan lahan

Forest

3-8

700-1000

Medm-Good

9-15

1000-1500

Fast

16-25

1500-2000

Ricef

>25

>2000

Dry Agr

Slope (%)

Elevasi (m)

Drainage

Land cover

<3

300-700

Baik-sedang

3-8

700-1000

Cepat

Perkebunan teh

Terhambat

Semak belukar

Tea estate

Level 3: Nilai

Shrubs

9-15

1000-1500

16-25

1500-2000

Sawah

>25

>2000

Ladang Pemukiman

Settlement Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana


PLANTATION AREA

SETTLEMENT AREA Kesesuaian lahan untuk pemukiman

Kesesuaian lahan untuk perkebunan

Level 2 : Bobot

Slope (%)

Level 3 : Nilai

Elevasi (m)

Drainage

Level 2 : Bobot

Land cover

<8

1000-1500

Baik

8-15

1500-2000

Sedang-cepat

Perkebunan teh

16-25

>2000

Terhambat

Semak belukar

Hutan

>25

Level 3 : Nilai

Sawah

Slope (%)

Elevasi (m)

Drainage

Land cover

< 10

300-700

Baik

10-15

700-1000

Sedang

Perkebunan teh

16-20

1000-1500

Cepat

Semak belukar

>20

1500-2000

Terhambat

Ladang

>2000


B= 0.217

0.8

0.6

0.6

Value

Value

1.0

0.8

Pemukiman

Multi Criteria Decision Making (MCDM) Compromise Programming (CP)

B= 0.149

0.4

 I d p = ∑ β ip x i* − xik  i =1

(

0.0

0.0 <3 %

3-8 %

9-15 %

16-25 %

300-700

>25 %

700-1000

1000-1500 1500-2000

>2000

1.0

B = 0.461 Value

0.6

B= 0.172

0.8

0.8

0.4

0.2

0.2

  

1/ p

Cepat

Drainase


dp = distance metrics

0.0

0.0 Sedang-baik

p

β i ∗ = weight for criteria based on preference level, where β i> 0, ∑ βi = 1

x = ideal point p p = distance parameter, range from 1 to

0.6

0.4

Terhambat

)

Elevasi (m )

Slope

Value

MODEL SINTHESIS

0.2

0.2

1.0

Sawah


Example: weight and intensity scale for Rice field Area

0.4

Hutan

Ladang

Pemukiman

1.0

Hutan

Hutan

P erkebunan Teh

Semak belukar

Sawah

Ladang

Pemukiman

∞

We use sensitivity analysis with 3 different values, such as: p = 1, 2 and ∞ (e.g. p>10).

Land cover



Distance Matrix value calculation for GIS

Database Spatial Digital Elevation Model (DEM)

Slope


Aspect


Example: for cultivation area model Drainage

Land cover



Cultivation area Model


Settlement

Estate

Dry land agriculture

Rice field Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana


Cultivation Area with p= 1, 2, 10 Technique Pengambilan Keputusan dengan Metode AHP Oleh: M. Buce Saleh & Tatang Tiryana

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Basic Decision Theory

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