diabstraksikan oleh: smno.psl.ppsub.sept2013
“Semua benda hidup dan mati yg terdapat secara alamiah di
bumi,
Bermanfaat bagi manusia,
Dapat dimanfaatkan oleh manusia,
untuk memenuhi kebutuhan hidupnya
Keberadaannya & ketersediaannya:
1. Sebaran geografisnya tdk merata
2. Pemanfaatannya tgt teknologi
3. Kalau diolah menghasilkan produk dan limbah
A Comprehensive Model
Land use = is a way of managing a large part of the human
environment in order to obtain benefits for human.
Land use
development
The complex
problems
Systems theory
is an interdisciplinary theory about the nature of
complex systems in nature, society, and science,
and is a framework by which one can investigate
and/or describe any group of objects that work
together to produce some result.
The Comprehensive Model
FIVE GEOMETRIES in Resources use system
Natural resources
geometry
Human demand
geometry
NATURAL RESOURCES USE
GEOMETRY
Natural Resources
Geometry
Resources Degradation
Geometry
SISTEM
sbg suatu pendekatan
1. Filosofis
Systems thinking is the process of
predicting, on the basis of anything at all,
how something influences another thing.
It has been defined as an approach to
problem solving, by viewing "problems" as
parts of an overall system, rather than
reacting to present outcomes or events and
potentially contributing to further
development of the undesired issue or
problem.
2. Prosedural
3. Alat bantu
analisis
FILOSOFI
“Sistem”:
Gugusan elemen-elemen yg saling
berinteraksi dan terorganisir perilakunya ke arah tujuan tertentu
Science systems thinkers consider that:
A system is a dynamic and complex whole, interacting as a structured functional unit;
Energy, material and information flow among the different elements that compose the system;
A system is a community situated within an environment;
energy, material and information flow from and to the surrounding environment via semipermeable membranes or boundaries;
Systems are often composed of entities seeking equilibrium but can exhibit oscillating, chaotic, or
exponential behavior.
“Tiga prasyarat aplikasinya”:
1. Tujuan dirumuskan dengan jelas
2. Proses pengambilan keputusan sentralisasi logis
3. Sekala waktu -------- jangka panjang
PROSEDUR
A conceptual framework is used in research
to outline possible courses of action or to
present a preferred approach to a system
analysis project.
The framework is built from a set of
concepts linked to a planned or existing
system of methods, behaviors, functions,
relationships, and objects. A conceptual
framework might, in computing terms, be
thought of as a relational model.
For example a conceptual framework of
accounting "seeks to identify the nature,
subject, purpose and broad content of
general-purpose financial reporting and the
qualitative characteristics that financial
information should possess".
“Tahapan Pokok”:
1. Analisis Kelayakan
2. Pemodelan Abstrak
3. Disain Sistem
4. Implementasi Sistem
5. Operasi Sistem
Need Assesment
Tahapan Pokok:
Evaluasi
Outcomes
ALAT BANTU
“Model Abstrak”:
Perilaku
esensialnya
dengan dunia nyata
“digunakan dalam”:
1. Perancangan / Disain Sistem
2. Menganalisis SISTEM ……………strukturnya
INPUT …...…….. beragam
STRUKTUR …….. fixed
OUTPUT ……….. Diamati perilakunya
3. Simulasi SISTEM
untuk sistem yang kompleks
sama
SIMULASI
SISTEM:
“Penggunaan Komputer ”:
OPERASINYA
A model is a simplified abstract view of the complex
reality.
A scientific model represents empirical objects,
phenomena, and physical processes in a logical way.
Attempts to formalize the principles of the empirical
sciences, use an interpretation to model reality, in the
same way logicians axiomatize the principles of logic.
The aim of these attempts is to construct a formal
system for which reality is the only interpretation. The
world is an interpretation (or model) of these sciences,
only insofar as these sciences are true.
Simulasi Komputer:
Disain Sistem
Strategi Pengelolaan Sistem
MODEL SISTEM
programming
For the scientist, a model is also a way in which the
human thought processes can be amplified.
Models that are rendered in software allow scientists to
leverage computational power to simulate, visualize,
manipulate and gain intuition about the entity,
phenomenon or process being represented.
PROGRAM
KOMPUTER
“Model dasar”: Model Matematik
SIMULASI
SISTEM:
METODOLOGI
Model lain diformulasikan menjadi
model matematik
“tahapan”:
1. Identifikasi subsistem / komponen sistem
2. Peubah input ( U(t) ) ……….. Stimulus
3. Peubah internal = peubah keadaan = peubah struktural, X(t)
4. Peubah Output, Y(t)
5. Formulasi hubungan teoritik antara U(t), X(t), dan Y(t)
6. Menjelaskan peubah eksogen
7. Interaksi antar komponen ………… DIAGRAM LINGKAR
8. Verifikasi model …….. Uji ……. Revisi
9. Aplikasi Model ……. Problem solving
A simulation is the implementation of a model over time.
A simulation brings a model to life and shows how a particular object or
phenomenon will behave. It is useful for testing, analysis or training where
real-world systems or concepts can be represented by a model
PEMODELAN
SISTEM:
RUANG LINGKUP
“Pemodelan”:
Serangkaian kegiatan pembuatan
model
MODEL: abstraksi dari suatu obyek
atau situasi aktual
MODEL KONSEP
1. Hubungan Langsung
2. Hubungan tidak langsung
3. Keterkaitan Timbal-balik /
Sebab-akibat / Fungsional
MATEMATIKA
4. Peubah - peubah
5. Parameter
Operasi Matematik:
Formula, Tanda, Aksioma
“MODEL SIMBOLIK” :
Simbol-simbol Matematik
JENIS-JENIS
MODEL
Angka
Simbol
Rumus
“Persamaan”
Ketidak-samaan
Fungsi
“MODEL IKONIK” :
“MODEL ANALOG” :
Model Fisik
1. Peta-peta geografis
2. Foto, Gambar, Lukisan
3. Prototipe
Model Diagramatik:
1. Hubungan-hubungan
2. …...
3. …..
A system is a set of interacting or interdependent entities, real or abstract, forming an
integrated whole.
The concept of an 'integrated whole' can also be stated in terms of a system embodying
a set of relationships which are differentiated from relationships of the set to other
12
elements, and from relationships between an element of the set and elements not a part
of the relational regime.
SIFAT
MODEL
PROBABILISTIK / STOKASTIK
Teknik Peluang
Memperhitungkan “uncertainty”
“DETERMINISTIK”:
Tidak memperhitungkan peluang kejadian
Systems Engineering is an interdisciplinary approach and means for enabling the
realization and deployment of successful systems. It can be viewed as the application of
engineering techniques to the engineering of systems, as well as the application of a
systems approach to engineering efforts.
Systems Engineering integrates other disciplines and specialty groups into a team effort,
forming a structured development process that proceeds from concept to production to
operation and disposal.
Systems Engineering considers both the business and the technical needs of all
customers, with the goal of providing a quality product that meets the user needs
MODEL DESKRIPTIF
FUNGSI
MODEL
Deskripsi matematik dari kondisi
dunia nyata
Scientific modelling is the process of generating abstract,
conceptual, graphical and/or mathematical models.
Science offers a growing collection of methods, techniques and
theory about all kinds of specialized scientific modelling.
Also a way to read elements easily which have been broken
down to the simplest form
“MODEL ALOKATIF” :
Komparasi alternatif untuk mendapatkan “optimal solution”
1. Seleksi Konsep
TAHAPAN
PEMODELAN
2. Konstruksi Model:
a. Black Box
b. Structural Approach
3. Implementasi Komputer
4. Validasi (keabsahan representasi)
1. Asumsi Model
2. Konsistensi Internal
3. Data Input ----- hitung parameter
4. Hubungan fungsional antar
peubah-peubah
5. Uji Model vs kondisi aktual
5. Sensitivitas
6. Stabilitas
7. Aplikasi Model
Scientific modelling is the process of generating abstract, conceptual, graphical
and/or mathematical models.
Science offers a growing collection of methods, techniques and theory about all
kinds of specialized scientific modelling.
Also a way to read elements easily which have been broken down to the
simplest form
PHASES OF SYSTEMS ANALYSIS
Recognition….
Definition and bounding of the PROBLEM
Identification of goals and objectives
Generation of solutions
MODELLING
Evaluation of potential courses of action
Implementation of results
Mengapa kita gunakan Analisis Sistem?
1. Kompleksitas obyek / fenomena /substansi penelitian
Multi-atribute
Multi fungsional
Multi dimensional Multi-variabel
2. Interaksi rumit yg melibatkan banyak hal
Korelasional
Pathways
Regresional
Struktural
3. Interaksi dinamik: Time-dependent , and
Constantly changing
4. Feed-back loops
Negative effects vs. Positive effects
Proses Abstraksi & Simplifikasi
PROSES PEMODELAN
INTRODUCTION
DEFINITION
HYPOTHESES
MODELLING
VALIDATION
INTEGRATION
SISTEM - MODEL - PROSES
Bounding - Word Model
Alternatives: Separate - Combination
Relevansi : Indikator - variabel - subsistem
Proses
: Linkages - Impacts
Hubungan : Linear - Non-linear - interaksi
Decision table:
Data
: Plotting - outliers
Analisis : Test - Estimation
Choice :
Verifikasi: Subyektif - reasonable
Uji Kritis: Eksperiment - Analisis/Simulasi
Sensitivity: Uncertainty - Resources - Interaksi
Communication
Conclusions
Proses Pemodelan
SISTEM: Approach
Simulasi Sistem
Analisis Sistem
Model vs. Pemodelan
Mathematical models: An exact science,
Its Practical Application:
1. A high degree of intuition
2. Practical experiences
3. Imagination
4. “Flair”
5. Problem define & bounding
Modelling refers to the process of generating a model as a conceptual representation of
some phenomenon.
Typically a model will refer only to some aspects of the phenomenon in question, and two models of
the same phenomenon may be essentially different, that is in which the difference is more than just a
simple renaming. This may be due to differing requirements of the model's end users or to conceptual
or aesthetic differences by the modellers and decisions made during the modelling process.
Aesthetic considerations that may influence the structure of a model might be the modeller's
preference for a reduced ontology, preferences regarding probabilistic models vis-a-vis deterministic
ones, discrete vs continuous time etc. For this reason users of a model need to understand the19
model's original purpose and the assumptions of its validity
DEFINITION & BOUNDING
IDENTIFIKASI dan PEMBATASAN Masalah penelitian
1. Alokasi sumberdaya penelitian
2. Aktivitas penelitian yang relevan
3. Kelancaran pencapaian tujuan
Proses pembatasan masalah:
1. Bersifat iteratif, tidak mungkin “sekali jadi”
2. Make a start in the right direction
3. Sustain initiative and momentum
System bounding: SPACE - TIME - SUB-SYSTEMS
Sample vs. Population
The whole systems vs. sets of sub-systems
COMPLEXITY AND MODELS
The real system
sangat kompleks
The hypotheses
to be tested
MODEL
Sub-systems
Trade-off:
complexity vs. simplicity
Proses Pengujian Model Hipotetik
The process of evaluating a model
A model is evaluated first and foremost by its consistency to empirical data; any model
inconsistent with reproducible observations must be modified or rejected. However, a fit to
empirical data alone is not sufficient for a model to be accepted as valid. Other factors
important in evaluating a model include:
Ability to explain past observations
Ability to predict future observations
Cost of use, especially in combination with other models
Refutability, enabling estimation of the degree of confidence in the model
WORD MODEL
Masalah penelitian dideskripsikan secara verbal, dengan menggunakan kata (istilah) yang relevan dan simple
Simbolisasi kata-kata atau istilah
Setiap simbol (simbol matematik) harus dapat diberi deskripsi penjelasan
maknanya secara jelas
A conceptual schema or conceptual data model is a map of concepts and their
relationships.
This describes the semantics of an organization and represents a series of assertions
about its nature.
Specifically, it describes the things of significance to an organization (entity classes),
about which it is inclined to collect information, and characteristics of (attributes) and
associations between pairs of those things of significance (relationships).
Pengembangan Model simbolik
Hubungan-hubungan verbal dipresentasikan dengan simbol-simbol yang relevan
GENERATION OF SOLUTION
Alternatif “solusi” jawaban permasalahan , berapa banyak?
Pada awalnya diidentifikasi sebanyak mungkin alternatif jawaban yang
mungkin
Penggabungan beberapa alternatif jawaban yang mungkin
digabungkan
A conceptual schema or conceptual data model is a map of concepts and their
relationships. This describes the semantics of an organization and represents a
series of assertions about its nature. Specifically, it describes the things of
significance to an organization (entity classes), about which it is inclined to collect
information, and characteristics of (attributes) and associations between pairs of
those things of significance (relationships).
A conceptual schema or conceptual data model is a map of concepts and their
relationships. This describes the semantics of an organization and represents a
series of assertions about its nature. Specifically, it describes the things of
significance to an organization (entity classes), about which it is inclined to collect
information, and characteristics of (attributes) and associations between pairs of
those things of significance (relationships).
HYPOTHESES
Tiga macam hipotesis:
1. Hypotheses of relevance: mengidentifikasi & mendefinisikan faktor, variabel, parameter, atau komponen
sistem yang relevan dg permasalahan
2. Hypotheses of processes: merangkaikan faktor-faktor atau komponen-komponen sistem yg relevan dengan
proses / perilaku sistem dan mengidentifikasi dampaknya thd sistem
3. Hypotheses of relationship: hubungan antar faktor, dan representasi hubungan tersebut dengan formulaformula matematika yg relevan, linear, non linear, interaktif.
A conceptual system is a system that is composed of non-physical objects, i.e. ideas or concepts. In
this context a system is taken to mean "an interrelated, interworking set of objects".
A conceptual system is simply a . There are no limitations on this kind of model whatsoever except
those of human imagination. If there is an experimentally verified correspondence between a
conceptual system and a physical system then that conceptual system models the physical system.
"values, ideas, and beliefs that make up every persons view of the world": that is a model of the
world; a conceptual system that is a model of a physical system (the world). The person who has
that model is a physical system.
Penjelasan / justifikasi Hipotesis
Justifikasi secara teoritis
Justifikasi berdasarkan hasil-hasil penelitian yang telah ada
MODEL CONSTRUCTION
Konstruksi Model
Manipulasi matematis
Data dikumpulkan dan diperiksa dg seksama untuk menguji penyimpangannya terhadap
hipotesis.
Grafik dibuat dan digambarkan untuk menganalisis hubungan yang ada dan bagaimana
sifat / bentuk hubungan itu
Uji statistik dilakukan untuk mengetahui tingkat signifikasinya
Simulation is the imitation of some real thing, state of affairs, or process. The act
of simulating something generally entails representing certain key characteristics
or behaviours of a selected physical or abstract system.
Simulation is used in many contexts, including the modeling of natural systems
or human systems in order to gain insight into their functioning.
Other contexts include simulation of technology for performance optimization,
safety engineering, testing, training and education.
Simulation can be used to show the eventual real effects of alternative conditions
and courses of action.
Proses seleksi / uji alternatif yang ada
VERIFICATION & VALIDATION
VERIFIKASI MODEL
1. Menguji apakah “general behavior of a MODEL” mampu
mencerminkan “the real system”
2. Apakah mekanisme atau proses yang di “model” sesuai
dengan yang terjadi dalam sistem
3. Verifikasi: subjective assessment of the success of the modelling
4. Inkonsistensi antara perilaku model dengan real-system harus
dapat diberikan penjelasannya
VALIDASI MODEL
1. Sampai seberapa jauh output dari model sesuai dengan
perilaku sistem yang sesungguhnya
2. Uji prosedur pemodelan
3. Uji statistik untuk mengetahui “adequacy of the model”
4.
Proses Pemodelan
SENSITIVITY ANALYSIS
Perubahan input variabel dan perubahan parameter menghasilkan variasi kinerja
model (diukur dari solusi model) ……… analisis sensitivitas
Variabel atau parameter yang sensitif bagi hasil model harus dicermati lebih
lanjut untuk menelaah apakah proses-proses yg terjadi dalam sistem telah di
“model” dengan benar
Validasi MODEL
Model validation is possibly the most important step in the model
building sequence. It is also one of the most overlooked.
Often the validation of a model seems to consist of nothing more than
quoting the R2 statistic from the fit (which measures the fraction of the
total variability in the response that is accounted for by the model).
PLANNING & INTEGRATION
PLANNING
Integrasi berbagai macam aktivitas, formulasi masalah, hipotesis, pengumpulan
data, penyusunan alternatif rencana dan implementasi rencana. Kegagalan
integrasi ini berdampak pada hilangnya komunikasi :
1. Antara data eksperimentasi dan model development
2. Antara simulasi model dengan implementasi model
3. Antara hasil prediksi model dengan implementasi model
4. Antara management practices dengan pengembangan
hipotesis yang baru
5. Implementasi hasil uji coba dengan hipotesis yg baru
DEVELOPMENT of MODEL
1. Kualitas data dan pemahaman terhadap fenomena sebabakibat (proses yang di model) umumnya POOR
2. Analisis sistem dan pengumpulan data harus dilengkapi
dengan mekanisme umpan-balik
3. Pelatihan dalam analisis sistem sangat diperlukan
4. Model sistem hanya dapat diperbaiki dengan jalan mengatasi
kelemahannya
5. Tim analisis sistem seyogyanya interdisiplin
PEMODELAN KUANTITATIF :
MATEMATIKA DAN STATISTIKA
MODEL STATISTIKA:
FENOMENA STOKASTIK
MODEL MATEMATIKA:
FENOMENA DETERMINISTIK
Deterministic Model Example
. An example of a deterministic model is a calculation to determine the return on a 5year investment with an annual interest rate of 7%, compounded monthly.
The model is just the equation below:
The inputs are the initial investment (P = $1000), annual interest rate (r = 7% = 0.07),
the compounding period (m = 12 months), and the number of years (Y = 5).
A parametric deterministic
model maps a set of input
variables to a set of output
variables.
Diunduh dari: …………… http://www.vertex42.com/ExcelArticles/mc/MonteCarloSimulation.html
Conceptual modelling framework
Diunduh dari: …………… http://2007.igem.org/wiki/index.php/Glasgow/Modeling
WHAT IS SYSTEM MODELLING ?
Worthwhile
Recognition
Problems
Amenable
Definitions
Compromise
Bounding
Objectives
Identification
Complexity
Simplification
Hierarchy
Priorities
Goals
Generality
Solution
Family
Generation
Modelling
Evaluation
Implementation
Selection
Inter-relationship
Feed-back
Stopping rules
Sensitivity & Assumptions
PHASES OF SYSTEM MODELLING
Recognition
Definition and bounding of the problems
Identification of goals and objectives
Generation of solution
MODELLING
Evaluation of potential courses of action
Implementation of results
Model evaluation
A crucial part of the modelling process is the evaluation of whether or not a given
mathematical model describes a system accurately. This question can be difficult to answer as
it involves several different types of evaluation.
Fit to empirical data
Usually the easiest part of model evaluation is checking whether a model fits
experimental measurements or other empirical data. In models with parameters, a
common approach to test this fit is to split the data into two disjoint subsets: training
data and verification data. The training data are used to estimate the model parameters.
An accurate model will closely match the verification data even though this data was
not used to set the model's parameters. This practice is referred to as cross-validation
in statistics.
Defining a metric to measure distances between observed and predicted data is a
useful tool of assessing model fit. In statistics, decision theory, and some economic
models, a loss function plays a similar role.
While it is rather straightforward to test the appropriateness of parameters, it can be
more difficult to test the validity of the general mathematical form of a model.
In general, more mathematical tools have been developed to test the fit of statistical
models than models involving Differential equations.
Tools from nonparametric statistics can sometimes be used to evaluate how well data
fits a known distribution or to come up with a general model that makes only minimal
assumptions about the model's mathematical form.
Scope of the model
Assessing the scope of a model, that is, determining what situations the
model is applicable to, can be less straightforward. If the model was
constructed based on a set of data, one must determine for which systems or
situations the known data is a "typical" set of data.
The question of whether the model describes well the properties of the
system between data points is called interpolation, and the same question for
events or data points outside the observed data is called extrapolation.
As an example of the typical limitations of the scope of a model, in evaluating
Newtonian classical mechanics, we can note that Newton made his
measurements without advanced equipment, so he could not measure
properties of particles travelling at speeds close to the speed of light.
Likewise, he did not measure the movements of molecules and other small
particles, but macro particles only.
It is then not surprising that his model does not extrapolate well into these
domains, even though his model is quite sufficient for ordinary life physics.
Philosophical considerations
Many types of modelling implicitly involve claims about causality. This is
usually (but not always) true of models involving differential equations.
As the purpose of modelling is to increase our understanding of the world,
the validity of a model rests not only on its fit to empirical observations, but
also on its ability to extrapolate to situations or data beyond those originally
described in the model.
One can argue that a model is worthless unless it provides some insight
which goes beyond what is already known from direct investigation of the
phenomenon being studied.
An example of such criticism is the argument that the mathematical models of
Optimal foraging theory do not offer insight that goes beyond the commonsense conclusions of evolution and other basic principles of ecology.
MODEL & MATEMATIK: Term
Variabel
Tipe
Konstante
Parameter
Likelihood
Dependent
Populasi
Probability
Analitik
Independent
Maximum
Sampel
Simulasi
Regressor
Modelling and Simulation
One application of scientific modelling is the field of "Modelling and Simulation", generally referred
to as "M&S".
M&S has a spectrum of applications which range from concept development and analysis, through
experimentation, measurement and verification, to disposal analysis.
Projects and programs may use hundreds of different simulations, simulators and model analysis
tools.
JENIS VARIABEL
Intervening
(Mediating)
Moderator
Independent
Dependent
INTRANEOUS
EXTRANEOUS
Concomitant
Confounding
Control
Variabel tergantung adalah variabel yang tercakup dalam hipotesis
penelitian, keragamannya dipengaruhi oleh variabel lain
Variabel bebas adalah variabel yang yang tercakup dalam hipotesis
penelitian dan berpengaruh atau mempengaruhi variabel
tergantung
Variabel antara (intervene variables) adalah variabel yang bersifat
menjadi perantara dari hubungan variabel bebas ke variabel
tergantung.
Variabel Moderator adalah variabel yang bersifat memperkuat atau
memperlemah pengaruh variabel bebas terhadap variabel
tergantung
Variabel pembaur (confounding variables) adalah suatu variabel yang tercakup
dalam hipotesis penelitian, akan tetapi muncul dalam penelitian dan berpengaruh
terhadap variabel tergantung dan pengaruh tersebut mencampuri atau berbaur
dengan variabel bebas
Variabel kendali (control variables) adalah variabel pembaur yang dapat
dikendalikan pada saat riset design. Pengendalian dapat dilakukan dengan cara
eksklusi (mengeluarkan obyek yang tidak memenuhi kriteria) dan inklusi
(menjadikan obyek yang memenuhi kriteria untuk diikutkan dalam sampel
penelitian) atau dengan blocking, yaitu membagi obyek penelitian menjadi
kelompok-kelompok yang relatif homogen.
Variabel penyerta (concomitant variables) adalah suatu variabel pembaur
(cofounding) yang tidak dapat dikendalikan saat riset design. Variabel ini tidak
dapat dikendalikan, sehingga tetap menyertai (terikut) dalam proses penelitian,
dengan konsekuensi harus diamati dan pengaruh baurnya harus dieliminir atau
dihilanggkan pada saat analisis data.
MODEL & MATEMATIK: Definition
Preliminary
Formal
Expression
Goodall
Mathematical
Mapping
Rules
Maynard-Smith
Representational
Words
Predicted values
Homomorph
Model
Physical
Comparison
Symbolic
Mathematical
Simplified
Data values
Simulation
Model adalah rencana, representasi, atau deskripsi yang menjelaskan suatu objek,
sistem, atau konsep, yang seringkali berupa penyederhanaan atau idealisasi.
Bentuknya dapat berupa model fisik (maket, bentuk prototipe), model citra (gambar
rancangan, citra komputer), atau rumusan matematis.
MODEL & MATEMATIK: Relatives
Advantages
Disadvantages
Distortion
Precise
Opaqueness
Abstract
Transfer
Complexity
Replacement
Communication
Eykhoff (1974) defined a mathematical model as 'a representation of the essential
aspects of an existing system (or a system to be constructed) which presents
knowledge of that system in usable form'.
Mathematical models can take many forms, including but not limited to dynamical
systems, statistical models, differential equations, or game theoretic models.
These and other types of models can overlap, with a given model involving a
variety of abstract structures
MODEL & MATEMATIK: Families
Types
Dynamics
Compartment
Stochastic
Multivariate
Network
Basis
Choices
A mathematical model uses mathematical language
to describe a system.
Mathematical models are used not only in the
natural sciences and engineering disciplines (such
as physics, biology, earth science, meteorology,
and engineering) but also in the social sciences
(such as economics, psychology, sociology and
political science); physicists, engineers, computer
scientists, and economists use mathematical
models most extensively.
The process of developing a mathematical model is
termed 'mathematical modelling' (also modeling).
BEBERAPA PENGERTIAN
MODEL DETERMINISTIK: Nilai-nilai yang diramal (diestimasi, diduga) dapat dihitung secara eksak.
MODEL STOKASTIK: Model-model yang diramal (diestimasi, diduga) tergantung pada distribusi
peluang
POPULASI: Keseluruhan individu-individu (atau area, unit, lokasi dll.) yang diteliti untuk mendapatkan
kesimpulan.
SAMPEL: sejumlah tertentu individu yang diambil dari POPULASI dan dianggap nilai-nilai yang
dihitung dari sampel dapat mewakili populasi secara keseluruhan
PARAMETER: Nilai-nilai karakteristik dari populasi
KONSTANTE, KOEFISIEAN: nilai-nilai karakteristik yang dihitung dari SAMPEL
VARIABEL DEPENDENT: Variabel yang diharapkan berubah nilainya disebabkan oleh adanya perubahan nilai
dari variabel lain
VARIABEL INDEPENDENT: variabel yang dapat menyebabkan terjadinya perubahan VARIABEL DEPENDENT.
44
BEBERAPA PENGERTIAN
MODEL FITTING: Proses pemilihan parameter (konstante dan/atau koefisien yang dapat
menghasilkan nilai-nilai ramalan paling mendekati nilai-nilai sesungguhnya
ANALYTICAL MODEL: Model yang formula-formulanya secara eksplisit diturunkan untuk
mendapatkan nilai-nilai ramalan, contohnya: MODEL REGRESI
MODEL MULTIVARIATE
EXPERIMENTAL DESIGN
STANDARD DISTRIBUTION, etc
SIMULATION MODEL: Model yang formula-formulanya diturunkan dengan serangkaian operasi arithmatik, misal:
Solusi persamaan diferensial
Aplikasi matrix
Penggunaan bilangan acak, dll.
A mathematical model usually describes a system by a set of variables and a set
of equations that establish relationships between the variables.
The values of the variables can be practically anything; real or integer numbers,
boolean values or strings, for example.
The variables represent some properties of the system, for example, measured
system outputs often in the form of signals, timing data, counters, and event
occurrence (yes/no).
The actual model is the set of functions that describe the relations between the
different variables.
DYNAMIC MODEL
MODELLING
SIMULATION
Dynamics
Equations
Computer
FORMAL
Language
Special
DYNAMO
CSMP
CSSL
General
BASIC
ANALYSIS
DYNAMIC MODEL
DIAGRAMS
SYMBOLS
RELATIONAL
LEVELS
AUXILIARY
VARIABLES
MATERIAL FLOW
RATE EQUATIONS
PARAMETER
SINK
INFORMATION FLOW
Data Flow Diagram (DFD) adalah suatu diagram yang menggunakan notasinotasi untuk menggambarkan arus dari data sistem, yang penggunaannya
sangat membantu untuk memahami sistem secara logika, tersruktur dan jelas.
DFD merupakan alat bantu dalam menggambarkan atau menjelaskan sistem
yang sedang berjalan logis.
DYNAMIC MODEL:
ORIGINS
Computers
Abstraction
Equations
Steps
Hypothesis
Discriminant Function
Simulation
Other
functions
Undestanding
Exponentials
Logistic
48
MATRIX MODEL
MATHEMATICS
Matrices
Operations
Additions
Substraction
Multiplication
Inversion
Eigen value
Dominant
Elements
Types
Eigen vector
Square
Rectangular
Diagonal
Identity
Vectors
Scalars
Row
Column
49
MATRIX MODEL
DEVELOPMENT
Interactions
Groups
Materials
cycles
Size
Stochastic
Markov
Models
Development stages
The term matrix model may refer to one of several concepts:
In theoretical physics, a matrix model is a system (usually a quantum mechanical system)
with matrix-valued physical quantities. See, for example, Lax pair.
The "old" matrix models are relevant for string theory in two spacetime dimensions. The
"new" matrix model is a synonym for Matrix theory.
Matrix population models are used to model wildlife and human population dynamics.
The Matrix Model of substance abuse treatment was a model developed by the Matrix
Institute in the 1980's to treat cocaine and methamphetamine addiction.
A concept from Algebraic logic.
50
STOCHASTIC MODEL
STOCHASTIC
Probabilities
History
Other Models
Statistical method
Dynamics
Stability
A statistical model is a set of mathematical equations which describe the behavior of an
object of study in terms of random variables and their associated probability distributions. If
the model has only one equation it is called a single-equation model, whereas if it has more
than one equation, it is known as a multiple-equation model.
In mathematical terms, a statistical model is frequently thought of as a pair (Y,P) where Y is
the set of possible observations and P the set of possible probability distributions on Y. It is
assumed that there is a distinct element of P which generates the observed data.
Statistical inference enables us to make statements about which element(s) of this set are
51
likely to be the true one.
STOCHASTIC MODEL
Spatial patern
Distribution
Pisson
Example
Poisson
Negative
Binomial
Binomial
Negative
Binomial
Others
Test
Fitting
In statistics, spatial analysis or spatial statistics includes any of the formal
techniques which study entities using their topological, geometric, or geographic
properties.
The phrase properly refers to a variety of techniques, many still in their early
development, using different analytic approaches and applied in fields as diverse
as astronomy, with its studies of the placement of galaxies in the cosmos, to
52
chip fabrication engineering, with its use of 'place and route' algorithms to build
complex wiring structures.
STOCHASTIC MODEL
ADDITIVE MODELS
Basic Model
Example
Error
Parameter
Estimates
Analysis
Variance
Orthogonal
Effects
Block
Experimental
Significance
Treatments
53
STOCHASTIC MODEL
REGRESSION
Model
Example
Error
Linear/ Nonlinear functions
Decomposition
Oxygen uptake
Equation
Theoritical
base
Reactions
Experimental
Empirical base
Assumptions
In statistics, regression analysis includes any techniques for modeling and analyzing several
variables, when the focus is on the relationship between a dependent variable and one or
more independent variables.
More specifically, regression analysis helps us understand how the typical value of the
dependent variable changes when any one of the independent variables is varied, while the
other independent variables are held fixed.
54
Most commonly, regression analysis estimates the conditional expectation of the dependent
variable given the independent variables — that is, the average value of the dependent
variable when the independent variables are held fixed.
Less commonly, the focus is on a quantile, or other location parameter of the conditional
distribution of the dependent variable given the independent variables. In all cases, the
estimation target is a function of the independent variables called the regression function.
In regression analysis, it is also of interest to characterize the variation of the dependent
variable around the regression function, which can be described by a probability distribution.
Regression analysis is widely used for prediction (including forecasting
of time-series data). Use of regression analysis for prediction has
substantial overlap with the field of machine learning.
Regression analysis is also used to understand which among the
independent variables are related to the dependent variable, and to
explore the forms of these relationships.
In restricted circumstances, regression analysis can be used to infer
causal relationships between the independent and dependent variables.
55
Underlying assumptions
Classical assumptions for regression analysis include:
The sample must be representative of the population for the inference prediction.
The error is assumed to be a random variable with a mean of zero conditional on
the explanatory variables.
The variables are error-free. If this is not so, modeling may be done using errorsin-variables model techniques.
The predictors must be linearly independent, i.e. it must not be possible to
express any predictor as a linear combination of the others. See Multicollinearity.
The errors are uncorrelated, that is, the variance-covariance matrix of the errors is
diagonal and each non-zero element is the variance of the error.
The variance of the error is constant across observations (homoscedasticity). If
not, weighted least squares or other methods might be used.
These are sufficient (but not all necessary) conditions for the least-squares
estimator to possess desirable properties, in particular, these assumptions imply
that the parameter estimates will be unbiased, consistent, and efficient in the
class of linear unbiased estimators. Many of these assumptions may be relaxed in
more advanced treatments.
56
STOCHASTIC MODEL
MARKOV
Analysis
Example
Assumptions
Advantages
Analysis
Disadvantage
Transition probabilities
Raised mire
What is a Markov Model?
Markov models are some of the most powerful tools available to
engineers and scientists for analyzing complex systems.
This analysis yields results for both the time dependent evolution of the
57
system and the steady state of the system.
MULTIVARIATE MODELS
METHODS
VARIATE
Variable
Classification
Dependent
Independent
Descriptive
Principal
Component
Analysis
Predictive
Discriminant Analysis
Cluster Analysis
Reciprocal
averaging
Canonical
Analysis
58
MULTIVARIATE MODEL
PRINCIPLE COMPONENT ANALYSIS
Requirement
Example
Correlation
Environment
Eigenvalues
Objectives
Eigenvectors
Organism
Regions
Principal Component Analysis (PCA) involves a mathematical procedure that
transforms a number of possibly correlated variables into a smaller number of
uncorrelated variables called principal components.
The first principal component accounts for as much of the variability in the data
as possible, and each succeeding component accounts for as much of the
remaining variability as possible.
59
MULTIVARIATE MODEL
CLUSTER ANALYSIS
Example
Spanning tree
Multivariate space
Demography
Rainfall regimes
Minimum
Similarity
Single linkage
Settlement patern
Distance
Cluster analysis or clustering is the assignment of a set of observations into
subsets (called clusters) so that observations in the same cluster are similar in
some sense. Clustering is a method of unsupervised learning, and a common
technique for statistical data analysis used in many fields, including machine
learning, data mining, pattern recognition, image analysis and bioinformatics.
Besides the term clustering, there are a number of terms with similar
meanings, including automatic classification, numerical taxonomy, botryology
and typological analysis.
60
CANONICAL
CORRELATION
Example
MULTIVARIATE MODEL
Correlation
Partitioned
Watershed
Urban area
Irrigation regions
Eigenvalues
Eigenvectors
Canonical correlation analysis (CCA) is a way of measuring the linear
relationship between two multidimensional variables.
It finds two bases, one for each variable, that are optimal with respect to
correlations and, at the same time, it finds the corresponding correlations. In
other words, it finds the two bases in which the correlation matrix between the
variables is diagonal and the correlations on the diagonal are maximized.
The dimensionality of these new bases is equal to or less than the smallest
dimensionality of the two variables.
61
MULTIVARIATE MODEL
Discriminant Function
Example
Discriminant
Calculation
Villages
Vehicles
Structures
Test
Discriminant function analysis involves the predicting of a categorical dependent
variable by one or more continuous or binary independent variables. It is
statistically the opposite of MANOVA.
It is useful in determining whether a set of variables is effective in predicting
category membership.
62
It is also a useful follow-up procedure to a MANOVA instead of doing a series of
one-way ANOVAs, for ascertaining how the groups differ on the composite of
OPTIMIZATION MODEL
OPTIMIZATION
Dynamic
Meanings
Indirect
Simulation
Minimization
Experimentation
Non-Linear
Linear
Objective function
Constraints
Solution
Examples
Maximization
Optimum Transportation Routes
Optimum irrigation scheme
Optimum Regional Spacing
OPTIMIZATION MODEL
A model used to find the best possible choice out of a set of alternatives. It may use the
mathematical expression of a problem to maximize or minimize some function. The
alternatives are frequently restricted by constraints on the values of the variables.
A simple example might be finding the most efficient transport pattern to carry
commodities from the point of supply to the markets, given the volumes of production
and demand, together with unit transport costs.
Read more: http://www.answers.com/topic/optimization-model-1#ixzz2JbXsisBX
Diunduh dari: ……………http://www.answers.com/topic/optimization-model-1
Ten Keys to Success in
Optimization Modeling
Richard E. Rosenthal
Operations Research Department
Naval Postgraduate School
INFORMS Atlanta, October 2003
Key #1: Communicate Early and Often
Mathematical formulation – kept up to date
Verbal description of formulation
Executive summary – in the right language
Mathematical Formulation
Index use
Given data (and units)
in lower case
Decision Variables (and units)
in UPPER CASE
Objectives and constraints
Verbal Description of Formulation
“Constraints ensure that one service facility is
assigned responsibility for each product line
p.”
You wonder why I mention this, but look at our
applied literature.
Non-mathematical Executive Summary
Jerry Brown’s Five Essential Steps:
• What is the problem?
• Why is the problem important?
• How will the problem be solved without you?
• How will you solve the problem?
• How will the problem be solved with your results, but
without you?
Key #2: Bound all Decisions
A trivial concept, too-often ignored
Remember all the formal “neighborhood”
assumptions underlying your optimization
method?
Bob Bixby tells of real customer MIP with only
51 variables and 40 constraints that could not
be solved… until bounds were added, and
then it solved in a flash.
Bound all Decisions
• Optimization is an excellent way to find data
errors, but it really exploits them
• Moderation is a virtue
• Bonus! You never have to deal with the
embarrassment (or the theory) of
unbounded models.
Key #3: Expect any Constraint to
Become an Objective, and Vice Versa
Real-world models are notorious for multiple, conflicting
objectives
Expert guidance from senior leaders is often interpreted as
constraints
These “constraints” are often infeasible
Discovering what can be done changes your concept of
what should be done
Contrary to impression of textbooks, alternate optima are
the rule, not the exception.
Key #4: Sensitivity Analysis in the Real World Is
Nothing Like Textbook SA
LP Sensitivity Analysis, Textbook Style
Disappointing in practice because theory creates limits.
•
Textbooks have sleek algorithms for one modification at a
time, all else held constant, e.g.,
minimize Sj cj Xj + dXk
Not very exciting in practice. So why is this stuff in all the
textbooks? What is worth talking about?
Sensitivity Analysis, Practitioner Style
Large-scale LP for optimizing airlift -- multiple time-space
muticommodity networks, linked together with nonnetwork constraints .
Initial results on realistic scenario: only 65% of required
cargo can be delivered on time.
Analysis of result revealed most of the undelivered cargo
was destined for City A from City B, so.. what if we
redirect some of this cargo to City A’?
Sensitivity analysis: add ~12,000 new rows and ~10,000
columns... on-time delivery improves to 85%.
Key #5: Bound the Dual Variables
Elastic constraints,
with a linear (or piece-wise linear) penalty per unit of
violation, bound the dual variables
“I’m willing to satisfy this restriction (constraint),
as long as it doesn’t get too expensive.
Otherwise, forget it;
I’ll deal with the consequences”
Key #6: Model Robustly
Your analysis should consider alternate future
scenarios, and render a single robust solution.
There may be many contingency plans,
but you only get one chance per year
to ask for the money to get ready.
Key #7: Eliminate Lots of Variables
Big models get to be big through Cartesian
products of indices
Find rules for eliminating lots of index tuples
before they are generated in the model
Sources of rules: mathematical reasoning and
common sense based on understanding of
the problem
You can often eliminate constraints too!
Example 1 of Variable Elimination
XD(a,i,r,t) = # of type a aircraft direct delivering cargo for
customer i on route r departing at time t
Allow variable to exist only if
Route r is a direct delivery route from customer i ’s origin
to i ’s destination
Aircraft type a is available at i ’s origin at t
Aircraft type a can fly route r ’s critical leg
Aircraft type a can carry some cargo type that customer
i demands
Time t is not before i ’s available-to-load time
Time t is not after i ’s required delivery date + maxlate –
travel time
Example 2 of Variable Elimination
Ann Bixby and Brian Downs of Aspen Technology
developed real-time Capable-to-Promise model for
large meatpacking company
One of their major efforts to bring solution times down low
enough was variable elimination.
Key #8: Incremental Implementation
In a complex model, add features
incrementally. Test each new feature on
small instances and take no prisoners.
When new features don’t work, there is either
a bug to be fixed or a new insight to be
gained. Either way, treasure the learning
experiences.
Incremental Implementation
Eliminate variables corresponding to airlifters switching
from long-haul to shuttle status, if there are no
foreseeable shuttle opportunities.
Euro
US
SWA
FOB
Feature tested with small example: removing the option
to make a seemingly foolish decision actually caused
degradation of objective function.
What happened?
Key #9: Persistence
“Any prescriptive model that suggests a plan
and then, when used again, ignores its own
prior advice…
… is bound to advise something needlessly
different, and lose the faith of its beneficiaries.”
Jerry Brown
Illustration of Persistence
There are initially 8 customers to serve. We must
choose serving site and equipment type.
Results for Initial Case with 8 Customers
Customer
Eqpt Type Site Distance
Cust01
Eqpt-01
HHH
353
Cust02
Eqpt-01
HHH
724
Cust03
Eqpt-01
HHH
773
Cust04
Eqpt-01
YYY
707
Cust05
Eqpt-01
YYY
719
Cust06
Eqpt-03
RRR
495
Cust07
Eqpt-01
HHH
442
Cust08
Eqpt-03
RRR
590
Illustration of Persistence
Just a moment after this solution is
announced, two high-priority customers call
in. The model is rerun with the 10
customers.
There are not enough assets to cover all 10
customers.
The new solution requires a major
reallocation of assets. Major changes in the
solution are highlighted.
Illustration of Persistence
Results for 10 Customers without Persistence
Customer
Eqpt Type
Site Dist (nm)
Cust01
Eqpt-01
HHH
353
Cust02
Eqpt-01
YYY
678
Cust03
Eqpt-01
YYY
703
Cust04
NOT SERVED
Cust05
Eqpt-03
RRR
705
Cust06
Eqpt-03
RRR
495
Cust07
Eqpt-01
HHH
442
Cust08
NOT SERVED
Cust09
Eqpt-01
HHH
353
Cust10
Eqpt-01
HHH
353
Illustration of Persistence
A persistent version of the model is run to
obtain a new optimal solution that
discourages major changes from the original
announced solution.
Add to objective function: penalties on
deviations from original solution, weighted by
severity of disruption.
Illustration of Persistence
Results for 10 Customers with Persistence
Customer
Eqpt Type Site Dist (nm)
Cust01
Eqpt-01
HHH
353
Cust02
Eqpt-01
HHH
724
Cust03
Eqpt-01
HHH
773
Cust04
NOT SERVED
Cust05
Eqpt-01
YYY
719
Cust06
Eqpt-02
RRR
495
Cust07
Eqpt-01
HHH
442
Cust08
NOT SERVED
Cust09
Eqpt-01
YYY
380
Cust10
Eqpt-01
RRR
363
Illustration of Persistence
Comparison of Solutions
Orig.
Subsequent
With persistence?
No
Yes
Customers
8
10
10
Objective function value
Customers not served
0
180.00 180.00
Original objective
206.67 151.75 155.20
Total
206.67 331.75 335.20
At a cost of 1% in the objective function, the persistent
solution causes no disruption to the announced plans,
other than substitution of the two new customers.
Key #10: Common Sense
• Heuristics are easy --- so easy we are tempted
to use them in lieu of more formal methods
• Heuristics may offer a first choice to assess a
“common sense” solution
• But, heuristics should not be your only choice
Common Sense
A formal optimization model takes longer to develop,
and solve
But it provides a qualitative bound on each heuristic
solution
Without this bound, our heuristic advice is of
completely unknown quality
This quality guarantee is key
Common Sense
It’s OK to use a heuristic,
but you should pair it with a traditional,
“calibrating” mathematical model
With no quality assessment,
you are betting your reputation
that nobody else is luckier than you are
10 Keys to Success in Optimization Modeling
#1 Write formulation,
communicate with execs
#2 Bound decisions
#3 Objectives and constraints
exchange roles (alt. optima
likely)
#4 Forget about sensitivity
analysis as you learned it
#5 Elasticize (bound duals)
#6 Model robustly
#7 Eliminate variables – avoid
generating them when you
can
#8 Incremental
implementation
#9 Model persistence
#10 Bound heuristics with
optimization
MODELLING PROCESS
System analysis
Processes
Introduction
Model
Bounding
Space
Time
Niche
Elements
Systems
Definition
Word Models
Impacts
Factorial
Confounding
Alternatives
Separate
Combinations
Hypotheses
Data
Modelling
Analysis
Choices
Validation
Plotting
Outliers
Test
Estimates
Conclusion
Integration
Communication
HYPOTHESES
MODELLING PROCESSES
Decision Table
Relevance
Variable
Species
Sub-systems
Processes
Linkages
Relationships
Linear
Non-Linear
Impacts
Interactive
A hypothesis (from Greek ὑπόθεσις; plural hypotheses) is a proposed explanation
for an observable phenomenon. The term derives from the Greek, ὑποτιθέναι –
hypotithenai meaning "to put under" or "to suppose." For a hypothesis to be put
forward as a scientific hypothesis, the scientific method requires that one can test
it.
Scientists generally base scientific hypotheses on previous observations that
cannot be satisfactorily explained with the available scientific theories. Even
though the words "hypothesis" and "theory" are often used synonymously in
common and informal usage, a scientific hypothesis is not the same as a
scientific theory – although the difference is sometimes more one of degree than
of principle.
94
HYPOTHESES
Hypotheses of Relevance: Mengidentifikasi dan
mendefinisikan variabel dan subsistem yang relevan dengan
permasalahan yang diteliti
Hypotheses of Processes: Menghubungkan subsistem (atau
variabel) di dalam permasalahan yang diteliti dan
mendefinisikan dampak (pengaruh) terhadap sistem yang
diteliti
Hypotheses of relationships: Merumuskan hubungan-hubungan antar
variabel dengan menggunakan formula-formula matematik (fungsi
linear, non-linear, interaksi, dll)
Hypotheses of relationships
1.
2.
3.
4.
5.
6.
7.
8.
Determinants of the sophistication of SFA. In terms of
specific hypotheses:
Hypothesis 1: There is a positive relationship between
perceived strategic importance of sales decisions and
level of information orientation.
Hypothesis 2: There is a positive relationship between
organizational slack and level of information
orientation.
Hypothesis 3: There is a negative relationship between
organizational control and level of information
orientation.
Hypothesis 4: There is a positive relationship between
integration of IT and sales and level of information
orientation.
Hypothesis 5: There is a positive relationship between
perceived strategic importance of sales decisions and
integration of IT and sales.
Hypothesis 6: There is a positive relationship between
organizational slack and integration of IT and sales.
Hypothesis 7: There is a negative relationship between
organizational control and integration of IT and sales.
Hypothesis 8: There is a positive relationship between
level of information orientation and a count of the
number of types of results of sales campaigns that are
measured.
Diunduh dari: http://www.sciencedirect.com/science/article/pii/S0019850107001149 ……………
Hypotheses of relationships
Path model of hypothesized causal
relationships among the lengths of
roots and mycorrhizal fungal hyphae,
three soil C pools and the percentage
of water-stable soil aggregates in a
chronosequence of prairie restorations.
Fine roots are 0.2–1 mm dia; very fine
roots are <0.2 mm dia.Single-headed
arrows indicate direct causal
relationships and double-headed
arrows indicate unanalyzed
correlations. Numbers are path
coefficients and proportion of total
variance explained (r2; shown in bold
italics) for each endogenous
(dependent) variable (n=49). The
numbers within ellipses represent the
proportion of unexplained variance
[(1−r2)1/2] and, thus, indicate the
relative contribution of all unmeasured
or unknown factors to each dependent
variable
Diunduh dari: ……………http://www.sciencedirect.com/science/article/pii/S0038071797002071
MODELLING PROCESSES
VALIDATION
Verification
Critical Test
Sensitivity
Analysis
Subjectives
Uncertainty
Analysis
Resources
Objectivities
Reasonableness
Experiments
Interactions
Model verification and validation (V&V) are
essential parts of the model development
process if models to be accepted and used to
support decision making
Model validation is possibly the most important step in the model building
sequence. It is also one of the most overlooked.
Often the validation of a model seems to consist of nothing more than quoting
the R2 statistic from the fit (which measures the fraction of the total variability in
98
the response that is accounted for by the model).
ROLE OF THE COMPUTER
Roles
Introduction
Reasons
Speed
Data
Algoritm
Comparison
Speed
Implication
Techniques
Errors
Plotting
Waste
Repetition
Checking
9/10
Modelling
Data
Program
High level
Algoritms
Manual
Calculator
Computer
Language
Information
FORTRAN
BASIC
ALGOL
Machine code
Special
DYNAMO. Etc.
Development
Conclusions
Programming
99
ROLE OF THE COMPUTER
DATA
Machine readable
Cautions
Availability
Sampling
Format
Punched card
Exchange
Paper tape
Format
Reanalysis
Magnetic
Tape
Data banks
Disc
100
DATA
Data adalah kumpulan angka, fakta, fenomena atau keadaan atau lainnya,
merupakan hasil pengamatan, pengukuran, atau pencacahan dan sebagainya
…
terhadap variabel suatu obyek, …..
yang berfungsi dapat membedakan obyek yang satu dengan lainnya pada
variabel yang sama
Data adalah catatan atas kumpulan fakta.
Data merupakan bentuk jamak dari datum, berasal dari bahasa Latin yang berarti
"sesuatu yang diberikan". Dalam penggunaan sehari-hari data berarti suatu
pernyataan yang diterima secara apa adanya. Pernyataan ini adalah hasil
pengukuran atau pengamatan suatu variabel yang bentuknya dapat berupa
angka, kata-kata, atau citra.
Dalam keilmuan (ilmiah), fakta dikumpulkan untuk menjadi data. Data kemudian
diolah sehingga dapat diutarakan secara jelas dan tepat sehingga dapat
dimengerti oleh orang lain yang tidak langsung mengalaminya sendiri, hal ini
dinamakan deskripsi. Pemilahan banyak data sesuai dengan persamaan atau
perbedaan yang dikandungnya dinamakan klasifikasi.
101
JENIS DATA
NOMINAL
• Komponen Nama (Nomos)
ORDINAL
• Komponen Nama
• Komponen Peringkat (Order)
INTERVAL
• Komponen Nama
• Komponen Peringkat (Order)
• Komponen Jarak (Interval)
• Nilai Nol tidak Mutlak
RATIO
• Komponen Nama
• Komponen Peringkat (Order)
• Komponen Jarak (Interval)
• Komponen Ratio
• Nilai Nol Mutlak
102
REFERENSI
Russell L. Ackoff (1999) Ackoff's Best: His Classic Writings on Management. (Wiley) ISBN 0-471-31634-2
Russell L. Ackoff (2010) Systems Thinking for Curious Managers. (Triarchy Press). ISBN 978-0-9562631-5-5
Béla H. Bánáthy (1996) Designing Social Systems in a Changing World (Contemporary Systems Thinking). (Springer) ISBN 0306-45251-0
Béla H. Bánáthy (2000) Guided Evolution of Society: A Systems View (Contemporary Systems Thinking). (Springer) ISBN 0306-46382-2
Ludwig von Bertalanffy (1976 - revised) General System theory: Foundations, Development, Applications. (George Braziller)
ISBN 0-807-60453-4
Fritjof Capra (1997) The Web of Life (HarperCollins) ISBN 0-00-654751-6
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