Defining Procedures for Decision Analysis



APPENDIX A

Introduction

The goal of this project is to develop a guide that aids users in the decision analysis procedure. The guide include an outline of a list of topics that are used in the decision-making process along with extensive information concerning input definitions, external and internal factors, and possible results of the decision. These topics allow a user to generate possibilities for commercialization. Researching published information on commercialization and decision making processes and interviewing industry experts will be the main source of information for the report. Brainstorming sessions also provide valuable information. A previous Engineering 466 team developed a report on what factors should be used in decision analysis. These results were taken into account and were used a starting point for the new report. Methodologies from the results of the Engineering 466 project were used to evaluate which decision-making processes would be the best to use in the implementation phase of the project. Further work by another Engineering 466 team was to investigate possible algorithms and their applications. The guide was constructed in coordination with the Engineering 466 team, identifying factors, applicable algorithms, and relevant examples.

First, the guide provides information concerning relevant algorithms that can be used for the software package. The team recommends using ANNs, genetic algorithms, or decision trees. The next section contains the functional software specification, which will provide future teams with a guide to begin designing a software package. The final reference material section includes the decision spreadsheet, scenario matrix and explanation, and a summary of the interviews conducted last semester.

466 Algorithm Report

The purpose of the algorithms repot was to explore a collection of algorithms and their functionality, as it would relate to each stage of the decision analysis process. The seven algorithms that were researched included fuzzy logic, Bayesian logic, artificial neural networks, decision tree, decision matrix, linear programming, and genetic algorithms. In researching these algorithms it was first necessary to identify the different parts or stages of the decision analysis process and then determine the important properties and variables of each stage. Based off the desired properties and the type of information and variables a set of criteria was determined with which to research and compare the different algorithms. After researching and comparing the different algorithms and the benefits and limitations, it was determined that the three algorithms that appear most promising in results and ease of application are artificial neural networks, decision trees, and genetic algorithms.

Artificial neural networks are useful for decision theory because they have the ability to learn and memorize data as well as create relationships amongst data. They are also able to work with the non-linearities making them an excellent tool for use in solving real world problems. Artificial neural networks can also be used for the accurate prediction of events. This is a very nice feature with application to decision theory because it makes it possible for a company to predict how certain factors will influence the success of their product and allows them to avoid making costly mistakes.

Decision trees are good for application to decision analysis because they can aid a company in developing an accurate and balanced picture of the risks and rewards that can result from making different decision or adjusting different factors. Decision trees are also especially useful in decision analysis when a lot of complex information needs to be accounted for in order to optimize profits and make the best decision.

Genetic Algorithms are useful in decision analysis because they make it possible to create a set of multi objective solutions that can be defined so that each solution is controlled in such a way that the results of the whole set are no worse than the results of any single set of solutions. The final decision between the sets of solutions can be made in an informed way using a deciding factor. The use of additional information from the evolutionary process could also be incorporated to improve the results being waited by the deciding factor.

The report begins on the following page.

Defining Procedures for Decision Analysis

Algorithms Report

Engr 466-02A

03/24/2002

Clients Name:

Dr. John Wm. Lamont

Dr. Ralph Patterson III

Faculty Advisors:

Dr. Keith Adams

Dr. John Wm. Lamont

Dr. Ralph Patterson III

Team Members:

Marvin Choo

Natasha Khan

Jesse Smith

Table of Contents

List of Figures iii

List of Tables iv

Executive Summary 1

Acknowledgment 1

Section 1.0: 2

Fuzzy Logic 2

What is Fuzzy Logic? 2

Applications of Fuzzy Logic 3

Fuzzy Expert Systems 3

Control 4

Implementation 4

References 4

Section 2.0: 5

Bayesian Logic 5

What is Bayesian Logic? 5

Applications of Bayesian Logic 5

Bayesian Network 6

Control 7

Implementation 7

References 7

Section 3.0: 8

ARTIFICIAL NEURAL NETWORKS 8

What is An Artificial Neural Network? 8

The Uses of Artificial Neural networks 8

The Advantages Of Using Artificial Neural Networks 8

The Limitations of ANNs 8

A Biological Neuron’s Input Output Structure 8

The Artificial Neuron 9

A Description Of How Neural Networks Work 10

Network Structure 11

How Neural Networks Learn 11

Conclusion 12

References 12

Section 4.0: 13

DECISION TREES 13

What Is a Decision Trees? 13

Input and Output of a Decision Tree 13

The Steps To Drawing A Decision Tree 13

Example of A Problem Solved Using Decision Trees 14

Explanation of The Decision Tree 15

Analyzing the Decision Tree 15

Calculations Carried Out On Decision Tree 15

End Result and Decision 17

References 17

Table of Contents

Section 5.0: 18

Decision Matrix 18

Background 18

Control Parameters 19

Benefits 19

Limitations 19

Applications 20

Reference 20

Section 6.0: 21

Linear Programming 21

Background 21

Control Parameters 23

Benefits 23

Limitations 23

Applications 24

References 24

Section 7.0: 25

Genetic Algorithm 25

Background 25

Control Parameters 26

Benefits 27

Limitations 27

Applications 27

Reference 28

List of Figures

Figure 1.1 Fuzzy Number………………………………………………………………………………… 2

Figure 1.2 Fuzzy Interval from 3.0 to 5.0……………………………………………………………….... 2

Figure 1.3 Fuzzy Expert System Flow…………………………………………………………………... 3

Figure 2.1 Simple Baysian Network for an Alarm………………………………………………………. 6

Figure 2.2 Bayesian Network Flow……………………………………………………………………… 6

Figure 3.1 A Perceptron’s schematic input/output structure……………………………………………... 9

Figure 3.2 Diagram of Input, Hidden, and Output Layers of An ANN…………………………………. 10

Figure 3.3 Diagram of Neural Network…………………………………………………………………. 11

Figure 4.1 Decision Tree Used To Solve The Above Problem…………………………………………. 14

Figure 4.2 Revised Decision Tree………………………………………………………………………. 17

Figure 6.1 Graphical Representation of The Linear Programming Problem…………………………… 23

Figure 7.1 Genetic Algorithm Process………………………………………….………………………. 26

List of Tables

Table 5.1 Decision Matrix Example ……………………………………………………………………. 19

Table 6.1 Comparison of Time Required ……………………………………………………………….. 21

Executive Summary

Around the world organizations are making imperative decisions influencing their products, processes, and services. It is the goal of this project, Defining Procedures for Decision Analysis, to explore the decision analysis process at each stage that occurs when developing and commercializing a product. The specific goal of the 466-02A team is to explore a collection of algorithms and their functionality, as it would relate to each stage of the decision analysis process. By exploring the essential decisions, a set of criterion will be developed with which to research and evaluate the algorithms. The end product will aid in developing a guide to help users logically approach and evaluate the decision analysis processes.

Acknowledgment

The group would like to acknowledge our advisors Dr. John Wm. Lamont, Dr. Ralph Patterson, and Dr. Keith Adams for all of their valuable guidance throughout the project.

Section 1.0:

Fuzzy Logic

What is Fuzzy Logic?

Fuzzy logic is a superset of Boolean Logic that makes use of a continuous range of truth-values, or partial truths. It is not strict binary. It uses linguistic input/output associations as a means to estimate the uncertainty in real life problems and decisions and to approximate non-absolute functions. It was introduced by Dr. Lotfi Zadeh of the University of Berkeley in the 1960’s in his attempts to model the human language and its uncertainties. Its use arises with the principle of incompatibility.

Principle of Incompatibility:

As the complexity of a system increases, it becomes more difficult and eventually impossible to make a precise statement about its behavior, eventually arriving at a point of complexity where the fuzzy logic method born in humans is the only way to get at the problem.

(originally identified and set forth by Lotfi A. Zadeh, Ph.D. University of California Berkeley) [Sowell, Thomas Fuzzy Logic for “Just Plain Folks” ]

In order to get a clear idea of fuzzy logic, it is necessary to look at a couple of simple examples. The first is the typical triangular fuzzy representation of the number 5, shown in figure 1.1. This displays the idea of partial truth. Right at the number 5 the value is 1 indicating that it is completely true. As you move away from 5 in either direction, the value does not drop immediately to zero. Instead the value drops off at a certain slope, indicating a certain degree of truth.

Figure 1.1 Fuzzy Number

Another example is shown in figure 1.2. This shows the fuzzy interval from 3.0 to 5.0. Across the interval the value is one and then at the endpoints the value slopes away or gets fuzzy.

Figure 1.2 Fuzzy Interval from 3.0 to 5.0

Applications of Fuzzy Logic

Fuzzy logic is useful in a wide range of problems and applications. It is often used for solving systems that are difficult to model with more common tools, systems that require the input or control a human, or systems that are not extremely precise or clearly defined. Most systems or applications of fuzzy logic use it in the form of fuzzy expert systems, which are systems that make use of the fuzzy logic system as their basis for control. Some of the common applications of fuzzy logic or fuzzy expert systems are:

( Decision Support

( Data Analysis

( Financial Systems

( Control Systems

( Pattern Recognition

( Operation Research

Fuzzy Expert Systems

Fuzzy expert systems are systems that use fuzzy logic as a rule-base with which to apply membership functions and an inference procedure for solving a wide range of problems. The general flow through of a fuzzy expert system is shown in figure 1.3.

Figure 1.3 Fuzzy Expert System Flow

Inputs

The inputs into a fuzzy expert can be anything that can be represented with value or degree of truth.

Fuzzification

Fuzzification is the process by which a fuzzy expert system takes in the actual values of a set of inputs and determines their degree of truth in relationship to each membership function or rule premise that is defined for the given system.

Inference

Inference is the process by which the truth values are processed according to the fuzzy rules and membership functions and applied to the conclusion of each of the separate rules. This results in each of the outputs of each rule being represented by a fuzzy subset. This process is most often done using minimum inferencing or product inferencing. In minimum inferencing, the output membership function is cut off at a value that is equal to the value of the computed degree of truth of the rule premise. In product inferencing, the output membership function is multiplied by the value of the computed degree of truth of the rule premise.

Composition

Composition is the process by which a single fuzzy subset is determined for each individual output by combining all of the individual fuzzy subsets for that given output. The most common used methods for combining the fuzzy subsets are maximum composition and summation composition. In maximum composition, the maximum truth value of all of the fuzzy subsets, assigned through the inference rule, is used to construct the combined output fuzzy subset. In summation composition, the sum of all of the fuzzy subsets, assigned through the inference rule, is used to construct the combined output fuzzy subset.

Defuzzification

Defuzzification is the process by which a fuzzy set for an output is changed back into a crisp exact number. There are a very large number of possible methods for defuzzification, but the maximum and centroid methods are a couple of the more common. In using the centroid method the center of gravity of the values comprising the output fuzzy set is selected as the representative crisp output value. In using the maximum method the maximum truth value that occurs in the output fuzzy set is selected as the representative crisp output value.

Outputs

The expected output of a fuzzy expert system is a crisp number representing the max, average, centroid, singleton, or some other representative value of the inference of the fuzzy expert system. The expected outputs are normally controlled by the user and are determined according to the system that is set up. Some example of outputs for common applications include:

( The answer to a decision

( The result of a data analysis

( A control signal

( A recognized pattern

Control

Control of the fuzzy expert system can be addressed in two aspects. One aspect is when a fuzzy expert system is being used in a control system to adjust or maintain a certain output. In this system a feedback loop is used to adjust the input and control the system behavior. The other aspect in which control can be addressed is when there is no feedback and the outputs are determined directly from the inputs. In this case all the control that is needed is defined within the member functions.

Implementation

One of the benefits of Fuzzy expert system is there ease of implementation. Fuzzy logic is based off natural thought and the human decision process. The rules and structure are also determined and modeled linguistically, so they are easy to implement and understand. This results in a simplified and easier development cycle and can provide a more usable and friendly performance.

References

Sowell, Thomas. Fuzzy Logic for “Just Plain Folks”

. Fuzzy Logic. 2000 SiteTerrific Web Solutions

Keller, Paul E.. What is Fuzzy Logic? < >

Section 2.0:

Bayesian Logic

What is Bayesian Logic?

Bayesian logic is a type of logic that uses probabilistic inference and inferential statistics to evaluate a set of known events and determine the future outcome. It is used heavily in decision making by quantifying uncertainty. It takes all the known events and background information of a situation and determines the probability that a particular outcome is true or takes place. Bayesian logic is named after Thomas Bayes, a Nonconformist minister and mathmaticiam, who first introduced the fundamental theorem of inverse probability, Bayes theorem.

Bayes Theorem

P(A|B) = P[A + B]/P[B]

Bayes Theorem, as shown, is a probability relation that shows the probability that a certain outcome, which could have been the result of multiple causes, was the result of a particular cause.

Applications of Bayesian Logic

Bayesian logic is useful in a wide range of problems and applications. It is often used for solving systems that are inherent with a lot of uncertainty in the preciseness and availability of knowledge. Most systems or applications of Bayesian logic use it in the form of Bayesian networks, which are systems that make use of the Bayesian logic system as their basis for control and computation. Some of the common applications of Bayesian logic or Bayesian networks are:

( Decision support, mainly regarding maintenance planning and risk-related issues

( Problems in the financial sector.

( Marketing strategies

( Business problems and uncertainties

Bayesian Network

Bayesian logic is usually used in the form of a Bayesian network, which is a method for creating a model to represent the uncertainty that is inherent in many situations, including:

uncertainty in the knowledge that experts posses

uncertainty in the application being modeled

uncertainty in the interpreting of knowledge in an application

uncertainty of the availability and preciseness of knowledge as related to an application

Bayesian networks are systems that use Bayesian logic as the underlying rule-base with which determine the probabilities of the various assertions and how to update them as more data is determined or gathered. A simple example of a Bayesian network is shown in figure 2.1.

Figure 2.1 Simple Baysian Network for an Alarm

In the above figure a node is represented by a circle and represents a unique assertion and the lines connecting the nodes represent the probability that the first node is the cause of the second node. For example the line connecting node B and node A represents the probability that a burglary is the cause of a particular outcome at node A. For each line connecting nodes there is a corresponding matrix which represents the probability P(N1|N2), that contains a precise value of N2 for each value of N1. The general flow of a Bayesian network is shown in figure 2.2.

Figure 2.2 Bayesian Network Flow

Inputs

The inputs to a Bayesian network are the probability or likelihood of each of the initial assertions taking place or being true.

Bayesian Network Process

The inputs are taken into the Bayesian network and then based on the Bayesian logic the corresponding probability or likelihood of each of the subsequent assertions in the Bayesian network is determined. This process continues until the probability or likelihood of each assertion has been determined.

OUTPUTS

The output is then the probability or likelihood of the assertions corresponding to the output nodes, allowing the user to make decisions and determine the outcomes for different applications based off incomplete or imprecise knowledge of the inputs.

Control

Control for Bayesian networks is determined by the underlying Bayesian logic. Since Bayesian logic is based on inferential statistics and probability, the network will always converge or produce an output. For accurate results it is necessary to be as thorough as possible and to model all situations.

Implementation

Bayesian networks are based heavily on inferential statistics and probability theory. As a result, they can be come very difficult to implement if the size of the network is large, if there are a large number of inputs, or if the user is not familiar with inferential statistics and probability theory.

References

Basics of Bayesian Inference and Belief Networks.

Allen, Sam. Bayes' Theorem.

Bayesian Networks . ................
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