Viva Presentation - Fuzzy Logic and Dempster-Shafer Theory to Detect The Risk of Disease Spreading

Fuzzy Logic and Dempster-Shafer Theory to Detect The Risk of Disease Spreading

Andino Maseleno

6 April 2015

Computer Science Program, Faculty of Science, Universiti Brunei Darussalam

Jalan Tungku Link, Gadong BE1401, Negara Brunei Darussalam

This research aims to combine the mathematical theory of evidence with the rule based logics to refinethe predictable output. Integrating Fuzzy Logic and Dempster-Shafer theory by calculating the similaritybetween Fuzzy membership function in the context to detect the risk of disease spreading and finally todevelop a realistic and useful Web mapping for displaying maps on a screen to locate the risk of diseasespreading. The risk of disease spreading include Highly Pathogenic Avian Influenza H5N1, AfricanTrypanosomiasis and skin disease. The risk of disease spreading is not classified according to higherdensity which is equal to higher risk. This research has considered population changes in an area to detectthe risk of disease spreading. Population density in the area include very low, low, medium, high and veryhigh. The result reveals that the system has successfully identified the risk of disease spreading, moreoverthe maps can be displayed as the visualization.

The novelty aspect of this work is that basic probability assignment is proposed based on the similaritymeasure between membership function. The similarity between Fuzzy membership function is calculatedto get a basic probability assignment. This work is recommended to human experts and physicians whospecializes in diagnosing and treatment of diseases. The human experts will find it useful as an aid in thedecision making process and confirmation of suspected cases. The highest percentage of the risk ofdisease spreading of Highly Pathogenic Avian Influenza H5N1 is 20 %. The highest percentage of the risk ofdisease spreading of African Trypanosomiasis is 17 %. The highest percentage of the risk of diseasespreading of skin disease is 22 %. In this research it is Fuzzy Logic and Dempster-Shafer theory, whichresulted in a 0 % rejection.

Keywords: Fuzzy Logic, Dempster-Shafer theory, the risk of disease spreading, Highly Pathogenic Avian Influenza H5N1, African Trypanosomiasis, skin disease.

Abstract

1. Introduction

2. Literature Review

3. Methodology

4. Implementation

5. Result and Discussion

6. Conclusions

Contents

Chapter 1 Introduction

Dealing with uncertainty is a fundamental issue for the human-like intelligence exhibited by machines or software. Evidence theory is an important tool of uncertainty modeling when both uncertainty origins from human's lack of knowledge of the physical world and uncertainty derives from the natural variability of the physical world are present in the problem under consideration. In decision making processes with human's lack of knowledge of the physical world and lack of the ability of measuring and modeling the physical world, the Fuzzy Logic and Dempster-Shafer mathematical theory of evidence have gained prominence as the methods of choice over traditional probabilistic methods. The fundamental and important object of the mathematical theory of evidence is a primitive function called a basic probability assignment. However, how to obtain basic probability assignment is still an open issue. The membership function of a Fuzzy set is a generalization of the indicator function in classical sets. In Fuzzy Logic, it represents the degree of truth as an extension of valuation.

1.1 Motivation

Dempster-Shafer mathematical theory of evidence is a powerful tool for combining accumulative evidence and changing prior knowledge in the presence of new evidence. It also allows for the direct representation of uncertainty of system responses where an imprecise input can be characterized by a set or an interval and the resulting output is a set or an interval. Fuzzy Logic is a logic operations method based on many-valued logic rather than binary logic or two-valued logic. Two-valued logic often considers 0 to be false and 1 to be true. Fuzzy Logic deals with truth values between 0 and 1, and these values are considered as intensity or degrees of truth. Dempster-Shafer mathematical theory of evidence, a probabilistic reasoning technique, is designed to deal with uncertainty and incompleteness of available information. Dempster-Shafer mathematical theory of evidence allows one to combine evidence from different sources and arrive at a degree of belief which is represented by a belief function that takes into account all the available evidence. Degree of belief is the expected truth value which is the relation between Fuzzy Logic and Dempster-Shafer mathematical theory of evidence.

1.1 Motivation (cont.)

In the absence of empirical data, experts in related fields provide necessary information. The fundamental objects of this theory of evidence are called focal elements, and the primitive function associated with it is called basic probability assignment. Focal elements are usually crisp subsets of some universal set. However, in certain situations focal elements may also be represented by Fuzzy numbers. There are many situations where human often face at the same time Fuzzy and non Fuzzy uncertainties. This suggests to combine Dempster-Shafer mathematical theory of evidence and Fuzzy sets frameworks. Thus, the goal of this work is to estimate basic probability assignments using Fuzzy membership functions which capture vagueness. The advantage of this method is a new method to obtain basic probability assignment proposed based on the similarity measure between membership function. This thesis proposes Fuzzy Logic and Dempster-Shafer mathematical theory of evidence by integrating Fuzzy Logic and Dempster-Shafer mathematical theory of evidence by calculating the similarity between Fuzzy membership function. This thesis implements Fuzzy Logic and Dempster-Shafer mathematical theory of evidence and Web mapping. Fuzzy Logic and Dempster-Shafer mathematical theory of evidence implement to detect the risk of disease spreading and Web mapping to locate the risk of disease spreading.


More than one billion people, one-sixth of the world's population, are affected by neglected diseases. There is an urgent need to develop better, more affordable systems for diseases that are devastating developing countries. Based on Cumulative Number of Confirmed Human Cases of Avian Influenza (H5N1) Reported to World Health Organization (WHO) in the 2013 from 15 countries, Indonesia has the largest number of death because of Avian Influenza which are 160 deaths (WHO, 2013). Based on World Health Organization (WHO) report in the 2013 skin diseases still remain common in many rural communities in developing countries, with serious economic and social consequences as well as health implications. Directly or indirectly, skin diseases are responsible for much disability and loss of economic potential, disfigurement, and distress due to symptoms such as itching or pain. Neglected tropical diseases kill an estimated 534,000 people world wide every year (WHO, 2009). World Health Organization reports that African Trypanosomiasis affects mostly poor populations living in remote rural areas of Africa that can be fatal if not properly treated. Sustainable elimination of African Trypanosomiasis as a public-health problem is feasible and requires continuous efforts and innovative approaches.


In this research, a novel combination of Fuzzy Logic and Dempster-Shafer mathematical theory of evidence are applied to detect the risk of disease spreading. Dempster-Shafer mathematical theory of evidence handles uncertain and incomplete information through the definition of two dual non additive measures which include plausibility and belief. These measures are derived from a density function, $m$, called a basic probability assignment or mass function. Glanville et al (Glanville, 2009) using map layer of Indonesian major cities represents those cities in Indonesia that have a population greater than 50,000. It is expected that such cities are likely to have at least one poultry market. The density of cities was calculated over an area of 100km, and the risk of disease spreading classified according to this density (higher density=higher risk). In this research, the risk of disease spreading is not classified according to higher density which is equal to higher risk. However, this research has considered population changes in areas to detect the risk of disease spreading. The risk of disease spreading describes five interpretations which include the risk of disease spreading should be very low, the risk of disease spreading should be low, the risk of disease spreading should be medium, the risk of disease spreading should be high, and the risk of disease spreading should be very high. These probabilities assign evidence to a proposition or hypothesis. The derivation of the basic probability assignment is the most crucial step since it represents the knowledge about the application as well as the uncertainty incorporates in the selected information source. Basic probability assignment definition remains a difficult problem to apply Dempster-Shafer theory to practical applications. Therefore, the experts provide opinion in terms of basic probability assignment for interval or crisp focal elements. Those basic probability assignments are proposed based on the similarity measure between membership function. Furthermore, the similarity between Fuzzy membership function is calculated to get basic probability assignment. Finally, this research shows how they can be effectively used in prediction of the risk of disease spreading.


1. To combine the mathematical theory of evidence with the rule based to improve the predictable output. Integrating Fuzzy Logic and Dempster-Shafer mathematical theory of evidence in the context to detect the risk of disease spreading.

2. To develop a realistic and useful Web mapping for displaying maps on a screen to locate the risk of disease spreading that can be of real usage.

3. To encounter the most important and unexpected enemies of the human been the epidemic diseases through the prediction of the risk of disease spreading.

1.2 Research Objectives

The thesis contributes novel approaches to detect the risk of disease spreading. The application has also been developed as research outcome. The contributions of the thesis are shown as follows:

1. The thesis proposes Fuzzy Logic and Dempster-Shafer mathematical theory of evidence in the context to find the highest basic probability assignment of the risk of disease spreading.

2. The thesis proposes a Web mapping for displaying maps on a screen to locate the risk of disease spreading that can be a real usages.

1.3 Research Contributions

Chapter 2Literature Review

Large amount of literature is available on Fuzzy Logic and its applications. Fuzzy Logic can handle problems with imprecise data and give more accurate results. Professor L.A. Zadeh introduced the concept of Fuzzy Logic (Zadeh, 1965); soon after, researchers used this theory for developing new algorithms and decision analysis. Fuzzy Logic has been applied successfully in hundreds of application domains including image processing, mobile robot navigation, distance relation, high energy physics, natural numbers, medicinal chemistry, robot manipulators, optimization of machining processes, power converters, control of permanent-magnet synchronous motors, and electric power systems.

2.1 Introduction

Several researchers have investigated the relationship between Fuzzy sets and Dempster-Shafer mathematical theory of evidence and suggested different ways of integrating them.

Integration within symbolic, rule-based models have been used for control and classification purposes (Yen, 1990), (Binaghi, 2000).

Yager and Filev attempted to present a Fuzzy inference system based on FuzzyDempster-Shafer mathematical theory of evidence which integrated the probabilistic information in the output (Yager, 1990). In their works, the consequent is shaped as a Dempster-Shafer belief structure, where each focal element has the same membership function.

Binaghi et al. (Binaghi, 2000) proposed a structure for classification tasks similar to that of Yager (Yager, 1990), where the focal element is a set representing the class label.

2.1 Introduction (cont.)

Dymova (Dymova, 2012) proposed a critical analysis of conventional operations on intuitionistic Fuzzy values and their applicability to the solution of multiple criteria decision making problems in the intuitionistic Fuzzy setting. Two sets of operations on intuitionistic Fuzzy values based on the interpretation of intuitionistic Fuzzy sets in the framework of the Dempster-Shafer theory of evidence are proposed and analysed.

Walijewski (Walijewski, 2002) concentrated on the role of Fuzzy operators, and on the problem of discretization of continuous attributes.

Dutta et al. (Dutta, 2011) studied Dempster-Shafer theory of evidence by considering focal elements as triangular Fuzzy number. The authors have devised a method for obtaining belief and plausibility measure from basic probability assignments assigned to Fuzzy focal elements.

Boudra et al. (Boudraa, 2004) estimated basic probability assignments using Fuzzy membership functions.


Ghasemi et al. (Ghasemi, 2013) studied the main characteristic of the proposed method where is that the rules of Fuzzy inference system are considered as evidences in which the firing level of each rule and Fuzzy Naive Bayes method are employed for calculating the basic probability assignment of focal element. In the Naive Bayes classifier, all variables are assumed to be nominal variables, which means that each variable has a finite number of values and also assumes independence of features. However, in large databases, the variables often take continuous values or have a large number of numerical values.

Binaghi et al. (Binaghi, 2000) presented a supervised classification model integrating Fuzzy reasoning and Dempster-Shafer propagation of evidence has been built on top of connectionist techniques to address classification tasks in which vagueness and ambiguity coexist. The approach is the integration within a Neuro-Fuzzy system of knowledge structures and inferences for evidential reasoning based on Dempster-Shafer theory. The common weakness of neural network, however, is a problem of determination of the optimal size of a network configuration, as this has a significant impact on the effectiveness of its performance.


The Dempster-Shafer theory originated from the concept of lower and upper probability induced by a multivalued mapping by Dempster(Dempster, 1967), (Dempster, 1968). Following this work his student Glenn Shafer (Shafer, 1976) further extended the theory in his book "A Mathematical Theory of Evidence", a more thorough explanation of belief functions. Dempster-Shafer mathematical theory of evidence is one of the important tool for decision making under uncertainty. Dempster-Shafer theory makes inferences from incomplete and uncertain knowledge, provided by different independent knowledge sources. A first advantage of Dempster-Shafer theory is its ability to deal with ignorance and missing information. In particular, it provides explicit estimation of imprecision and conflict between information from different sources and can deal with any unions of hypotheses.


Dempster-Shafer mathematical theory of evidence is a formal framework for plausible reasoning which provides techniques for characterizing the evidences by considering all the available evidences. Dempster-Shafer theory has been used in decision making.

Lyu et al. (Lyu, 2010) studied Dempster-Shafer theory for the reasoning with imprecise context.

Yao et al. (Yao, 2011) used Dempster-Shafer theory for the multi-attribute decision making problems with incomplete information by identify all possible focal elements from the incomplete decision matrix, and then calculate the basic probability assignment of each focal element and the belief function of each decision alternative.


Yu et al. (Yu, 2012) used Dempster-Shafer Theory as an applied approach to scenario forecasting based on imprecise probability.

Uphoff et al. (Uphoff, 2013) studied application of Dempster-Shafer theory to task mapping under epistemic uncertainty. Dempster-Shafer mathematical theory of evidence implies a type of uncertainty associated with conditions of ambiguity through the data by dealing with ignorance and missing information. This characteristic is due to using a combination of evidence weight from different sources to obtain a new evidence weight.


Population density and urbanization are two major factors affecting disease spreading. People who live in close proximity to one another spread diseases more quickly and easily (Jones, 2008). Also affecting the spread of encountering new diseases is migration: this increases as humans move into previously uninhabited lands because of population growth, or as humans migrate into areas where they do not have resistance to certain diseases(Anonymous, 2012). Disease in a population increases with the density of that population. High densities makes it easier for parasites to find hosts and spread the disease. Population density is a measurement of the number of people in an area. It is an average number. Population density is calculated by dividing the number of people by an area. Population density is usually shown as the number of people per square kilometer (Geography, 2013). In this research, population density is a parameter in the algorithm.Population density of an area may change over time. In recent decades, some cities have seen their urban centers lose population density, as residents spread farther out to suburbs and exurbs (Fee, 2011).

2.2 Risk Factor Identification

Population density affect the disease spreading within a population and other populations because a population that is very dense will generally see a faster disease spreading due to the larger amount of contact between individuals. In a population that is not very dense, close contact is much less likely to occur, thus halting the disease spreading. Disease spreading and population density are highly correlated (Yang, 2012), (Yoneyama, 2012), (Padua, 2012). Population density is measured by the average of the number of contacts with susceptible individuals by each individual in the population during a fixed length time period (Tarwater, 2001).

2.2 Risk Factor Identification (cont.)

Population density and growth are significant drivers for the emergence of different categories of infectious diseases (Jones, 2008). Most diseases require that their host organisms come into close contact with another compatible organism in order to spread, meaning that denser populations of suitable hosts promote faster spread of a disease and that less-dense populations inhibit disease communication. Because disease prevention relies so heavily on contact between potential carriers, lower population densities have an increased chance of controlling disease spreading. In this study, a novel combination of Fuzzy Logic and Dempster-Shafer mathematical theory of evidence are applied to detect the risk of disease spreading. The risk of disease spreading is not classified according to higher density which is equal to higher risk. This research has considered population changes in an area to detect the risk of disease spreading. Population density in an area can be very low, low, medium, high and very high.

2.2 Risk Factor Identification (cont.)

A map is a visual representation of an area, a symbolic depiction highlighting relationships between elements of that space such as objects, regions, and themes (Njue, 2010). People have used maps for centuries to represent their environment. Maps are used to show locations, distances, directions and the size of areas. Maps also display geographic relationships, differences, clusters and patterns. Maps are used for navigation, exploration, illustration and communication in the public and private sectors (Nations, 2000). Nearly every area of scientific enquiry uses maps in some form or another. Maps, in short, are an indispensable tool for many aspects of professional and academic work.

2.3 Web Mapping

Cartography is the art and science of making maps. To create modern, high-quality cartography requires the use of appropriate technology. This provides efficient processes that amplify human creative and expressive skills in order to communicate the essential spatial message (ESRI, 2004). Cartography has been affected by the information revolution somewhat later than other fields. Early computers were good at storing numbers and text. Maps, in contrast, are complex, and digital mapping requires large data storage capacity and fast computing resources. Furthermore, mapping is fundamentally a graphical application, and early computers had limited graphical output capabilities. The earliest mapping applications implemented on computers in the 1960s did not therefore find wide application beyond a few government and academic projects. It took until the 1980s for commercial geographic information systems to reach a level of capability that would lead to their rapid adoption, for example, in local and regional government, urban planning, environmental agencies, mineral exploration, the utility sectors and commercial marketing and real estate firms.

2.3 Web Mapping (cartography...)

Web mapping is the process of designing, implementing, generating and delivering maps on the World Wide Web (Kresse, 2012). While Web mapping primarily deals with technological issues, Web cartography additionally studies theoretic aspects: the use of Web maps, the evaluation and optimization of techniques and workflows, the usability of Web maps, social aspects, and more. The Web mapping applications are based on the common client-server concept, which describes a relationship between two programs: a client program, Web browser, that sends a request to a server program that then executes the request and returns the requested information (Havlickova, 2009). Clients and Servers often operate on separate hardware over computer network. A client is typically a Web browser. Common Web browsers on the market include Internet Explorer, Mozilla Firefox, and Google Chrome. Server, on the other hand, is a high-performance host that provides services and sharing resources with multiple clients. A map rendering engine is usually built on top of a Web server and linked with a back end GIS database ready to retrieve and render data. The client communicates with server by sending HTTP request, the server in turn process the request, respond and send back HTML documents, maps and images for client display. The client communicates with server by sending HTTP request, the server in turn process the request, respond and send back HTML documents, maps and images for client display (Jiang, 2010). In the case of Web mapping applications the server should be able to work with geographic data and that is why it is necessary to

2.3 Web Mapping (web mapping is..)

The Web mapping server is the engine behind the maps. The mapping server or Web mapping program needs to be configured to communicate between the Web server and assemble data layers into an appropriate image. A map is not possible without some sort of mapping information for display. Mapping data is often referred to as spatial or geospatial data and can be used in an array of desktop mapping programs or Web mapping servers. Mapping data to outbreak of the disease uses spatial and non-spatial data in ArcGIS format. There are variety of health surveillance systems that help supplement existing public health system by focusing on Web mapping (Turton, 2008), (Freifeld, 2014). Several researchers have investigated the maps to contribute to meet international targets for reduced malaria illness and death (Hay, 2009), (Gething, 2011). Those methods are not to locate the risk of disease spreading. This research is aimed to develop a realistic and useful Web mapping for displaying maps on a screen to locate the risk of disease spreading so that action may be taken.

2.3 Web Mapping (The Web Mapping server is..)

Fuzzy Logic and Dempster-Shafer mathematical theory of evidence implement to detect the risk of disease spreading and Web mapping to locate the risk of disease spreading. The set of linguistic variables and their meanings is compatible and consistent with the set of conditional rules used, the overall outcome of the qualitative process is translated into objective and quantifiable results. Fuzzy mathematical tools and the calculus of Fuzzy IF-THEN rules provide a most useful paradigm for the automation and implementation of an extensive body of human knowledge heretofore not embodied in the quantitative modeling process. These mathematical tools provide a means of sharing, communicating, and transferring this human subjective knowledge of systems and processes.

The next chapter, Chapter 3, discusses methodology which is used in the thesis. As part of this, Chapter 3 explains uncertainty reasoning, Dempster-Shafer mathematical theory of evidence, Fuzzy Logic theory, Fuzzy Logic and Dempster-Shafer mathematical theory of evidence, system processes and database.

2.4 Summary

Chapter 3Methodology

3.1 IntroductionThis chapter explains uncertainty reasoning, Dempster-Shafer mathematical theory of evidence, Fuzzy Logic, Fuzzy Logic and Dempster-Shafer mathematical theory of evidence, system processes, and database. Precise and certain rules usually can not model all concepts with generality and conciseness at the same time on the contrary, some degree of imprecision allows to formalize real-world criteria with a limited number of rules. Imperfection is a general term used to describe rules softened in different ways: from gradualness, where a known property may be present at different levels, to uncertainty, where some information is missing either because of a lack of awareness and understanding of a set of information or due to an intrinsic aleatory in the context being analyzed (Sottara, 2010).Probability theory provides a consistent framework for dealing with uncertain knowledge for a robust and reliable recognition of complex event (Romdhane, 2010).

3.1 Introduction (cont.)Dempster-Shafer theory is a mathematical theory of evidence that assigns probabilities to sets.The Dempster-Shafer mathematical theory of evidence is based on probability theory. The Dempster-Shafer evidential theory is a method about uncertainty reasoning, and this theory reduces the requirements of the knowledge of prior probability and conditional probability. In the process, it has able to synthesize the evidence from different sources and dealing with uncertainty. One of the most important features of Dempster-Shafer mathematical theory of evidence is that the model is designed to deal with varying levels of precision regarding the information and no further assumptions are needed to represent the information.

3.1 Introduction (cont.)Fuzzy Logic is based on the theory of Fuzzy sets, where an object's membership of a set is more gradual rather than just member or not a member. Fuzzy Logic uses the whole interval of real numbers between zero or False and one or True to develop a logic as a basis for rules of inference. In this research, a novel combination of Fuzzy Logic and Dempster-Shafer mathematical theory of evidence are applied to the system. This chapter presents a model integrating Tsukamoto Fuzzy reasoning and Dempster-Shafer mathematical theory of evidence. The salient aspect of the approach is the integration within Tsukamoto Fuzzy reasoning and inferences for evidential reasoning based on Dempster-Shafer mathematical theory of evidence. The system is constructed using open source components that allow for easy customization, and by utilizing open standards the server can be accessed by other clients with very little effort on the part of expert users who require the ability to carry out more advanced analysis than is possible using the Web based client.

Uncertainty is a general concept that reflects human lack of sureness about something or someone, ranging from just short of complete sureness with an almost complete lack of conviction about an outcome. The fundamental structure of uncertainty model contains following three components which include the description of information uncertainty or rules; the description of evidence uncertainty or facts; and the spread of uncertainty (Li, 2010).

Reasoning theories are divided into certainty reasoning theories and uncertainty reasoning theories. Certainty thinking was once and will be still prevailing in different disciplines. In the Cartesian philosophy, mathematics was the only accurate knowledge learning to provide. With the combination of mathematics and physics, all sorts of natural and social phenomena could be explained in science. Leibniz, philosopher and mathematician, was convinced that symbolic language of science could construct the universal logic and logical calculus, and all phenomena could be clearer. Newton'sabsolute time-space sure that all the observable physical quantity in principle could be in infiniteaccurate measurement and its foundation was the uncertainty of physical laws. An unknown world was deterministic for perfectly rational policy makers in the traditional decision science view. A man could get the reflect of maximization as long as according to the principle which marginal benefit equals marginal cost decision. However, the world is uncertain (Yanfei, 2013).

3.2 Uncertainty reasoning

Decisions are often taken on the basis of imperfect information and knowledge (imprecise, uncertain, incomplete) provided by several more or less reliable sources and depending on the states of the world: decisions can be taken in certain, risky or uncertain environment (Tacnet, 2011). The lack of certainty is ubiquitous and happens in every single event people encounter in the real world. Whether it rains or not tomorrow is uncertain; whether there is a flight delay is uncertain. Just as Socrates, was a classical Greek (Athenian) philosopher credited as one of the founders of Western philosophy, in ancient Greek said, "as for me, all I know is I know nothing." Uncertainty distinguishes from a certainty in the degree of belief or confidence. If certainty is referred to as a perception or belief that a certain system or phenomenon can experience or not, uncertainty indicates a lack of confidence or trust in an article of knowledge or decision. Uncertainty is a term used in subtly different ways in a number of fields, including philosophy, physics, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable and/or stochastic environments, as well as due to ignorance and/or indolence (Norvig, 2013). According to the Cambridge Dictionary, "uncertainty is a situation in which something is not known, or something that is not known or certain (Cambridge, 2013).

3.2 Uncertainty reasoning (cont.)

Uncertainty arises from different sources in various forms, and is classified in different ways by different communities. According to the origin of uncertainty, it is categorized into aleatoryuncertainty or epistemic uncertainty. Aleatory uncertainty derives from the natural variability of the physical world. It reflects the inherent randomness in nature. It exists naturally regardless of human knowledge. For example, in an event of flipping a coin, the coin comes up heads or tails with some randomness. Even if researchers do many experiments and know the probability of coming up heads, researchers still cannot predict the exact result in the next turn. Aleatory uncertainty cannot be eliminated or reduced by collecting more knowledge or information. No matter whether people know it or not, this uncertainty stays there all the time. Aleatory uncertainty is sometimes also referred to as natural variability, objective uncertainty, external uncertainty, random uncertainty, stochastic uncertainty, inherent uncertainty, irreducible uncertainty, fundamental uncertainty, real world uncertainty, or primary uncertainty. Epistemic uncertainty origins from human's lack of knowledge of the physical world and lack of the ability of measuring and modelling the physical world. Unlike aleatory uncertainty, given more knowledge of the problem and proper methods, epistemic uncertainty can be reduced and sometimes can even be eliminated. For example, the estimation of the distance between Bandar Seri Begawan and Kuala Belait can be more precise if people have known the distance from Bandar Seri Begawan to Tutong. Epistemic uncertainty is sometimes also called knowledge uncertainty, subjective uncertainty, internal uncertainty, incompleteness, functional uncertainty, informative uncertainty, or secondary uncertainty. Dempster-Shafer mathematical theory of evidence can deal with both aleatory and epistemic uncertainty.

3.2 Uncertaintiy reasoning (cont.)

It is difficult to avoid uncertainty when attempting to make models of the real world. Uncertainty is inherent to natural phenomena, and it is impossible to create a perfect representation of reality. Classic mathematics deals with ideal worlds where perfect geometric figures exist and can verify extraordinary conditions. The formalisation of Fuzzy sets started in the 1960s with the works of Zadeh (Zadeh, 1965) in Fuzzy sets and Dempster(Dempster, 1968) in belief functions. Belief functions offer a non Bayesian method for quantifying subjective evaluations by using probability. In the 1970s, it was further developed by Shafer, whose book Mathematical Theory of Evidence (Shafer, 1976) remains a classic in belief functions, or the so-called Theory of Evidence. This theory has been also called the Dempster-Shafer Mathematical Theory of Evidence. In the 1980s, the scientific community working with Artificial Intelligence got involved in using the theory of evidence in applications. The Dempster-Shafer theory or the theory of belief functions is a mathematical theory of evidence which can be interpreted as a generalization of probability theory in which the elements of the sample space to which nonzero probability mass is attributed are not single points but sets. The sets that get nonzero mass are called focal elements. The sum of these probability masses is one, however, the basic difference between Dempster-Shafer mathematical theory of evidence and traditional probability theory is that the focal elements of a Dempster-Shafer structure may overlap one another. The Dempster-Shafer mathematical theory of evidence also provides methods to represent and combine weights of evidence.

3.3 Dempster Shafer mathematical theory of evidence

3.3.1 ROE (bpa defines..)

3.3.1 Representation of evidence






In decision making processes with human's lack of knowledge of the physical world and lack of the ability of measuring and modelling the physical world, the Fuzzy Logic and Dempster-Shafer mathematical theory of evidence have gained prominence as the methods of choice over traditional probabilistic methods. The fundamental and important object of the mathematical theory of evidence is the primitive function called a basic probability assignment.

In the absence of empirical data, experts in related field provide necessary information. However how to obtain basic probability assignment is still an open issue. The membership function of a Fuzzy set is a generalization of the indicator function in classical sets. In Fuzzy Logic, it represents the degree of truth as an extension of valuation. Fuzzy Logic is a logic operation method based on many-valued logic rather than binary logic or two-valued logic.

Dempster-Shafer mathematical theory of evidence, a probabilistic reasoning technique, is designed to deal with uncertainty and incompleteness of available information. Dempster-Shafer mathematical theory of evidence allows one to combine evidence from different sources and arrive at a degree of belief which is represented by a belief function that takes into account all the available evidence. The degree of belief is expecting a truth value which is the relation between Fuzzy Logic and Dempster-Shafer mathematical theory of evidence.


3.3.2 Evidence combination

3.3.2 Evidence combination (!)

3.4 Fuzzy Logic

3.4 Fuzzy Logic (cont.)






3.5 Fuzzy Logic and Dempster-Shafer mathematical theory of evidence

The membership function of a Fuzzy set is a generalization of the indicator function in classical sets. In Fuzzy Logic, it represents the degree of truth as an extension of valuation. Properties of membership function are:

1. The membership function should be strictly monotonically increasing, or strictly monotonically decreasing, or strictly monotonically increasing then strictly monotonically decreasing with the increasing value of elements in the universe of discourse X. This term is given by the equation

2. The membership function should be continuous or piecewise continuous.

3. The membership function should be differentiable to provide smooth results.

4. The membership function should be of simple straight segments to make the process of fuzzy models easy and to high accuracy.

3.5 Fuzzy Logic and Dempster-Shafer mathematical theory of evidence (cont.)

A new method to obtain basic probability assignment is proposed based on the similarity measure between membership function. This thesis proposes Fuzzy Logic and Dempster-Shafer mathematical theory of evidence by calculating the similarity measure between Fuzzy membership function. Method to integrate Fuzzy Logic and Dempster-Shafer mathematical theory of evidence as follows:




Flowchart of Fuzzy Logic and Dempster-Shafer

People often have to make decisions based on uncertain awareness and understanding of a set of information, not only in their private lives, but also in professional activity. Therefore, any reasoning method that tries to replicate human reasoning must be able to draw conclusions from uncertain models and uncertain data. Models may be uncertain because of indeterminism in the real world or because of human lack of knowledge. Furthermore, data may be incomplete because of pieces of information may be not available in a diagnostic case, ambiguous because of a pronoun in a sentence may refer to different subjects, erroneous because of patients may lie to their doctors, or imprecise because of the limited precision of measuring devices, subjective estimations, or natural language.

Summary of Chapter 3

The Dempster-Shafer mathematical theory of evidence has attracted considerable attention as a promising method of dealing with some of the basic problem arising in combination of evidence and data fusion. Tsukamoto Fuzzy reasoning does the mapping from given input to an output using Fuzzy Logic.Tsukamoto Fuzzy reasoning models have a number of rules based on if-then conditions. In fact, these rules are easy to learn and use and can be modified according to the situation. It helps to make decisions and can be used in decision analysis. The next chapter discusses the implementation of Fuzzy Logic and Dempster-Shafer mathematical theory of evidence to the risk of disease spreading and Web mapping to locate the risk of disease spreading.

Summary of Chapter 3 (cont.)

Chapter 4Implementation

Fuzzy logic and Dempster-Shafer mathematical theory of evidence contribute new ideas to detect the risk of disease spreading. The risk of disease spreading is not classified according to higher density which is equal to higher risk. This thesis considers population changes in an area to detect the risk of disease spreading. Population density in areas which include very low, low, medium, high and very high. The result reveals that in areas which are in close proximity to Kendal and Temanggung, the highest basic probability assignment value of the risk of disease spreading of Highly Pathogenic Avian Influenza H5N1 is very low which is equal to 0.20. In areas which are in close proximity to Angola and Zambia, the highest basic probability assignment value of the risk of disease spreading of African Trypanosomiasis is very low which is equal to 0.173. In areas which are in close proximity to Bandung and Purwakarta, the highest basic probability assignment value of the risk of disease spreading of skin disease is low which is equal to 0.22.

In chapter 5, results and discussions are presented, which include the risk of disease spreading of Highly Pathogenic Avian Influenza H5N1, the risk of disease spreading of African Trypanosomiasis, and the risk of disease spreading of skin disease.


Chapter 5Result and Discussion

In this chapter, the result reveals that in areas which are in close proximity to Kendal and Temanggung that the risk of disease spreading of Highly Pathogenic Avian Influenza H5N1 is very low, which means the risk of disease spreading of Highly Pathogenic Avian Influenza H5N1 is very rare but cannot be excluded. In areas which are in close proximity to Angola and Zambia that the risk of disease spreading of African Trypanosomiasis is very low, which means the risk of disease spreading of African Trypanosomiasis is very rare but cannot be excluded. In areas which are in close proximity to Bandung and Purwakarta that the risk of disease spreading of skin disease is low, which means the risk of disease spreading of skin disease is rare but does occur. An implementation of applying Fuzzy Logic and Dempster-Shafer theory in solving a decision problem in the risk of disease spreading shows that it does improve the decision results.


This research visualizes the risk of disease spreading considering the connections between regions for the global spread of infection and population density. Furthermore, the vagueness present in the definition of terms is consistent with the information contained in the conditional rules when observing some complex process. While this work has been done in applying Fuzzy Logic and Dempster-Shafer theory in solving real world disease problems, the preceding discussion of the Fuzzy Logic and Dempster-Shafer theory together with the implementation given, indicates a very promising new starting point in the application of this theory.


Chapter 6 - Conclusion

IntroductionThis chapter summarises the conclusions of the research, research contributions and directions for future work suggested. Early warning system of the risk of disease spreading is important in interrupting the transmission cycle of the parasite and progress of the disease to the late stage. Early warning is the provision of timely and effective information, through identifying institutions, that allows individuals exposed to a hazard to take action to avoid or reduce their risk and prepare for effective response. Therefore, cost effective, simple, rapid, robust and reliable methods, are urgently needed. There is also an urgent need for accurate tools for the diagnosis of the disease spreading, a new initiative for the development of new diagnostic tests to support the control of disease.

Population density is a major factor affecting disease spreading within a population and other populations because a population that is very dense will generally see a faster disease spreading due to the larger amount of contact between individuals. In a population that is not very dense, close contact is much less likely to occur, thus halting the disease spreading. Disease in a population increases with the density of that population. High population density makes it easier for parasites to find hosts and the disease spreading. Population density is a measurement of the number of people in an area. It is an average number. Population density is calculated by dividing the number of people by an area. Population density is usually shown as the number of people per square kilometer. This research has considered Fuzzy Logic and Dempster-Shafer mathematical theory of evidence to detect the risk of disease spreading. The risk of disease spreading is not classified according to higher density which is equal to higher risk. This research has considered population changes in an area to detect the risk of disease spreading. Population density in areas which include very low, low, medium, high and very high. The result reveals that the system has successfully identified the existence of disease and the risk of disease spreading, moreover the maps can be displayed as the visualization. Web mapping is also used for displaying maps on a screen to visualize the result of the identification process.

Introduction (cont.)

Conclusions of the researchIn Chapter 3, this research has described Fuzzy Logic and Dempster-Shafer mathematical theory of evidence. Dempster-Shafer mathematical theory of evidence is a theory of uncertainty which was first proposed by Arthur Dempster and extended by Glenn Shafer. The Dempster-Shafer theory is a mathematical theory of evidence based on belief functions and plausible reasoning, which is used to combine separate pieces of information, evidence, to calculate the probability of an event. Dempster-Shafer mathematical theory of evidence allows us to combine evidence from different sources and arrive at a degree of belief which is represented by a belief function that takes into account all the available evidence. In Dempster-Shafer mathematical theory of evidence, evidence can be associated with multiple possible events. There are two basic components in Dempster-Shafer mathematical theory of evidence which include the basic probability assignment and the rule of combination. Dempster-Shafer mathematical theory of evidence can make inferences from the incomplete and uncertain knowledge, provided by different independent knowledge sources. This research presented a novel combination of Fuzzy Logic and Dempster-Shafer mathematical theory of evidence which are applied to the system. A new method to obtain basic probability assignment is proposed based on the similarity measure between membership function. The integration within Tsukamoto Fuzzy reasoning and inferences for evidential reasoning based on Dempster-Shafer mathematical theory of evidence by calculating the similarity between Fuzzy membership function.

Next, in chapter 4, this research focused on implementation using Fuzzy Logic and Dempster-Shafer mathematical theory of evidence to the risk of disease spreading and Web mapping to locate the risk of disease spreading.

In chapter 5, results and discussions of the research are presented. In Kendal and Temanggung, the highest basic probability assignment value of the risk of disease spreading of Highly Pathogenic Avian Influenza H5N1 is very low which is equal to 0.20. It means the risk of disease spreading of Highly Pathogenic Avian Influenza H5N1 is very rare but cannot be excluded. The risk of disease spreading of Highly Pathogenic Avian Influenza H5N1 in areas which include Batang, Kendal, Kota Magelang, Kota Salatiga, Kota Semarang, Magelang, Semarang, Temanggung, and Wonosobo. In Angola and Zambia, the highest basic probability assignment value of the risk of disease spreading of African Trypanosomiasis is very low which is equal to 0.173. It means the risk of disease spreading of African Trypanosomiasis is very rare but cannot be excluded. The risk of disease spreading of African Trypanosomiasis in areas which include Angola, Botswana, Congo, Congo DRC, Malawi, Mozambique, Namibia, Tanzania, Zambia and Zimbabwe. In Bandung and Purwakarta, the highest basic probability assignment value of the risk of disease spreading of skin disease is low which is equal to 0.22. It means the risk of disease spreading of skin disease is rare but does occur. The risk of disease spreading of skin disease in areas which include Bandung, Cianjur, Garut, Karawang, Kota Bandung, Kota Cimahi, Purwakarta, Subang and Sumedang. Figure~\ref{fig:bpaconclusions} shows the basic probability assignment of the disease.

Conclusions of the research

Research ContributionsThis section states the contributions of the thesis. This research proposed Fuzzy Logic and Dempster-Shafer mathematical theory of evidence to detect the risk of disease spreading and Web mapping to locate the risk of disease spreading. A novel combination of Fuzzy logic and Dempster-Shafer mathematical theory of evidence are Integrating Fuzzy Logic and Dempster-Shafer mathematical theory of evidence by calculating the similarity between Fuzzy membership function in the context to detect the risk of disease spreading. This detection system of disease spreading is applied to detect the risk of disease spreading include Highly Pathogenic Avian Influenza H5N1, African Trypanosomiasis and skin disease. A computer system that can make decision-making. The computer can make inferences and arrive at a specific conclusion. The system provides powerful and flexible means for obtaining solutions to a disease spreading detection problem that often cannot be dealt with by other, more traditional and orthodox methods. Thus, their use is proliferating to many sectors of human social and technological life, where their applications are proving to be critical in the process of decision support and problem solving.

The simplest possible method for using probabilities to quantify the uncertainty in a database is that of attaching a probability to every member of a relation, and to use these values to provide the probability that a particular value is the correct answer to a particular query. An expert in providing knowledge is uncertain in the form of rules with the possibility, the rules are probability value. The knowledge is uncertain in the collection of basic events can be directly used to draw conclusions in simple cases, however, in many cases the various events associated with each other. Reasoning under uncertainty that used some of mathematical expressions, gave them a different interpretation which is each piece of evidence may support a subset containing several hypotheses.


This is a generalization of the pure probabilistic framework in which every finding corresponds to a value of a variable. This research has presented integrating Fuzzy Logic and Dempster-Shafer mathematical theory of evidence in the context to detect the risk of disease spreading. The highest percentage of the risk of disease spreading of Highly Pathogenic Avian Influenza H5N1 is 20%. The highest percentage of the risk of disease spreading of African Trypanosomiasis is 17 %. The highest percentage of the risk of disease spreading of skin disease is 22 %. In this research it is Fuzzy Logic and Dempster-Shafer theory, which resulted in a 0 % rejection. And also this research has developed Web mapping for displaying maps on a screen to locate the risk of disease spreading. Finally, Fuzzy Logic and Dempster-Shafer mathematical theory of evidence have shown good results.


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Viva Presentation - Fuzzy Logic and Dempster-Shafer Theory to Detect The Risk of Disease Spreading