Seminar I

1. Is there any a Novel Best Theory for uncertainty? AndinoMaseleno andinomaseleno@yahoo.com DEPARTMENT OF COMPUTER SCIENCE FACULTY OF SCIENCE UNIVERSITI BRUNEI DARUSSALAM Wednesday, september 14, 2011

2. FUZZY LOGIC So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality. In the early 1960s, L.A. Zadeh, a professor at the University of California at Berkeley well respected for his contributions to the development of system theories, began to feel that traditional systems analysis techniques were too precise for many complex real-world problems. The idea of grade of membership, which is the concept that became the backbone of fuzzy set theory, occurred to him in 1964, which lead to the publication of his seminal paper on fuzzy sets in 1965 and the birth of fuzzy logic technology. The concept of fuzzy sets and fuzzy logic encountered sharp criticism from the academic community; however, scholars and scientists around the world—ranging from psychology, sociology, philosophy and economics to natural sciences and engineering—became Zadeh’s followers.

3. TRADITIONAL REPRESENTATION OF LOGIC Slow Fast Speed = 0 Speed = 1 bool speed; get the speed if ( speed == 0) { // speed is slow } else { // speed is fast }

5. What are fuzzy sets?[ 0.0 – 0.25 ] Slow [ 0.25 – 0.50 ] Fast [ 0.50 – 0.75 ] Fastest [ 0.75 – 1.00 ]

6. FUZZY LOGIC REPRESENTATION CONT. Slowest Fastest Slow Fast float speed; get the speed if ((speed >= 0.0)&&(speed < 0.25)) { // speed is slowest } else if ((speed >= 0.25)&&(speed < 0.5)) { // speed is slow } else if ((speed >= 0.5)&&(speed < 0.75)) { // speed is fast } else // speed >= 0.75 && speed < 1.0 { // speed is fastest }

9. Find centroids: Location where membership is 100%7

10. Dempster-Shafer theory The Dempster-Shafer theory was first introduced by Dempster in the 1968 and then extended by shafer in the 1976, but the kind of reasoning the theory uses can be found as far back as the seventeenth century. This theory is actually an extension to classic probabilistic uncertainty modeling. Whereas the Bayesian theory requires probabilities for each question of interest, belief functions allow us to base degrees of belief for on question on probabilities for a related question. These degrees of belief may or may not have the mathematical properties of probabilities will depend on how closely the two questions are related. In terms of previous work using Dempster-Shafer theory, most prior research with this system has been theoretical, for example, in pursuing the use of belief functions for propagating uncertainty in AI/expert systems in addition or instead of using probabilities. Dempster Shafer theory of evidence has attracted considerable attention within the AI community as a promising method of dealing with uncertainty in expert systems as Zadeh said in his paper in the 1986.

11. Dempster-Shafer Theory The Dempster-Shafer theory could be considered as a generalization of probability theory. A mapping a set of values: ᴦ: x -> PΩ, where PΩis the set of all non fuzzy subsets from Ω. Assume a probability measure ρ over x; now, what can be said about a probability measure over Ωis induced by ᴦ?This is abasic question, where Dempster showed that for every B Ω, P(B) belongs to the following intervals: where AjPΩis any nonempty member ofᴦand

12. Dempster-Shafer Theory Shafer introduced his evidence theory and defined bel and pls functions. Consider a referential set Ω ={w1, w2,…wn}; a body of evidence is defined as follows: {A1, A2,…, Al} {m1, m2,…,ml} in which each Aj is a focal element, and mj is the corresponding mass value. Evidence theory could be considered as a direct generalization of Bayesian statistics. One may think of mass value as probability density values; but in evidence theory, mass values are assigned to the subsets of Ω instead of the elements of Ω; so, it conveys a higher level of uncertainty and is capable of modeling both ignorance and indeterminism. Shafer defined the concepts of belief and plausibility as two measures over the subsets of in axiomatic manner and then he showed that bel and pls with the following definitions were belief and plausibility functions.

13. Neural network Trend that contributed to research in fuzzy model identification is the increasing visibility of neural network research in the late 1980s. Because of certain similarities between neural networks and fuzzy logic, researchers began to investigate ways to combine the two technologies. The most important outcome of this trend is the development of various techniques for identifying the parameters in a fuzzy system using neural network learning techniques. A system built this way is called a neuro-fuzzy system.

14. Neural Network How do they work? The network is trained with a set of known facts that cover the solution space During the training the weights in the network are adjusted until the correct answer is given for all the facts in the training set After training, the weights are fixed and the network answers questions not in the training data. These “answers” are consistent with the training data

15. Inspiration from Neurobiology A neuron: many-inputs / one-output unit output can be excited or not excited incoming signals from other neurons determine if the neuron shall excite ("fire") Output subject to attenuation in the synapses, which are junction parts of the neuron

16. Synapse concept The synapse resistance to the incoming signal can be changed during a "learning" process [1949] Hebb’s Rule: If an input of a neuron is repeatedly and persistently causing the neuron to fire, a metabolic change happens in the synapse of that particular input to reduce its resistance

17. Mathematical representation The neuron calculates a weighted sum of inputs and compares it to a threshold. If the sum is higher than the threshold, the output is set to 1, otherwise to -1. Non-linearity

18. GENETIC ALGORITHM The 1990s is an era of new computational paradigms. In addition to fuzzy logic and neural networks, a third nonconventional computational paradigm also became popular —evolutionary computing, which includes genetic algorithms, evolutionary strategies, and evolutionary programming. Genetic algorithms (GA) and evolutionary strategies are optimization techniques that attempt to avoid being easily trapped in local minima by simultaneously exploring multiple points in the search space and by generating new points based on the Darwinian theory of evolution— survival of the fittest. The popularity of GA in the 1990s inspired the use of GA for optimizing parameters in fuzzy systems. Various synergistic combinations of neural networks, genetic algorithms, and fuzzy logic help people to view them as complementary. To distinguish these paradigms from the conventional methodologies based on precise formulations, Zadeh introduced the term soft computing in the early 1990s.

19. Genetic Algorithm Competition Reproduction Selection Survive Based on Darwinian Paradigm Intrinsically a robust search and optimization mechanism

20. Genetic Algorithm Inspired by Darwinian Paradigm or natural evolution Population of individuals Individual is feasible solution to problem Each individual is characterized by a Fitness function Higher fitness is better solution Based on their fitness, parents are selected to reproduce offspring for a new generation Fitter individuals have more chance to reproduce New generation has same size as old generation; old generation dies Offspring has combination of properties of two parents If well designed, population will converge to optimal solution

21. Genetic Algorithm Initialize Population Evaluate Fitness Yes satisfy constraints ? No Randomly Vary Individuals Select Survivors Output Results

22. So far… Avian Influenza warning system with Dempster Shafer Theory and Web Map Shortest Path Routing with Hopfield Neural Network and Dempster Shafer Theory Dempster Shafer Theory with Fuzzy Logic Membership Function to Determine Student Research Interest

23. Thank You I wish I could finish all the things I started