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Part I Information Flow Modelling: Tools and Approaches

Part I Information Flow Modelling: Tools and Approaches. INFORMATION MANAGEMENT IN THE NEW MILLENNIUM: SOME CHALLENGES Opportunities and challenges Demand for information Information theory Visualization of information · colour and information,

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Part I Information Flow Modelling: Tools and Approaches

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  1. Part I Information Flow Modelling: Tools and Approaches

  2. INFORMATION MANAGEMENT IN THE NEW MILLENNIUM: SOME CHALLENGES Opportunities and challenges Demand for information Information theory Visualization of information · colour and information, · complexity and clarity of human perception, · use of multi-media, internet, and WWW screens, · animation for scientific visualizations, · design of efficient computer interfaces. Information based integration Information modelling tools Cyberspace, virtual reality and ars electronica

  3. Of some interest here may be the fact that one of the best graphical representations of information was developed in 1869 by Charles Minard. It depicts the losses suffered by Napoleon’s army in the Russian campaign of 1812. Six variables were plotted in that graph which tells a rich coherent story with its multivariate data, far more enlightening than just a single number posed again time. Minard’s chart is still regarded as one of the best graphical representation of data ever drawn.

  4. INFORMATION FLOW: ANALYTICAL MODELLING PLATFORM Introduction and the modelling approach

  5. An autonomous subsystem is usually functioning in external environment which determines the decision-making process. Its knowledge could be described by the following: • characteristics of the internal environment (relationship between the actions of the elements of a system), • characteristics of the external environment (relationship between variables describing the environment and its dynamics), • the range of information about variables describing external environment. • The formal representation of the above knowledge is presented in this Chapter.

  6. Energy E E1 C1 Information C The general character of energy/information replacement

  7. Energy E E1=Emin Aopt Action A Action/energy dependence for given amount of information

  8. VC=E[bTß] With this modelling tool one can easily extract knowledge about autonomous agents functioning in various decision situations where external environment is static. A sample of such knowledge, codified as production rules, is presented next.

  9. RULE 11 IFan external environment of an autonomous agent is static, AND it is described by random variables, THEN the value of an information structure that represents the flow of information between the agent and its environment depends on interaction between agent members, correlation between random variables, and their variance. RULE 12 IF an external environment of an autonomous agent is static, AND it is described by a random variable, THEN the value of information about this variable realization is proportional to the value of its variance. RULE 13 IF an external environment of an autonomous agent is static, AND it is described by random variables, THEN full information has the value that is always greater or equal to the value of any other information structure. RULE 14 IF an external environment of an autonomous agent is static, AND there is no interaction in the internal environment, THEN it is enough to restrict the information flow only to observation; organizing an information exchange does not improve the value of a resulting information structure.

  10. Modelling dynamic environment X(t) = (w1 + w2)X(t-1) - w1w2X(t-2) + m(t)

  11. w2 B 1 -1 A 0 1 w1 E C -1 D A independent stochastic process BD first order autoregressive process EC first order autoregressive process shaded area inside the square stable stochastic process area outside the square explosive stochastic process External environments of different character on the (w1,w2) plain.

  12. Information: realization of variables describing the state of external environment in epoch T X(T) Distribution of information: observation and communication within the agent g[X(T)] Information structure: observation and communication C Decision making: choosing the optimal action based on the information structure a(T) Information flow evaluation: VC Recommendations for the distribution of information

  13. RULE 24 IF an external environment of an autonomous agent is described by stochastic process, AND information is not delayed, THEN the value of full information is, for each decision situation, greater than the values of other possible information structures. RULE 25 IF an external environment of an autonomous agent is described by stochastic process, AND information is not delayed, AND there is no interaction in the internal environment, THEN there is no need for communication inside the agent. RULE 26 IF an external environment of an autonomous agent is described by stochastic process, AND information is not delayed, THEN the more uncertain the realizations in the external environment the bigger the value of the information about these realizations.

  14. INFORMATION FLOW: SOFT MODELLING PLATFORM Introduction to qualitative modelling and simulation Qualitative vs. quantitative modelling

  15. Real-life system Real-life behaviour mathematical modelling mathematical analysis Quantitative description Analytic solution relaxation qualitative modelling qualitative simulation Qualitative model Qualitative behaviour Qualitative vs. quantitative representation

  16. In a broader context, there are following motivations for developing qualitative models of real-life systems: (a) to provide simpler computational mechanisms than those already existing, (b) to provide s description for systems where traditional methods are ineffective, (c) to provide modelling approach that mimics more closely our common sense and intuition, (d) to provide modelling methods for reasoning with partial, uncertain or incomplete information, and for effective explanation facilities.

  17. Approaches to qualitative modelling: • qualitative constraints or QSIM technique developed originally by Kuipers • confluences or ENVISION arithmetic first introduced by de Kleer and Brown • (c) qualitative process theory formulated by Forbus

  18. set of initial conditions (states) set of possible next state transitions succesor states (consistent state transitions) The general view of QSIM simulation process

  19. d/dt X M(X) V A d/dt Representation of the oscillating spring - qualitative structure

  20. Qualitative modelling in static environment The are the following functional constraints (denoted as M) between the corresponding state variables: (i) M (external_environment; information_structure) (ii) M (external_environment; value_of_information_structure) (iii) M (information_structure; value_of_information_structure) (iv) M (internal_environment; value_of_information_structure)

  21. external_environment M M internal_environment information_structure M M value_of_information_structure Simple abstract representation for the evaluation of information flow

  22. Behaviour Structure  X2, s2 X1, s2   M+ M+   r q VC +   M+ M+  0 r 1 0 VC q VALUE_OF_INFORMATION_STRUCTURE Structure and behaviour for information structure C2

  23. RULE 2 IF an external environment of an autonomous agent is static, AND it is described by random variables, AND there is an interaction between agent elements and correlation between random variables, THEN the value of decentralised information structure (created only by observation) increases with increasing correlation and interaction

  24. Soft modelling for informational flow Signed directed graphs Decision tree classifiers Connectionist systems – neural networks

  25. Signed directed graph (SDG) is one of the simplest models that can be used for qualitative reasoning. Any SDG can be viewed as signed digraph and as such consists of three components: node, directed branch, and sign. A node corresponds to a process variable, branch represents the influence between two nodes, and the sign distinguishes between influences of positive and negative character. The states of variables are represented by qualitative values “+, -, or 0” indicating whether the current value of the variable is “higher than, lower than, or equal to” its nominal value.

  26. w + + d L1 + + + + LV + + q s + + + _ a L2 SDG model of informational balance of an agent

  27. w + + d LV + _ a SDG model - final simplification

  28. (i) solution pattern for a positive change in d (ii) solution pattern for a positive change in w (iii) solution pattern for a positive change in a

  29. Decision tree classifiers are used successfully in many diverse areas. Their most important feature is the capability of capturing descriptive decision-making knowledge from the supplied data. They are also attractive for the following reasons: • capability of generating arbitrarily complex decision boundaries from a given set of training samples, • short training time allowing for frequent trainings, • ability of revealing information about the problem they are applied to.

  30. The application area of a decision tree is seen as a universe of objects. Objects belong to disjoint set of classes and are described by the set of attributes. Two objects can be distinguished only if they have different values for at least one attribute. For example, the agent decision situation can be described by the following attributes: external_environment, with possible values static or dynamic, internal_environment, with values independent_actions and dependent_actions, type_of_dynamics, with continuous values of w, correlation, with continuous values of r from the set of [-1, 1], delay_of_information, with continuous values of  from the set of [0, ). A particular object (particular decision situation) may be represented as: external_environment = static, correlation = 0.5, internal_environment = dependent_actions, delay_of_information = 2

  31. internal_environment independent_actions dependent_actions do_not_exchange_information -1 < correlation < 1 true false exchange_information do_not_exchange_information Decision tree classifier for agent decision-making

  32. Last Figure: A decision tree that classifies agent decision-making concerning the flow of information in static environment as either exchange_information or do_not_exchange_information The following rules can be delivered from the tree: Rule 1 IF an external environment of an agent is static AND it is described by random variables AND there is no interaction in the internal environment THEN communication (exchange of information) between agent elements is not necessary Rule 2 IF an external environment of an agent is static AND it is described by random variables AND there is interaction in the internal environment AND the relationship between variables describing the external environment is of statistical character THEN exchange of information between agent elements should be organised

  33. NEURAL NETWORKS Adaptation, or the ability to learn, is the most important property of neural networks. A neural network can be trained to map a set of input patterns onto a corresponding set of output patterns simply by means of exposure to examples of the mapping. This training is performed by gradually adapting the internal weights of the network, so as to reduce differences between the actual network outputs (for a given set of inputs) and the desired network outputs. Neural networks which learn mappings between sets of patterns are called mapping neural networks. A key property of mapping networks is their ability to produce reasonable output vectors for input patterns outside of the set of training examples. The above is especially important in areas such as discussed in this Chapter, i.e. areas for which it is possible to develop only a very limited number of IF...THEN rules and thus also to make inferences only for a very limited number of decision situations.

  34. decisions concerning the flow of information observation exchange of information correlation (R) dynamics (T) interaction (I) delay (D) process (W) characteristics of an agent A three layer 5-10-2 neural network

  35. Fundamentals of fuzzy sets and fuzzy logic • A new theory, its applications and modeling power • A new theory extending our capabilities in modeling uncertainty • Fuzzy set theory provides a major newer paradigm in modeling and reasoning with uncertainty. Though there were several forerunners in science and philosophy, in particular in the areas of multivalued logics and vague concepts, Lotfi A. Zadeh, a professor at University of California at Berkeley was the first to propose a theory of fuzzy sets and an associated logic, namely fuzzy logic (Zadeh, 1965). Essentially, a fuzzy set is a set whose members may have degrees of membership between 0 and 1, as opposed to classical sets where each element must have either 0 or 1 as the membership degree—if 0, the element is completely outside the set; if 1, the element is completely in the set. As classical logic is based on classical set theory, fuzzy logic is based on fuzzy set theory. • Zadeh, L.A. (1965): Fuzzy sets, Information and Control 8(3):338–353.

  36. Major industrial application areas The first wave: Process control The first industrial application of fuzzy logic was in the area of fuzzy controllers. It was done by two Danish civil engineers, L.P. Holmblad and J.J. Østergaard, who around 1980 at the company F.L. Schmidt developed a fuzzy controller for cement kilns. Their results were published in 1982 (Holmblad & Østergaard, 1982). Their results were not much notice in the West, but they certainly were in Japan. The Japanese caught the idea, and applied it in an automatic-drive fuzzy control system for subway trains in Sendai City. The final product was extremely successful, and was generally praised as superior to other comparable systems based on classical control. This success encouraged a rapid increase in the Japanese’s interest in fuzzy controller during the late 1980s. This led to applications in other areas, like elevator control systems and air conditioning systems. In the early 1990s, the Japanese began to apply fuzzy controller in consumer products, like camcorders, washing machines, vacuum cleaners, and cars. The Japanese success led to increased interest in Europe and the US in fuzzy controller techniques. L.P. Holmblad and J.J. Østergaard (1982): Control of a cement kiln by fuzzy logic. In M.M. Gupta and E. Sanchez, Eds., Fuzzy Information and Decision Processes, North-Holland, New York, pp. 389–399.

  37. The second wave: information systems The second wave of fuzzy logic systems started in Europe in the early 1990s, namely in the area of information systems, in particular in databases and information retrieval. The first fuzzy logic based search engine was developed by the author in collaboration with professor R.R. Yager, Machine Intelligence Institute, US. It was aimed for application netbased commerce systems, namely, at that time the only in the world, the French Minitel. It was first demonstrated to the public at the Joint International Conference of Artificial Intelligence in 1992 in Chambery, France. In 1999, the technique was adopted by the Danish search engine Jubii. The several ideas and results applied in the technique were published; see, for instance, (Larsen & Yager, 1993, 1997). Internet and the Web gave new interest to application of fuzzy logic technology. In the net based society we have an enormous amount of information and knowledge electronic accessible for decision makers and human in general. Much of this information is inherently uncertain—lack of precision, vague concepts, more or less reliable information, etc. On the other hand, to be useful, users must be able to utilize it, despite the uncertainties. Larsen, H.L., and Yager, R.R.: The use of fuzzy relational thesauri for classificatory problem solving in information retrieval and expert systems. IEEE J. on System, Man, and Cybernetics 23(1):31–41, 1993. Larsen, H.L., and Yager, R.R.: Query Fuzzification for Internet Information retrieval. In Dubois, D., Prade H., and Yager, R.R., Eds., Fuzzy Set methods in Information Engineering: A Guided Tour of Applications, John Wiley & Sons, pp. 291–310, 1997. Henrik

  38. Fuzzy logic and fuzzy sets Classical set theory The set (concept, predicate) A is characterized by a membership function m: X → {0, 1} μ(x)=1 x€A μ(x)=0 x∉A

  39. Fuzzy set theory Set A has no sharp border line. It is a fuzzy subset of X, characterized by a membership function μ: X → [0, 1] μ(x) is the element x’s degree of membership in A Example 1: A = tall Example 2: A = about the value a

  40. Fuzzy Sets and Membership Functions • Fuzzy sets describe vague concepts • Fuzzy sets admits partial membership • The degree of belonging to a fuzzy set is described by the Membership Function (MF) • MF maps an input (crisp) value into a membership value

  41. A B Logical Operations with Fuzzy Sets Fuzzy Sets A, B Fuzzy AND Fuzzy NOT Fuzzy OR

  42. Why Fuzzy Logic ? • FL is conceptually easy to understand • The concepts behind the successful implementation of a fuzzy expert are natural and very simple • FL is flexible • Modularity can be easily implemented in a fuzzy logic framework. Rules can be add on top of existing knowledge-base • FL is tolerant of imprecise data • Everything is imprecise if we look close enough. Fuzzy logic builds on the process rather than on the precision • FL can be built of top of experience of experts • Expertise built over years by planetary scientists, geologists, astrobiologists etc. can be easily incorporated into the system • FL is based on natural language • The basis for fuzzy logic is the basis for human communication

  43. FUZZY LOGIC IMPACT Updated figures regarding the number of papers in the INSPEC and MATH.SCI.NET Databases in which fuzzy appears in title. This information was compiled by Camille Wanat, Head, Engineering Library, UC Berkeley. INSPEC - "fuzzy" in the title 1970-1979: 569 1980-1989: 2,403 1990-1999: 23,210 2000-present: 21,147 Total: 47,329 MathSciNet - "fuzzy" in the title 1970-1979: 443 1980-1989: 2,465 1990-1999: 5,487 2000-present: 5,504 Total: 13,899

  44. IMPACT …….. JOURNALS (“fuzzy” or “soft computing” in title) 1. Fuzzy Sets and Systems 2. IEEE Transactions on Fuzzy Systems 3. Fuzzy Optimization and Decision Making 4. Journal of Intelligent & Fuzzy Systems 5. Fuzzy Economic Review 6. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 7. Journal of Japan Society for Fuzzy Theory and Systems 8. International Journal of Fuzzy Systems 9. Soft Computing 10. International Journal of Approximate Reasoning--Soft Computing in Recognition and Search 11. Intelligent Automation and Soft Computing 12. Journal of Multiple-Valued Logic and Soft Computing 13. Mathware and Soft Computing 14. Biomedical Soft Computing and Human Sciences 15. Applied Soft Computing

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