Keywords: knowledge fusion, graphical representation, sampling aggregation, KL divergence, information granulation, uncertainty.

This paper addresses the problem of learning graphical models using structure learning algorithms and the fusion of graphical representations such as Bayesian networks or decision networks representative for human decision makers or distributed agents in a network structure. We present in the first part of the paper a new enhanced parameterized structure learning approach. The new generalization approach calculates in advance k steps regarding the choosen scoring function. Another parameter computes the number of best evaluated network structures as the number of calculated good operations. The comparison with different other learning structure approaches shows good results when using specific quality measures [1]. A concurrent fusion method to aggregate expert knowledge stored in distributed knowledge bases or probability distributions is also described [2]. Experimental results of a case study show that our approach can improve the efficiency of learning structure algorithms for knowledge fusion applications.

Among the various types of decision support systems, decision-theoretic models and rule-based systems have gained considerable attraction. Decision-theoretic models dispose of a sound mathematical basis and comfortable knowledge engineering tools. Rule-based systems provide an efficient execution architecture and represent knowledge in an explicit, intelligible way. In this paper, we consider fuzzy rule-based systems as a special type of condensed decision model as a basis for the information granulation [3]. In general, granulation is hierarchical in nature. Modes of information granulation play important roles in a wide variety of methods, approaches and techniques. Aspects like human reasoning and concept formation need not only crisp granules, but also fuzzy granules are important to express attributes and specific values. Applying the theory of fuzzy information granulation consists of fuzzification, granulation and fuzzy granulation as a combination of fuzzification and granulation. Fuzzy granulation underlies the concept of linguistic variables and fuzzy if-then rules. These concepts play a major role for dealing with applications under imprecision and uncertainty.

Here, we neither stick to a particular inference scheme nor to a special defuzzification operator. The important point to realize is simply the following: once an inference scheme and a defuzzification operator have been determined, each fuzzy rule base can be associated with a function. We can determine a granulation as set of fuzzy partitions, i.e. a fuzzy partition for each variable in a network structure. We can also denote the class of permitted granulations. The quality of a rule base depends on several factors, notably its approximation quality and its complexity. We can use different levels of granulation based on their collection of granules to evaluate the benefits of knowledge representation as a transformation process into an efficient alternative form which is more suitable for the decision maker. A medical decision maker for instance determines the granules of a human head or abdomen region. Another attempt in this context is the modification of the propositional knowledge bases or the speedup learning approach in the field of machine learning. Consider especially the real time decision makers behaviour [4] with time, monetary or storage capacity restrictions. Granular computing techniques helps abstracting information and processing information on different levels of abstraction. The way in which humans and especially decision makers employ information granulation to make rational decisions in an environment of partial knowledge, partial certainty and partial truth should be viewed as a major role model in decision theory for machine intelligence.

1

A. Holland, M. Fathi, "Creating Graphical Models as Representation of Personalized Skill Profiles", in "Proceedings IEEE Systems, Man and Cybernetics", SMC 2005, Big Island, Hawaii, USA, October 2005. doi:10.1109/ICSMC.2005.1571205

2

A. Holland, M. Fathi, "Concurrent Fusion via Sampling and lin-OP Aggregation", in "Proceedings Modeling Decisions for Artificial Intelligence", MDAI 2006, 84-00-08415-2, Tarragona, Catalunia, Spain, April 2006.

3

A. Mueller, D. Stoyan, "Comparison Methods for Stochastic Models and Risks", Wiley Series in Probability and Statistics, John Wiley & Sons, 2002.

4

A. Freßman, R. Maximini, T. Sauer "Towards Collaborative Agent-based Knowledge Support for Time-critical and Business Critical Processes", in "Third Conference Professional Knowledge Management", Lecture Notes in Artificial Intelligence, Vol. 3782, 420-430, Kaiserslautern, Germany, 2006.

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