Andrzej Skowron (Warsaw U, Poland)

TITLE: Toward Rough-Granular Computing

DATE: May 14, 9:20am-10:10am

ABSTRACT: Developing methods for approximation of compound concepts expressing the result of perception belongs to the main challenges of Perception Based Computing (PBC). The perceived concepts are expressed in natural language. We discuss the rough-granular approach to approximation of such concepts from sensory data and domain knowledge. This additional knowledge, represented by ontology of concepts, is used to make it feasible searching for features (condition attributes) relevant for the approximation of concepts on different levels of the concept hierarchy defined by a given ontology. We report several experiments of the proposed methodology for approximation of compound concepts from sensory data and domain knowledge. The approach is illustrated by examples relative to interactions of agents, ontology approximation, adaptive hierarchical learning of compound concepts and skills, behavioral pattern identification, planning, conflict analysis and negotiations, and perception-based reasoning.

Sadaaki Miyamoto (U of Tsukuba, Japan)

TITLE: Data Clustering and Rough Sets

DATE: May 14, 10:10am-11:00am

ABSTRACT: Although the approaches are fundamentally different, the derivation of decision rules from information systems in the form of tables can be compared to supervised classification in pattern recognition; in the latter case classification rules should be derived from the classes of given points in a feature space. We moreover notice that methods of unsupervised classification (in other words, data clustering) in pattern recognition are closely related to supervised classification techniques. This observation leads us to the discussion of clustering for information systems by observing relations between the two methods in the pattern classification. We thus discuss a number of methods of data clustering of information tables without decision attributes on the basis of rough set approach in this paper. Current clustering algorithms using rough sets as well as new algorithms motivated from pattern classification techniques are considered. Moreover agglomerative clustering is generalized into a method of poset-valued clustering for discussing structures of information systems using new notations in relational databases. Illustrative examples are given.

Lotfi A. Zadeh (U of California, Berkeley, USA)

TITLE: Granular Computing and Rough Set Theory

DATE: May 16, 9:00am-9:50am

ABSTRACT: Granulation plays an essential role in human cognition and has a position of centrality in both granular computing and rough set theory. Informally, granulation involves partitioning of an object into granules, with a granule being a clump of elements drawn together by indistinguishability, equivalence, similarity, proximity or functionality. For example, an interval is a granule; so is a fuzzy interval; so is a Gaussian distribution; and so is an equivalence class in rough set theory. A granular variable is a variable which takes granules as values. Basically, granular computing is a mode of computation in which the objects of computation are granular variables. A granular value, X, may be interpreted as a representation of the state of imprecise knowledge about the true value of X. In this sense, granular computing may be viewed as a system of concepts and techniques for computing with variables whose values are either not known precisely or need not be known precisely. A concept which serves to precisiate the concept of a granule is that of a generalized constraint. The concept of a generalized constraint is the centerpiece of granular computing. In granular computing, computation/deduction is viewed as a sequence of operations involving combination, projection, qualification, propagation and counterpropagation of generalized constraints. The principal deduction rule in granular computing is the extension principle.

Yiyu Yao (U of Regina, Canada)

TITLE: Decision-Theoretic Rough Set Models

DATE: May 16, 9:50am-10:40am

ABSTRACT: Decision-theoretic rough set models are a probabilistic extension of the algebraic rough set model. The required parameters for defining probabilistic lower and upper approximations are calculated based on more familiar notions of costs (risks) through the well-known Bayesian decision procedure. We review and revisit the decision-theoretic models and present new results. It is shown that we need to consider additional issues in probabilistic rough set models.