SC740 SEMINAR REPORT 13 for Frederick L. Jones

PRESENTER: Dr. Theresa Beaubouef

OVERVIEW

Dr. Theresa Beaubouef’s presentation began with an introduction to "rough set theory". Rough sets have been used to represent ambiguity, vagueness and general uncertainty. Rough set theory has become a well established mechanism for uncertainty management in many applied fields, e.g., relational database design and management.

Some of the areas in database design and management that Dr. Theresa Beaubouef highlighted as areas in which rough set theory is already being applied are the following: (1) modification of the underlying database model to incorporate rough sets (2) merging of rough set theory with fuzzy set theory in database query design (3) rough querying of crisp data, etc.

AN INTRODUCTION TO ROUGH SETS AS A MECHANISM FOR UNCERTAINITY MANAGEMENT

Dr. Theresa Beaubouef’s presentation began with an introduction to "rough set theory". Rough sets have been used to represent ambiguity, vagueness and general uncertainty. A rough set A is a set defined by the relation A = (U, R) where U is the "universe" and R is the "indiscernability relation" that partitions the "universe". Thus, A = (U, R) partitions the universe into equivalence sets.

Given a rough set x Í U, there is a lower approximation and an upper approximation for R. The lower approximation R_x = { x ' U | |x|_R Í X } and an upper approximation R_x = { x ' U | |x|_R Ç X }. For example, if U = {medium, tiny, big, small, little, gigantic … }, then R = { {small, tiny, little, …}, {medium, …}, {big, gigantic, …} }. Then, a rough set is that group of sets that have the same upper and lower approximation.

ROUGH SET MANAGEMENT IN DATABASE DESIGN AND MANAGEMENT

Rough set theory has become a well established mechanism for uncertainty management in many applied fields, e.g., relational database design and management. Some of the areas in database design and management that Dr. Theresa Beaubouef highlighted as areas in which rough set theory is already being applied are the following: (1) modification of the underlying database model to incorporate rough sets (2) merging of rough set theory with fuzzy set theory in database query design (3) rough querying of crisp data, etc.

Concerning the modification of the underlying database model to incorporate rough sets, Dr. Beaubouef noted that relational databases are already based on set theory. Thus, a rough relational database model can easily be created to partition database domains into equivalence classes and to create approximation regions for certain and possible query results.

Concerning the merging of rough set theory with fuzzy set theory in database query design, Dr. Beaubouef noted that there can be fuzzy degree of set membership within rough sets. For example, a fuzzy rough set could be defined by having the membership function defined as follows: (1) m _x(Rx) = 1, if the set is in the positive region, and (2) m _x(U - Rx) = 0, if the set is in the negative region, and (3) 0 < m _x(Rx - Rx ) < 1, if the set is in a boundary region.

Dr. Beaubouef covered the following additional topics: (1)the rough querying of crisp data, (2)rough set SQL, (3)rough set information theoretic measures of uncertainty such as "accuracy", which measures the degree of completeness of knowledge about a given rough set, (4)rough sets and natural language processing, and (5)rough set test generation.

To areas for future research in the application of rough set management of uncertainty to database design and management that Dr. Beaubouef specifically mentioned were (1)the use of rough set techniques with spatial data and (2)the use of rough sets in Object Oriented databases.

SUMMARY AND CONCLUSIONS

Dr. Theresa Beaubouef’s presentation began with an introduction to "rough set theory". Rough sets have been used to represent ambiguity, vagueness and general uncertainty. Rough set theory has become a well established mechanism for uncertainty management in many applied fields, e.g., database design and management.

The areas in database design and management that Dr. Theresa Beaubouef highlighted as areas in which rough set theory is already being applied are the following: (1) modification of the underlying database model to incorporate rough sets (2) merging of rough set theory with fuzzy set theory in database query design (3) rough querying of crisp data, (4)rough set SQL, (5)rough set information theoretic measures of uncertainty, (6)rough sets and natural language processing, and (7)rough set test generation.

Two areas for future research in the application of rough set management of uncertainty to database design and management that Dr. Beaubouef specifically mentioned were (1)the use of rough set techniques with spatial data and (2)the use of rough sets in Object Oriented databases. From the above mentioned two areas for future research, Dr. Beaubouef has shown that uncertainty management via rough set techniques has wide applicability in the database field.