1. Unsupervised Rough Set Classification Using GAs Reporter: Yanan Yean

2. Abstract How genetic algorithm can be used to develop rough sets. A rough set genome consists of upper and lower bounds for sets in a partition. A complete description of design and implementation of rough set genomes. Used to provide an unsupervised rough set classification of highway sections.

3. 1.Introduction Pawlak: rough set can be used to learn rules in an expert system.(1982,1984) Lingras: interval-valued patterns for the development of rough neural computing techniques.(1996,1998) Lingras and Davies: the rough genetic algorithm(2000) Vinterbo and Øhrn: a rough set approach for feature selection in unsupervied clustering.(1997) This paper proposed a genetic encoding for rough set theoretic evolutionary computing.

4. 2. Brief review of genetic algorithm Typically, an organism is a single genome represented as a vector of length n:

5. 3. Rough set R ⊆ U × U an equivalence relation on U The pair A = (U, R) is called an approximation space U/R = E 1, E 2,...., E n, where E i is an equivalence class of R. it is not possible to differentiate the elements within the same equivalence class, one may not be able to obtain a precise representation for an arbitrary set X ⊆ U in terms of elementary sets in A.

6. A(X) is the union of all the elementary sets which are subsets of X A(X) is the union of all the elementary sets which have a non-empty intersection with X any subsets X, Y ⊆ U, the following properties hold (Pawlak,1982):

7. Yao et al. (1994) described various generalizations of rough sets by relaxing the assumptions of an underlying equivalence relation. Properties (C1)–(C4) can be obtained from (P1)–(P8) and the fact that X i ∩ X j = ∅, i ≠ j.

8. 4. Rough set genome and its evaluation Let U = {u 1, u 2,..., u n } U/P = {X 1, X 2,..., X m }.

9. The quality of a conventional classification scheme is determined using the within-group error (Sharma and Werner, 1981) given by: define three corresponding types of within-group-errors,∆ 1, ∆ 2, and ∆ 3 as:

10. A possible precision measure can be defined following Pawlak (1982) as: The objective of the genetic algorithms will then be to maximize the quantity: p=[0,1], ∆ total =[200,15000] p: the importance of the precision measure in determining the quality of a rough set genome. e: the importance of within group-errors relative to the size of boundary region.

11. 5. Rough set classification of highways The present study is based on the same sample of 264 monthly traffic patterns recorded between 1987 and 1991 on Alberta highways used by Lingras (1995, 2001). The same sample collection was useful in analyzing the rough set classification and useful for fine tuning the parameters. The hypothetical classification scheme consisted of three classes: 1. Commuter/business, 2. Long distance, and 3. Recreational.

12. Genetic algorithms attempt to evolve a genome such that the value of an objective function is maximal.

14. 6.Summary and conclusions A rough set genome consists of the objects to be classified represented using a string indicating object consists of upper and lower parts. A conventional genome used for classification can be evaluated using the with-in-group error. This study proposed a general formulation for evaluating rough set classification scheme.