Discussion and Conclusions

From Figure 6, it is easily seen that the numbers of rules by the proposed mining

algorithm are greater than those by FDM. The taxonomic structures can gather purchased

items into general classes, thus being able to generating additional large itemsets. The large

amounts of rules may, however, cause humans hard to interpret them. Thus, the support and

the confidence values in the proposed algorithm can be set at a higher value than those set by

FDM. For example, when the minimum support value is set at 1000, the number of rules can

be reduced to below 250 (from Figure 4).

7. Discussion and Conclusions

In this paper, we have proposed a fuzzy multiple-level data-mining algorithm that can

process transaction data with quantitative values and discover interesting patterns among 0

2000 4000 6000 8000 10000 12000

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 min-confidence

number of rules

FDM The proposed method

them. The rules thus mined exhibit quantitative regularity on multiple levels and can be used

to provide suggestions to appropriate supervisors. Compared to conventional crisp-set mining

methods for quantitative data, our approach gets smoother mining results due to its fuzzy

membership characteristics. The mined rules are expressed in linguistic terms, which are more

natural and understandable for human beings. The proposed mining algorithm can also be

degraded into a conventional non-fuzzy mining algorithm by assigning a single membership

function with values always equal to 1 for quantity larger than 0.

When compared to fuzzy mining methods, which take all fuzzy regions into

consideration, our method achieves better time complexity since only the most important

fuzzy term is used for each item. If all fuzzy terms are considered, the possible combinational

searches are large. Therefore, a trade-off exists between rule completeness and time

complexity.

Our proposed algorithm does not find association rules for items on the same paths in

given hierarchy trees. Such rules can however be found to analyze interesting behavior among

these items by slightly modifying the proposed algorithm. For example, it may be that a

certain brand of milk is found to be the most popular for its chocolate flavor from a rule that

states that if the brand of milk has high sales figures, then chocolate-flavored milk also has

high sales figures.

Our algorithm can also be easily modified to allow users to assign their items or terms of

interest. The rules thus mined can therefore satisfy users' requirements. For example, users

can require that only items with high sales quantities are mined, which would greatly reduce

the mining time.

Although the proposed method works well in data mining for quantitative values, it is

just a beginning. There is still much work to be done in this field. In the future, we will first

extend our proposed algorithm to resolve the two problems stated above. Our method also

assumes that membership functions are known in advance. In [15-17], we proposed some

fuzzy learning methods to automatically derive membership functions. We will therefore

attempt to dynamically adjust the membership functions in the proposed mining algorithm to

avoid the bottleneck of membership function acquisition. We will also attempt to design

specific data-mining models for various problem domains.

Acknowledgment

The authors would like to thank the anonymous referees for their very constructive

comments. This research was supported by the National Science Council of the Republic of

China under contract NSC89-2213-E-214-003.

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