Attribute selection with fuzzy decision reducts

TLDR: This paper introduces the concept of fuzzy decision reducts, dependent on an increasing attribute subset measure, and presents a generalization of the classical rough set framework for data-based attribute selection and reduction using fuzzy tolerance relations.

About: This article is published in Information Sciences.The article was published on 2010-01-01 and is currently open access. It has received 227 citations till now. The article focuses on the topics: Attribute domain & Fuzzy set operations.

Figures

Table 5: CPU results

Table 1: Data set characteristics

Figure 3: CPU results: a) RMSE versus subset size b) RMSE increase versus subset size reduction

Figure 1: Modified QuickReduct to obtain a fuzzy M-decision superreduct to degree α.

Figure 2: Spambase results: a) Classification accuracy versus subset size b) Accuracy drop versus subset size reduction

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Aberystwyth university attribute selection with fuzzy decision reducts" ?

Therefore, within the context of fuzzy rough set theory, the authors present a generalization of the classical rough set framework for databased attribute selection and reduction using fuzzy tolerance relations. The paper unifies existing work in this direction, and introduces the concept of fuzzy decision reducts, dependent on an increasing attribute subset measure. Experimental results demonstrate the potential of fuzzy decision reducts to discover shorter attribute subsets, leading to decision models with a better coverage and with comparable, or even higher accuracy. 

Q2. How many measures were selected for each of the fuzzy-rough measures?

For each of the fuzzy-rough measures introduced, the authors ran QuickReduct once with α = 1, and a second time with a fixed α < 1; in particular, a value of α = 0.95 was deemed a suitable overall choice for most measures, except for g, which requires a much higher threshold, and for which α = 0.9999 was selected. 

Q3. What is the way to interpret the results?

When interpreting these results, one should always keep in mind the trade-off between accuracy (RMSE) and attribute subset size: a higher accuracy (lower RSME) is of course desirable, but so is a smaller subset size, i.e., the less conditional attributes there are in the reduced data set, the stronger its generalization capacity. 

Q4. What is the general definition of fuzzy decision reducts?

In the general definition that the authors propose, the authors require an increasing [0, 1]-valued measure, so as to guarantee that the larger an attribute subset, the higher its degree of fuzzy decision reducthood (monotonicity), which is in analogy to other approaches to define a degree of approximating decision classes [43, 44]. 

Q5. What are the evaluation measures in the previous subsections?

As the authors have shown, the evaluation measures γ, γ′, δ, δ′, f and g introduced in the previous subsections all give rise to corresponding fuzzy decision reducts. 

Q6. How much accuracy can be achieved with fuzzy -decision reducts?

as seen in Figure 2b), if a 1% accuracy drop is permissible, fuzzy γ-decision reducts manage to reduce the subset size by over 40%, while with g a reduction of the data set by more than 63% is possible. 

Q7. What is the effect of the heuristic on the and f subset?

This affects QuickReduct’s operation adversely; when all of the considered subsets in a given iteration evaluate to 0, the heuristic is forced to select one without any information about its true merit. 

Q8. What is the default distance weighting for the K-nearest neighbour classifier?

In their experiments, the authors have used the very simple K-nearest neighbour classifier [1], implemented in Weka [53] as IBk, with default parameters (K = 1, no distance weighting). 

Q9. What is the difference between the two experiments?

Their experiments clearly endorse the benefit of using fuzzy decision reducts, showing a greater flexibility and better potential to produce good-sized, highquality attribute subsets than the crisp decision reducts that have been used so far in fuzzy-rough data analysis.