FSSC: An Algorithm for Classifying Numerical Data Using Fuzzy Soft Set Theory

Bana Handaga, Tutut Herawan, Mustafa Mat Deris
DOI: 10.4018/ijfsa.2012100102
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Abstract

Introduced is a new algorithm for the classification of numerical data using the theory of fuzzy soft set, named Fuzzy Soft Set Classifier (FSSC). The algorithm uses the fuzzy approach in the pre-processing stage to obtain features, and similarity concept in the process of classification. It can be applied not only to binary-valued datasets, but also be able to classify the data that consists of real numbers. Comparison tests on seven datasets from UCI Machine Learning Repository have been carried out. It is shown that the proposed algorithm provides better accuracy and higher accuracy as compared to the baseline algorithm using soft set theory.
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Introduction

In 1999, D. Molodtsov introduced the notion of a soft set as a collection of approximate descriptions of an object (Molodtsov, 1999). This initial description of the object has an approximate nature, and we do not need to introduce the notion of exact solution. The absence of any restrictions on the approximate description in soft set makes this theory very convenient and easily applicable in practice (Herawan et al., 2009, Herawan, Rose, & Deris, 2010; Herawan & Deris, 2010; Xiuqin et al., 2011b). Applications of soft set in areas ranging from decision problems to texture classifications have surged in recent years (Maji et al., 2002; Mushrif et al., 2006; Roy & Maji, 2007; Feng et al., 2010).

The soft set theory can work well on the parameters that have a binary number (Herawan, Deris, & Abawajy, 2010a; Xiuqin et al., 2011a), but still difficult to work with parameters that have real numbers. To overcome this problem, Maji et al. have studied a more general concept, namely the theory of fuzzy soft set, which can be used with the parameters in the form of real numbers (Maji et al., 2001). These results further expand the scope of applications of soft set theory (Hongwu et al., 2011). One of the potential applications of fuzzy soft set theory is numerical data classification. There are two important concepts underlying the application of the theory of soft set in numerical classification problems. Firstly, the concept of decision making problems based on fuzzy soft set theory, and secondly is the concept of measuring similarity between two fuzzy soft set. Based on an application of soft set in a decision making problem presented by Maji et al. (2002), Mushrif et al. (2006) presented a novel method for classification of natural textures using the notions of soft set theory, all features on the natural textures consist of a numeric (real) data type, have a value between [0,1] and the algorithm used to classify the natural texture is very similar to the algorithms used by Roy and Maji (2007) in the decision making problems with the theory of fuzzy soft set. The algorithm was successfully classify natural texture with very high accuracy when compared with conventional classification methods such as Bayes classifier and a minimum distance classifier based on Euclidean distance. He has also proved that the computation time for classification is much less as compared to with Bayes classification method.

Measuring similarity or distance between two entities is a key step for several data mining and knowledge discovering task, such as classification and clustering. Similarity measures quantify the extent to which different patterns, signals, images or sets are alike. The studies on measuring the similarity between soft set have been carried out (Majumdar & Samanta, 2008; Kharal, 2010). They then extended their research to measure the similarity of fuzzy soft set and describe how it can be applied to medical diagnosis to detect whether a person is suffering from a certain disease (Majumdar & Samanta, 2010).

This paper proposes a new classification approach based on fuzzy soft set theory, using similarity between two soft set. We call this classifier as a Fuzzy Soft Set Classifier (FSSC). The proposed approach results in high degree of accuracy and with low computational complexity as compared to soft set classification based on decision making problem. Seven types of UCI data set have been used have been used for comparing the proposed fuzzy soft set classifier and the soft set classifier suggested by Mushrif et al. (2006).

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