Fuzzy Classification using Self-Adaptive Algorithm to Generate Membership Function

Fuzzy Classification using Self-Adaptive Algorithm to Generate Membership Function

Hemant Jalota (Indian Institute of Technology Mandi, India) and Manoj Thakur (Indian Institute of Technology Mandi, India)
Copyright: © 2016 |Pages: 30
DOI: 10.4018/978-1-4666-9888-8.ch004
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In Fuzzy classification, assigning (or constructing) membership function to sample data on the basis of their attributes is a vital task. In this paper an algorithm is proposed to generate membership function using genetic algorithm (GA). Correlation coefficient is used to select the attributes for generating membership function w.r.t. the class and to classify the data without any human expert's instructions. Membership function is initially assigned using historical data and then the shape and size is updated using BEX-PM (Thakur, 2014) genetic algorithm to classify the data. Proposed methodology tries to make use of lesser fuzzy rule. The performance of the method is compared with other existing methodology on the basis of accuracy rate to classify Iris, Wine and Pima data set.
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1. Introduction

Fuzzy set theory (Zadeh, 1965) generalizes the idea of classical set theory and presents an inherent approach of tackling the situations by incorporating vagueness in the model. It can be easily used as a tool to incorporate uncertainty and imprecision present in the problem. Fuzzy set theory has lot of applications in engineering, sciences and economics etc. (Dubois, 1980; Jones, 1986; George, 2008).

In fuzzy set theory, ’Fuzzification’ is one of the essential step to handle the uncertainty of the problem. It is done by converting crisp values into fuzzy number via assigning membership function with the help of some methodology. Membership function represents the degree of confidence on the fuzzy event. There are various methods mentioned in literature to generate the membership function from the given data and meanwhile solve the real life problem (Burkhardt, 1992; Slany, 1996; Pal, 1999; Ammar, 2003; Yu, 2011; Kumar, 2011).

Many real life scenarios try to find the structure formed by the observed data, using which one can classify the data on the basis of similar attributes, features or by some other patterns. Classification is a supervised learning algorithm which, based on sample training data set which contain the observations (or instances) with known membership, tries to identify the category (sub-populations) to which a new observation belongs. Zimmermann (2010) investigated that fuzzy theory is good option to improve existing perceptions of data mining. Fuzzy Classification (Chen, 2001) is an area where fuzzy set theory is used to classify the data. The vagueness and ambiguity of the data while classification can be handled by means of fuzzy classification system. To handle uncertain perception of fuzzy classification, membership function, which represents its imprecision, is assign to it. Assigning membership on the basis of uncertain information from the historical data (Medasani, 1998) is most important task of fuzzy classification. Effectiveness of fuzzy rule-based classification algorithms are extensively dependent upon the membership functions used (Cox, 1994).

In fuzzy classification, after assigning membership function the next important task is to search for suitable fuzzy rules. There are a number of methods introduced in the literature which may be used to create membership function from the given data. These methods may be broadly categorized into two groups viz. manual or direct approaches and automatic or indirect approaches (Pedrycz, 2013). Direct approaches use subjective information available with respect to the problem at hand, usually relatively expensive for larger data sets and increase complexity of the problem (Kreinovich, 2007; Pendharkar, 2003; Bilgiç, 2000). Also, these approaches need domain expert's knowledge. Many times it is possible that the domain experts are unable to articulate his/her experience precisely and authentically. On the other hand, this limitation can be overcome by indirect approaches as they only use problem data set to build membership functions (Chen, 2001; Bilgiç, 2000; Chen, 2000).

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