Fuzzy Logic and Principal Components Analysis

Data analysis is the process of collecting and processing data with the aim of extracting significant and sound results to aid in decision making in almost every field where data collection is possible. However, when the number of variables involved in a process increase, processing of such data becomes more difficult. One way of alleviating such problems, is to reduce the number of variables to be processed in such a way that, the reduced version still represents great part of the variation in the data. This is achieved by the technique named Principal Component Analysis (PCA). One other aspect considered in this study is the case when the interpretation of data is not very easy, as some data values may not definitely be assigned to a sub group of interest. Handling such situations is becoming possible through the theory of fuzzy logic. This enables the partial assignment of data to different sub groups, through the use of fuzzy membership functions. Using different fuzzy membership functions, it is possible to generate different membership data sets. Application of PCA to such data produced some interesting results that can be handy in selecting the type of the membership functions. Keywords: Fuzzy logic, fuzzy set, fuzzy membership, covariance matrix, correlation matrix, principal component analysis.