Data-driven identification of key variables: A fuzzy set approach

In this dissertation, we investigate a problem raised from a real-world application, surface mount manufacturing. The problem can be abstracted as a general problem: to identify key variables that contribute to a partition of a given data set. We have developed two algorithms that can be applied to dealing with this problem. Both algorithms are based on fuzzy sets, fuzzy measures, fuzzy integrals, and evolutionary strategies.;The second algorithm is based on the idea that each data point can be considered as an evaluation function of an object with respect to several features. Fuzzy measures are used to weight different features, and fuzzy integrals are used to define partitions of data points. An evolutionary strategy is again used to identify the optimal fuzzy measure under which values of fuzzy integral of data points define a partition which is as close as possible to a given partition. Both algorithms are tested on the benchmark data, the Iris data set.;A by-product of our investigation is a method for constructing fuzzy measures from a given data set by solving fuzzy relation equations. Moreover, we have also developed a theoretically justified method for approximate solutions of fuzzy relation equations.;The first algorithm is based on the idea that by employing different Mahalanobis metrics, one can weight variables differently. It is called an evolutionary fuzzy c-means algorithm. The algorithm involves a search for an optimal Mahalanobis metric under which the fuzzy c-means algorithm derives a fuzzy partition that is as close as possible to a given partition.