Principles for constructing three-way approximations of fuzzy sets: A comparative evaluation based on unsupervised learning

Three-way approximations of fuzzy sets are an important scheme of granular computing, by abstracting a fuzzy set to its discrete three option-alternatives which adhere to human cognitive behaviors and reduce the computational burden. The key point of such three-way approximations of fuzzy sets is how to choose a suitable design leading to their realization. Undesired three-way approximations might be produced if the selected mechanism is unsuitable to data distribution. In this study, the principles for constructing three-way approximations of fuzzy sets are summarized. The following taxonomy of these principles is provided, namely (i) uncertainty balance-based principle, (ii) prototype-based principle, and (iii) model-based invoking the tradeoff between classification error and the number of data that have to be classified. A number of detailed optimization models are discussed in detail. To evaluate the performance of different construction principles, a general unsupervised learning framework based on three-way approximations of fuzzy sets is exhibited. Some synthetic data sets along with sixteen data sets from UCI repository are involved for experiments. Friedman testing followed by Holm-Bonferroni testing are exploited to test the performance significance of the proposed criteria, which can provide insights and deliver guidance when choosing a principle for constructing three-way approximations of fuzzy sets in the real-world scenarios. The research methods in this paper can also be extended to supervised and semi-supervised learning areas. (c) 2020 Elsevier B.V. All rights reserved.

Automated summary

This paper summarizes the principles for constructing three-way approximations of fuzzy sets, presents three classification principles, and discusses various optimization models. Through experiments to evaluate the performance of different construction principles, methods for selecting construction principles in real-world scenarios are proposed. The research methods can also be extended to supervised and semi-supervised learning areas.