Double-quantitative multigranulation rough fuzzy set based on logical operations in multi-source decision systems

Fuzzy phenomena exist widely in real life, and with the rapid development of big data technology we may gather information from multiple sources. So it is extremely meaningful to study fuzzy concepts in the context of multiple information sources. In this study, six novel kinds of double-quantitative multigranulation rough fuzzy set models are proposed. Both absolute and relative information are taken into account by utilizing the logical conjunction and disjunction operators to define the lower and upper approximations. Four decision regions can be computed based on the results of approximations, and the corresponding four decision rules are established. Some basic propositions of these models are discussed. The relationships among the six double-quantitative multigranulation rough fuzzy set models are analysed. The corresponding algorithms of obtaining four decision regions are given and the time complexity of them are analysed. Later a weather example is employed to illustrate that our models can divide data sets to the positive region, the negative region, the lower boundary region, and the upper boundary region, where the samples in the positive region completely support the concept set, the samples in the negative region completely oppose the concept set, and the samples in the lower and upper boundary may support or oppose the concept set. Finally, an experiment is conducted to demonstrate that our models perform better than the mean fusion method in terms of decision-making.