Transformation and learning of the non-equidimensional hesitant fuzzy information based on an extended generative adversarial network

Abstract

In the subjective evaluation process, the hesitant fuzzy set (HFS), as a convenient and robust presentation tool, cannot only suitably address the decision makers’ (DMs’) or experts’ hesitant and uncertain issues but also can arise the dimension curse puzzle. Furthermore, the decision-making result is just derived according to the given objective and subjective information, without considering the DM’s subjective evaluation and the environment’s dynamic influence. Unlike the previous studies, this paper tries to address them from the deep learning viewpoint. To this end, we first define the non-equidimensional HFS (NHFS) and then introduce the equidimensional and classification characters into the NHFS to further develop the equidimensional HFS (EHFS) and the EHFS with the optimal classification result. Then, the equidimensional hesitant fuzzy-generative adversarial network (EHF-GAN) model is proposed to transform the hesitant fuzzy information from the non-equidimensional to the equidimensional form. The generalization and the convergence of the new model are proven to show the models’ reasonability. In addition, the double-learning algorithm of the EHF-GAN model is designed, which can fuse the DMs’ dynamic judgments and derive the optimal decision-making results. Lastly, this paper applies the proposed model and algorithm to an illustrative example of the new smart city enterprises and then shows their feasibility and effectiveness.