Supervised Learning Method of Parallel Classified Hesitant Information and its Application in the Smart Home System Selection

In the group decision-making process, experts and decision makers can sometimes provide subjective evaluation information with classification labels. To effectively deal with it and make a reasonable decision, two key issues should be addressed first, which include the information representation and consensus classification model in the above-mentioned uncertain information environment. To do so, this article extends the hesitant fuzzy set (HFS), which has been a hot and effective presentation tool in recent years, to the classification HFS (CHFS), the parallel HFS, and the parallel CHFS. Thus, we can mathematically present three types of evaluation information with classification labels or parallel characteristics in the consensus classification process. Then, to model the parallel classified hesitant fuzzy information and help further consensus classification, this article proposes a supervised learning algorithm and proves its generalization and optimization. In addition, based on the supervised learning algorithm and the obtained classification probability information, we develop a consensus classification method in the parallel classified hesitant fuzzy environment to derive the optimal consensus classification results. Finally, this article applies the proposed algorithm and methods to a real example of smart home system selection, which can show their rationality and feasibility.