Because of COVID-19, factories are facing many difficulties, such as shortage of workers and social alienation . How to improve production performance under limited labor resources is an urgent problem for global manufacturing factories . This work studies an energy-efficient job-shop scheduling problem with limited workers . Those workers can have multiskills . A many-objective model with five objectives, that is : 1) makespan; 2) total tardiness; 3) total idle time; 4) total worker cost; and 5) total energy, is built . To solve this many-objective optimization problem (MaOP), a novel fitness evaluation mechanism (FEM) based on fuzzy correlation entropy (FCE) is adopted . Two construction methods for reference points are proposed to build the bridge between MaOP and a fuzzy set . Based on FCE and cluster methods, an environmental selection mechanism (ESM) is proposed to achieve a balance between solution convergence and diversity . With the proposed FEM and ESM, two many-objective evolutionary algorithms are proposed to solve MaOP . The effect of FCE-based FEM and ESM on the performance of algorithms is verified via experiments . The proposed algorithms are compared with four well-known peers to test their performance . The extensive experimental results show that they are very competitive for the considered many-objective scheduling problem.