This paper presents a fuzzy dominance-based analytical sorting method as an advancement to the existing multi-objective evolutionary algorithms (MOEA). Evolutionary algorithms (EAs), on account of their sorting schemes, may not establish clear discrimination amongst solutions while solving many-objective optimization problems. Moreover, these algorithms are also criticized for issues such as uncertain termination criterion and difficulty in selecting a final solution from the set of Pareto optimal solutions for practical purposes. An alternate approach, referred here as equitable fuzzy sorting genetic algorithm (EFSGA), is proposed in this paper to address these vital issues. Objective functions are defined as fuzzy objectives and competing solutions are provided an overall activation score (OAS) based on their respective fuzzy objective values. Subsequently, OAS is used to assign an explicit fuzzy dominance ranking to these solutions for improved sorting process. Benchmark optimization problems, used as case studies, are optimized using proposed algorithm with three other prevailing methods. Performance indices are obtained to evaluate various aspects of the proposed algorithm and present a comparison with existing methods. It is shown that the EFSGA exhibits strong discrimination ability and provides unambiguous termination criterion. The proposed approach can also help user in selecting final solution from the set of Pareto optimal solutions.