This paper describes a fuzzy hierarchical analytic approach to determine the weighting of subjective judgments. In addition, it presents a nonadditive fuzzy integral technique to evaluate a green engineering industry case as a fuzzy multicriteria decision-making (FMCDM) problem. When the investment strategies are evaluated from various aspects, such as economic effectiveness, technical feasibility, and environmental regulation, it can be regarded as an FMCDM problem. Since stakeholders cannot clearly estimate each considered criterion in terms of numerical values for the anticipated alternatives/strategies, fuzziness is considered to be applicable. Consequently, this paper uses triangular fuzzy numbers to establish weights and anticipated achievement values. By ranking fuzzy weights and fuzzy synthetic utility values, we can determine the relative importance of criteria and decide the best strategies. This paper applies what is called a lambda fuzzy measure and nonadditive fuzzy integral technique to evaluate the synthetic performance of green engineering strategies for aquatic products processors in Taiwan. In addition, we demonstrate that the nonadditive fuzzy integral is an effective evaluation and appears to be appropriate, especially when the criteria are not independent.