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The parametrically generalized sufficient efficiency conditions for mult iobjective fractional programming based on the hybrid (Φ,Ψ,ρ,ζ,θ)-invexities are developed and then efficient solutions to the multiobjective fractional programming problems are established. Plus, the obtained results on sufficient efficiency condition s are generalized to the case of the ǫ-efficient solutions. The results thus obtained generalize and unify a wider range of investigations on the theory and applications to the multiobjective fractional programming based on the hybrid (Φ,Ψ,ρ,ζ,θ)-invexity frameworks.

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Hybrid (&amp;#934;,&amp;#936;, &amp;#961;, &amp;#950;, &amp;#952;)&amp;#8722;invexity frameworks and efficiency conditions for multiobjective fractional programming problems