Generalized (ℱ, b, ϕ, ρ, θ)-univex n-set functions and semiparametric duality models in multiobjective fractional subset programming

whereAn is the n-fold product of the σ-algebraA of subsets of a given set X ,Fi,Gi, i∈ p ≡ {1,2, . . . , p}, and Hj , j ∈ q, are real-valued functions defined on An, and for each i ∈ p, Gi(S) > 0 for all S∈An such that Hj(S) 0, j ∈ q. This paper is essentially a continuation of the investigation that was initiated in the companion paper [6] where some information about multiobjective fractional programming problems involving point-functions as well as n-set functions was presented, a fairly comprehensive list of references for multiobjective fractional subset programming problems was provided, a brief overview of the available results pertaining to multiobjective fractional subset programming problems was given, and numerous sets of semiparametric sufficient efficiency conditions under various generalized ( ,b,φ,ρ,θ)-univexity assumptions were established. These and some other related material that were discussed in [6] will not be repeated in the present paper. Making use of the semiparametric sufficient efficiency criteria developed in [6] in conjunction with a certain necessary efficiency result that will be recalled in the next section, here we will construct several semiparametric duality models for (P) with varying degrees of generality and, in each case, prove appropriate weak, strong, and strict converse duality theorems under a number of generalized ( ,b,φ,ρ,θ)-univexity conditions.