An analytic method based on plane decomposition for solving two-stage fuzzy EV programming problem.

In recent advances for fuzzy dynamic modeling problem, two-stage equivalent value (EV) programming as an alternative optimization technology has been put forward to make the problem tractable in fuzzy decision-making systems. The main purpose of this paper is to provide a new methodology for computing fuzzy EV programming problem with a finite number of second-stage realizations, which is analytic and systematic rather than approximate strategy. Firstly, we provide two EV definitions in the sense of Lebesgue-Stieltjes (L-S) integral, where two L-S measures are characterized by different nondecreasing functions. Meanwhile, several properties of EV operator are presented to facilitate us to model with this operator. Secondly, for two-stage fuzzy EV programming problem, the second-stage feasibility set and fuzzy elementary feasibility set are defined. Moreover, we demonstrate the convexity of the second-stage feasibility set and recourse function, and establish the supporting hyperplane of the recourse function. Then, a new plane decomposition algorithm is developed to solve two-stage fuzzy EV programming problem, which adds iteratively feasibility and optimality cuts to the relaxed formulation of its first-stage programming problem. Finally, an illustrative example shows the solution details, and demonstrates the applicability of this proposed method.