Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...

in this paper, a novel approach for multi response optimization is presented. in the proposed approach, response variables in treatments combination occur with a certain probability. moreover, we assume that each treatment has a network style. because of the probabilistic nature of treatment combination, the proposed approach can compute the efficiency of each treatment under the desirable reli...

convexity theory and duality theory are important issues in math- ematical programming. within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. finally,...

We study the discrete optimization problem under the distributionally robustframework. We optimize the Entropic Value-at-Risk, which is a coherentrisk measure and is also known as Bernstein approximation for the chanceconstraint. We propose an efficient approximation algorithm to resolve theproblem via solving a sequence of nominal problems. The computationalresults show...

Stochastic Approach to Vehicle Routing Problem: Development and Theories Abstract In this article, a chance constrained (CCP) formulation of the Vehicle Routing Problem (VRP) is proposed. The reality is that once we convert some special form of probabilistic constraint into their equivalent deterministic form then a nonlinear constraint generates. Knowing that reliable computer software...

Constraint-admissible sets have been widely used in the study of control of systems with hard constraints. This paper proposes a generalization of the maximal constraint admissible set for constrained linear discrete time system to the case where chance or probabilistic constraints are present. Defined in the most obvious way, the maximal probabilistic constraint-admissible set is not invariant...

This paper considers linear discrete-time systems with additive disturbances, and designs a Model Predictive Control (MPC) law incorporating dynamic feedback gain to minimise quadratic cost function subject single chance constraint. The is selected online we provide two selection methods based on minimising upper bounds predicted costs. constraint defined as discounted sum of violation probabil...

We propose a stochastic MPC scheme using an optimization over the initial state for predicted trajectory. Considering linear discrete-time systems under unbounded additive disturbances subject to chance constraints, we use constraint tightening based on probabilistic reachable sets design MPC. The avoids infeasibility issues arising from by including as decision variable. show that stabilizing ...