Since the T-S fuzzy system can approximate any nonlinear system with arbitrary accuracy, it is also expected to be a suitable approach to observe the states of a stochastic nonlinear system. Up to date, a few state estimators for stochastic T-S fuzzy systems have been proposed and applied to various fields without rigorous proof. In this paper, we first derive a sufficient condition based on th...

Stochastic optimization problems provide a means to model uncertainty in the input data where the uncertainty is modeled by a probability distribution over the possible realizations of the data. We consider the well-studied paradigm of stochastic recourse models, in which the realized input is revealed through a series of stages and one can take decisions in each stage in response to the new in...

Separable sublinear functions are used to provide upper bounds on the recourse function of a stochastic program. The resulting problem's objective involves the inf-convolution of convex functions. A dual of this problem is formulated to obtain an implementable procedure to calculate the bound. Function evaluations for the resulting convex program only require a small number of single integratio...

Let ξ := ξ(ω) (s×1) be a random vector defined on a probability space (Ω, S, P ); F, PF the distribution function and the probability measure corresponding to the random vector ξ. Let, moreover, g0(x, z), g1 0(y, z) be functions defined on Rn × Rs and Rn1 × Rs; fi(x, z), gi(y), i = 1, . . . , m functions defined on Rn × Rs and Rn1 ; h := h(z) (m × 1) a vector function defined on Rs, h ′ (z) = (...

With stochastic integer programming as the motivating application, we investigate techniques to use integrality constraints to obtain improved cuts within a Benders decomposition algorithm. We compare the effect of using cuts in two ways: (i) cut-and-project, where integrality constraints are used to derive cuts in the extended variable space, and Benders cuts are then used to project the resul...

The aim of this paper is to price European options for underlying assets with stochastic volatility (SV) in Heston model in 1993 using fuzzy set theory. The main idea is to transform the probability distribution of stochastic volatility to its possibility distribution (from ‘volatility smile to volatility frown’) and reduce the problem to a fuzzy stochastic process for underlying asset with a n...

Let W be an arbitrary subset of IR and posW the positive hull of W . We are concerned with conditions under which one can guarantee continuity properties for posW as a function of W . The results are then applied in the context of semi-infinite linear programs and stochastic programs with recourse.

We present an algorithm for solving stochastic integer programming problems with recourse, based on a dual decomposition scheme and Lagrangian relaxation. The approach can be applied to multi-stage problems with mixed-integer variables in each time stage. Numerical experience is presented for some two-stage test problems.

Two-stage stochastic programs with random right-hand side are considered. Veriiable suucient conditions for the existence of second-order directional derivatives of marginal values are presented. The central role of the strong convexity of the expected recourse function as well as of a Lipschitz stability result for optimal sets is emphasized.