Critical environmental and human health concerns are associated with the rapidly growing fields of nanotechnology and manufactured nanomaterials (MNMs). The main risk arises from occupational exposure via chronic inhalation of nanoparticles. This research presents a chance-constrained nonlinear programming (CCNLP) optimization approach, which is developed to maximize the nanaomaterial productio...

Extensions of the ML type system based on con strained type schemes have been proposed for lan guages with overloading Type inference in these sys tems requires solving the following satis ability prob lem Given a set of type assumptions C over nite types and a type basis A is there is a substitution S that satis es C in that A CS is derivable Un der arbitrary overloading the problem is undecid...

In this paper, we deal with multiobjective integer programming problems involving random variable coefficients in objective functions and/or constraints. After reformulation of them on the basis of a probability maximization model for the chance constrained programming, incorporating fuzzy goals of the decision maker for the objective functions, we propose an interactive fuzzy satisficing metho...

This paper is concerned with the fuzzy support vector classification, in which both of the type of the output training point and the value of the final fuzzy classification function are triangle fuzzy number. First, the fuzzy classification problem is formulated as a fuzzy chance constrained programming. Then, we transform this programming into its equivalence quadratic programming. Final, a fu...

The term probabilistic constrained programming means the same as chance constrained programming, i.e., optimization of a function subject to certain conditions where at least one is formulated so that a condition, involving random variables, should hold with a prescribed probability. The probability is usually not prescribed exactly but a lower bound is given instead which is in practice near u...

To model combinatorial decision problems involving uncertainty and probability, we have proposed “stochastic constraint programming” [3]. This extends constraint programming with stochastic variables, chance constraints and optimized expectations. We propose extending the OPL modelling language [1] with these features, and show how they can be compiled away using some simple rules.