Convergence is an issue being widely concerned about. Thus, in this paper, we mainly put forward two types of concepts of convergence in mean and convergence in distribution for the sequence of uncertain random variables. Then some of theorems are proved to show the relations among the three convergence concepts that are convergence in mean, convergence in measure and convergence in distributio...

* Correspondence: [email protected] Department of Medical Education, Faculty of Medicine, 06490, Bahçelievler, Ankara, Turkey Full list of author information is available at the end of the article Abstract In this article, a method is developed to transform the chance-constrained programming problem into a deterministic problem. We have considered a chance-constrained programming problem u...

In this paper, we deal with fuzzy random variables for inputs andoutputs in Data Envelopment Analysis (DEA). These variables are considered as fuzzyrandom flat LR numbers with known distribution. The problem is to find a method forconverting the imprecise chance-constrained DEA model into a crisp one. This can bedone by first, defuzzification of imprecise probability by constructing a suitablem...

How did I get to become a cell biologist? Or, more generally, why do things happen the way they do? The answer provided by the philosopher Democritus and later adopted by Jacques Monod is "everything existing in the universe is the fruit of chance and necessity." While I read Monod's book Chance and Necessity as an undergraduate student, little did I appreciate the accuracy of this citation and...

We provide an explicit gradient formula for linear chance constraints under a (possibly singular) multivariate Gaussian distribution. This formula allows one to reduce the calculus of gradients to the calculus of values of the same type of chance constraints (in smaller dimension and with different distribution parameters). This is an important aspect for the numerical solution of stochastic op...

This paper aims to propose a two-step approach for day-ahead hourly scheduling in a distribution system operation, which contains two operation costs, the operation cost at substation level and feeder level. In the first step, the objective is to minimize the electric power purchase from the day-ahead market with the stochastic optimization. The historical data of dayahead hourly electric power...

This article proposes a method for identifying potential self-adequate sub-networks in the existing power distribution grid. These can be equipped with control and protection schemes to form microgrids capable of sustaining local loads during systems contingencies, thereby mitigating disasters. Towards best microgrid candidates, this work formulates chance-constrained optimal network partitioni...