The process of deterioration of repairable systems with each repair is modeled using converging geometric-type processes. It is proved that the expectation of the number of repairs in each interval of time is infinite. A new regularization procedure is suggested and the corresponding optimization problem is discussed.

Imprecise probability framework is usually dedicated to decision processes. In recent work, we have shown that this framework can also be used to compute an interval-valued signal containing all outputs of processes involving a coherent family of conventional linear filters. This approach is based on a very straightforward extension of the expectation operator involving appropriate concave capa...

We develop a class of lower bounds on the expectation of a convex function. The bounds utilize the first two moments of the underlying random variable, whose support is contained in a bounded interval or hyperrectangle. Our bounds have applications to stochastic programs whose random parameters are known only through limitedmoment information. Computational results are presented for two-stage s...

In this paper we consider two ways to generalize the mathematical expectation of a random variable, the Choquet expectation and Peng’s g-expectation. An open question has been, after making suitable restrictions to the class of random variables acted on by the Choquet expectation, for what class of expectation do these two definitions coincide? In this paper we provide a necessary and sufficien...

Pitch intervals are central to most musical systems, which utilize pitch at the expense of other acoustic dimensions. It seemed plausible that pitch might uniquely permit precise perception of the interval separating two sounds, as this could help explain its importance in music. To explore this notion, a simple discrimination task was used to measure the precision of interval perception for th...

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

The notion of a $D$-poset was introduced in a connection withquantum mechanical models. In this paper, we introduce theconditional expectation of  random variables on theK^{o}pka's $D$-Poset and prove the basic properties ofconditional expectation on this  structure.