This paper addresses the problem of sensitivity analysis for finite-horizon performance measures of general Markov chains. We derive closed-form expressions and associated unbiased gradient estimators for the derivatives of finite products of Markov kernels by measure-valued differentiation (MVD). In the MVD setting, the derivatives of Markov kernels, called D-derivatives, are defined with resp...

In this paper, we firstly invoke gradual Hausdorff metric to define a new additive fuzzy-valued measure on the ordinary measurable space. Then, from the view of a fuzzy number as a crisp interval of gradual numbers, we show that the new fuzzy-valued measure can be characterized by two gradual number-valued measures. Finally, we investigate some of its properties and structural characterizations.

The semigroup-valued integral of M. Sion [S] is reformulated for a general notion of approximation by sums of values taken by a set function integrand. A convergence in measure theorem is established, which yields both his pointwise dominated convergence theorem as well as an integrability criterion which specializes to his existence theorem. In [S] M. Sion introduced and developed an "integral...

This paper considers minimization of incompletely specified multi-valued functions using functional decomposition. While functional decomposition was originally created for the minimization of logic circuits, this paper uses the decomposition process for both machine learning and logic synthesis of multi-valued functions. As it turns out, the minimization of logic circuits can be used in the co...

In this work, we study concentration properties for vector valued maps. In particular, we describe inequalities which capture the exact dimensional behavior of Lipschitz maps with values in Rk. To this task, we study in particular a domination principle for projections which might be of independent interest. We further compare our conclusions to earlier results by Pinelis in the Gaussian case, ...

We give a comprehensive treatment of Sturm–Liouville operators whose coefficients are measures including a full discussion of self-adjoint extensions and boundary conditions, resolvents, and Weyl–Titchmarsh–Kodaira theory. We avoid previous technical restrictions and, at the same time, extend all results to a larger class of operators. Our operators include classical Sturm– Liouville operators,...

Multi-valued logics can be effectively used to reason about incomplete and/or inconsistent systems, e.g. during early software requirements or as the systems evolve. In our earlier work we identified a useful family of multi-valued logics: those specified over finite distributive lattices where negation preserves involution, i.e., , , -/.0for every element of the logic. Model-checking over this...

A great deal of recent theoretical work in inference has involved extending classical logic in some way. I argue that these extensions share two properties: firstly, the formal addition of truth values encoding intermediate levels of validity between true (i.e., valid) and false (i.e., invalid) and, secondly, the addition of truth values encoding intermediate levels of certainty between true or...

In this article, we introduce a perturbed system of generalized mixed quasi-equilibrium-like problems involving multi-valued mappings in Hilbert spaces. To calculate the approximate solutions of the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems, firstly we develop a perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems,...