Dempster’s rule, non-normalized conjunctive rule, Yager’s rule and Dubois-Prade’s rule for belief functions combination are generalized to be applicable to hyper-power sets according to the DSm theory. A comparison of the rules with DSm rule of combination is presented. A series of examples is included.

In this paper we consider various multi-component splittings based on the trapezoidal rule and the implicit midpoint rule. It will be shown that an important requirement on such methods is internal stability. The methods will be applied to initial-boundary value problems. Along with a theoretical analysis, some numerical test results will be presented.

Motivated by applications to crowdsourcing, we study voting rules that output a correct ranking of alternatives by quality from a large collection of noisy input rankings. We seek voting rules that are supremely robust to noise, in the sense of being correct in the face of any “reasonable” type of noise. We show that there is such a voting rule, which we call the modal ranking rule. Moreover, w...

Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...

We introduce the strong quasi-liberal rule, which is an extension of the strong liberal rule in Kasher and Rubinstein (1997) through the requirement of at least one agreement. We provide an axiomatic characterization of strong quasi-liberal rule. Similarly, we generalize the order of the rule (associated with the degree of minimum agreement requirement) to match the Consent Rules in Samet and S...

Given a function f ∈ C[0, 1] and some q ∈ (0, 1), we look at the approximation for the Hadamard finite-part integral = ∫ 1 0 x−q−1f(x)dx based on a piecewise linear interpolant for f at n equispaced nodes (i.e., the product trapezoidal rule). The main purpose of this paper is to give sufficient conditions for the sequence of approximations to converge against the correct value of the integral i...

In this paper we apply a quadrature method based on the tensor product trapezoidal rule to the solution of a singular integral equation over the two-dimensional torus. We prove that this method is stable if and only if a certain numerical symbol does not vanish. For a special kernel function, we present a plot of numerically computed symbol values and, for symmetric kernels (Mikhlin-Giraud kern...

The wave digital concept for numerical integration of partial differential equations leads to algorithms with highly advantageous features as robustness, full localness and massive parallelism. However, the required synthesis of an internally multidimensionally passive reference circuit, from which the algorithm is derived, usually demands an in-depth knowledge of circuit theory and a high leve...

-In this paper, the asymptotic bit operation cost of a family of quadrature formulas, especially suitable for evaluation of improper integrals, is studied. More precisely, we consider the family of quadrature formulas obtained by applying k times the variable transformation x : sinh(y) and then the trapezoidal rule to the transformed integral. We prove that, if the integrand function is analyti...