The theory of fuzzy measures has a great potential for real world applications, but limited by the lack of suitable identifying methods. This research proposes a bisection algorithm based on Sugeno’s λ-fuzzy measures. The proposed method is simple enough to suit the practical applications for the required data is similar to the traditional weighted-sum method. The computing complexity of this m...

In this paper we compare two real root isolation methods using Descartes’ Rule of Signs: the Interval Bisection method, and the Continued Fractions method. We present some time-saving improvements to both methods. Comparing computation times we conclude that the Continued Fractions method works much faster save for the case of very many very large roots.

The use of numerical tools to solve challenging problems in mathematics has exploded in the past several decades. The purpose of this paper is to compare the results of two different types of numerical methods in finding solutions to the eigenvalue problem for a second-order elliptic differential equation subject to boundary and transmission conditions. The transmission conditions result from j...

Residue Number System (RNS) has computational advantages for large integer arithmetic. It provides the benefits of parallel, carry-free, and high-speed arithmetic in addition, subtraction, and multiplication. However, overflow detection, sign detection, magnitude detection, and division are time-consuming operations in RNS. The most interesting one of the above operations is division, and many ...

Algorithms for polynomial real root isolation are ubiquitous in computational real algebraic geometry but few lower bounds are known for their maximum computing time functions. One exception is the continued fractions method due to Vincent (1836) and recommended by Uspensky (1948). Collins and Akritas (1976) proved that the maximum computing time of the method is at least exponential in the len...

The note presents results of applying several Alpha-Beta search enhancements in the game of giveaway checkers with a real-value state evaluation function. In particular, the MTD-bi (bisection) algorithm is tested and compared (1) with MTD(f ) and (2) with Alpha-Beta search enhanced with transposition tables and the history heuristic. The results show that in the real-value domain the MTD(f ) al...

In this paper we adapt the well-known parametric approach from fractional programming to solve a class of fractional programs with a noncompact feasible region. Such fractional problems belong to an important class of single component preventive maintenance models. Moreover, for a special but important subclass we show that the subproblems occurring in this parametric approach are easy solvable...

Bisection search is the most efficient algorithm for locating a unique point X∗ ∈ [0, 1] when we are able to query an oracle only about whether X∗ lies to the left or right of a point x of our choosing. We study a noisy version of this classic problem, where the oracle’s response is correct only with probability p. The probabilistic bisection algorithm (PBA) introduced by Horstein [IEEE Trans. ...

An extension of the LQR/LQG methodology to systems with saturating actuators, referred to as SLQR/SLQG, where S stands for saturating, is obtained. The development is based on the method of stochastic linearization, whereby the saturation is replaced by a xed gain, calculated as a function of the variance of the signal at its input. Using the stochastically linearized system and the Lagrange mu...

We continue our recent work on finite-sample, i.e., non-asymptotic, inference with two-step, monotone incomplete data from Nd(μ,Σ), a multivariate normal population with mean μ and covariance matrix Σ. Under the assumption that Σ is block-diagonal when partitioned according to the two-step pattern, we derive the distributions of the diagonal blocks of b Σ and of the estimated regression matrix,...