Uncertainty propagation in complex engineering systems with fuzzy variables constitutes a significant challenge. This paper proposes a Polynomial Chaos type spectral approach based on orthogonal function expansion. A fuzzy variable is represented as a set of interval variables via the membership function. The interval variables are further transformed into the standard interval [−1,1]. Smooth n...

This paper deals with the problem of linear programming with inexact data represented by real closed intervals. Optimization problems with interval data arise in practical computations and they are of theoretical interest for more than forty years. We extend the concept of duality gap (DG), the difference between the primal and its dual optimal value, into interval linear programming. We consid...

Finding bounding sets to solutions to systems of algebraic equations with uncertainties in the coefficients, as well as finding mathematically rigorous but rapid location of all solutions to nonlinear systems or finding global optima, involves bounding the solution sets to systems of equations with wide interval coefficients. The interval Gauss–Seidel algorithm has various properties that make ...

In the paper an interesting application of fuzzy approach is presented. The problem of stability analysis of uncertain linear systems with coefficients described by fuzzy functions is studied. Each coefficient is considered as a variable interval parametrized by the degree of confidence in validity of the corresponding model. The higher the confidence level is the smaller is the interval in whi...

In this paper, the Multiple Attribute Group Decision Making (MAGDM) problems is based on the attribute weights calculated from completely unknown information using the Maximal Entropy OWA weights. The interval-valued intuitionistic fuzzy ordered weighted averaging (IIFOWA) operator is utilized to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the dec...

In this paper, a strategic decision making model for the sustainable development of marine renewable energy is proposed, and specific application to United Kingdom (UK) demonstrated. As an island nation UK benefits from significant potential which providing increasing contribution UK's portfolio. The paper investigates question how makers can be aided reach on types projects should chosen given...

In this paper, we consider the bilevel linear programming problem (BLPP) where all coefficients in are interval type-2 triangular fuzzy numbers (IT2TFNs). First, convert a BLPP with IT2TFN parameters to an BLPP. next step, solve BLPPs and obtain optimal solution as IT2TFN.

The usual way to determine the asymptotic behavior of the Chebyshev coefficients for a function is to apply the method of steepest descent to the integral representation of the coefficients. However, the procedure is usually laborious. We prove an asymptotic upper bound on the Chebyshev coefficients for the kth integral of a function. The tightness of this upper bound is then analyzed for the c...

A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of such methods in the context of rigorous computing (where we need guarantees on the accuracy of the result), and from the complexity point of view. It is well-kn...