In some cases, our uncertainty about about a quantity can be described by an interval of its possible values. If we have two or more pieces of interval information about the same quantity, then we can conclude that the actual value belongs to the intersection of these intervals. In general, we may need a fuzzy number to represent our partial knowledge. A fuzzy number can be viewed as a collecti...

This paper proposes the concepts of a neutrosophic number and a trapezoidal neutrosophic number (TNN), the basic operational relations of TNNs, and the score function of TNN. Then, we develop a trapezoidal neutrosophic weighted arithmetic averaging (TNWAA) operator and a trapezoidal neutrosophic weighted geometric averaging (TNWGA) operator to aggregate TNN information and investigate their pro...

AUC is an important parameter in pharmacokinetic studies. There are different ways to calculate AUC. Sometime, the statistician or pharmacokineticist has to choose one particular method to calculate AUC depending on the actual concentration data. Among many pharmacokinetic approaches and modeling analyses, traditional trapezoidal, log-linear trapezoidal, Lagrange polynomial integration, and Pur...

The trapezoidal rule for the numerical integration of first-order ordinary differential equations is shown to possess, for a certain type of problem, an undesirable property. The removal of this difficulty is shown to be straightforward, resulting in a modified trapezoidal rule. Whilst this latent difficulty is slight (and probably rare in practice), the fact that the proposed modification invo...

ClassSm variable transformationswith integerm for finite-range integrals were introduced by the author (Numerical Integration IV, International series of Numerical Mathematics, Basel, 1993, pp. 359–373) about a decade ago. These transformations “periodize” the integrand functions in a way that enables the trapezoidal rule to achieve very high accuracy, especially with even m. In a recent work b...

The article is devoted to the problem of multi-criteria decision making. As application used equipment selection problem. analysis existing methods for solving this given. a method fuzzy TOPSIS (The Technique Order Preference by Similarity Ideal Solution) proposed. This based on ideal solution approach. issues practical implementation are discussed in details. results test at all stages present...

In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. Th...

There exist some fuzziness and uncertainty in the process of ecological construction. The aim of this paper is to develop a direct and an effective simplified method for obtaining the cost-sharing scheme when some interested parties form a cooperative coalition to improve the ecological environment of Min River together. Firstly, we propose the solution concept of the least square prenucleolus ...

In this paper, a numerical method for solving fuzzy Fredholm integral equations of the second kind is introduced. We apply the trapezoidal rule to compute the Riemann integrals.This kind of integral equations convert to a linear system. Then, by solving the linear system , unknowns are determined. Finally, an algorithm is presented to solve the fuzzy integral equation by using the trapezoidal r...