2 How to Create Instances of Fuzzy Numbers 3 2.1 Arbitrary Fuzzy Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Definition by Side Functions . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Definition by α-cut Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Definition with Generating Functions Omitted: Shadowed Sets . . . . . . 6 2.2 Us...

Ganesan and Veeramani [Fuzzy linear programs with trapezoidal fuzzy numbers, Annals of Operations Research 143 (2006) 305-315.] proposed a new method for solving a special type of fuzzy linear programming problems. In this paper a new method, named as Mehar’s method, is proposed for solving the same type of fuzzy linear programming problems and it is shown that it is easy to apply the Mehar’s m...

The numerical computation of P{X > x} can be accomplished in a variety of ways. An appealing class of methods may be derived from the contour integral connecting P{X > x} and its Fourier representation. Statisticians have largely focused on deriving saddlepoint approximations for this contour integral. The accuracy of such approximations is generally understood in vague terms only and, perhaps ...

1 Motivation We want to numerically approximate coefficients in a Fourier series. The first step is to see how the trapezoidal rule applies when numerically computing the integral (2π) −1 2π 0 F (t)dt, where F (t) is a continuous, 2π-periodic function. Applying the trapezoidal rule with the stepsize taken to be h = 2π/n for some integer n ≥ 1 results in (2π) −1 2π 0 F (t)dt ≈ 1 n n−1 j=0 Y j , ...

in a previous work, we introduced particular fuzzy numbers anddiscussed some of their properties. in this paper we use the comparison methodintroduced by dorohonceanu and marin[5] to compare between these fuzzynumbers.

this paper considers the fuzzy inventory model for deteriorating items for power demand under fully backlogged conditions. we define various factors which are affecting the inventory cost by using the shortage costs. an intention of this paper is to study the inventory modelling through fuzzy environment. inventory parameters, such as holding cost, shortage cost, purchasing cost and deteriorati...

in this paper a network comprising alternative branching nodes with probabilistic outcomes is considered. in other words, network nodes are probabilistic with exclusive-or receiver and exclusive-or emitter. first, an analytical approach is proposed to simplify the structure of network. then, it is assumed that the duration of activities is positive trapezoidal fuzzy number (tfn). this paper com...

In this paper we use the Triangular and Trapezoidal Fuzzy Numbers as tools for assessing student Mathematical Modelling (MM) skills. Fuzzy Numbers play a fundamental role in fuzzy mathematics analogous to the role played by the ordinary numbers in classical mathematics, On the other hand, MM appears today as a dynamic tool for teaching and learning mathematics, because it connects mathematics w...

The fuzzy regression control chart is a functional technique to evaluate the process in which the average has a trend and the data represents a linguistic or approximate value. In this study, the theoretical structure of the “α-level fuzzy midrange for α-cut fuzzy X ~ -regression control chart” is proposed for triangular (TFN) and trapezoidal (TrFN) membership functions. In addition, the real w...

Inventory model under risk that demand is uncertain is recognized. In this paper, the fuzzy demand per day and fuzzy lead time on a cycle in fuzzy inventory control system are assumed to trapezoidal distribution, trapezoidal fuzzy number by decision maker. A fuzzy inventory model under manager’s preference for order quantity is presented first. This model is given by fuzzy total annual inventor...