Representing fuzzy numbers for fuzzy calculus

In this paper we illustrate the LU representation of fuzzy numbers and present an LU-fuzzy calculator, in order to explain the use of the LU-fuzzy model and to show the advantage of the parametrization. The model can be applied either in the level-cut or in generalized LR frames. The hand-like fuzzy calculator has been developed for the MSWindows platform and produces the basic fuzzy calculus: the arithmetic operations (scalar multiplication, addition, subtraction, multiplication, division) and the fuzzy extension of many univariate functions (exponential, logarithm, power with numeric or fuzzy exponent, sin, arcsin, cos, arccos, tan, arctan, square root, Gaussian, hyperbolic sinh, cosh, tanh and inverses, erf and erfc error functions, cumulative standard normal distribution).Fuzzy Sets, LU-fuzzy Calculator, Fuzzy Calculus, Parametric LU represemtation

Approximation of fuzzy numbers by convolution method

In this paper we consider how to use the convolution method to construct approximations, which consist of fuzzy numbers sequences with good properties, for a general fuzzy number. It shows that this convolution method can generate differentiable approximations in finite steps for fuzzy numbers which have finite non-differentiable points. In the previous work, this convolution method only can be used to construct differentiable approximations for continuous fuzzy numbers whose possible non-differentiable points are the two endpoints of 1-cut. The constructing of smoothers is a key step in the construction process of approximations. It further points out that, if appropriately choose the smoothers, then one can use the convolution method to provide approximations which are differentiable, Lipschitz and preserve the core at the same time.Comment: Submitted to Fuzzy Sets and System at Sep 18 201

Interval LU-fuzzy arithmetic in the Black and Scholes option pricing

In financial markets people have to cope with a lot of uncertainty while making decisions. Many models have been introduced in the last years to handle vagueness but it is very difficult to capture together all the fundamental characteristics of real markets. Fuzzy modeling for finance seems to have some challenging features describing the financial markets behavior; in this paper we show that the vagueness induced by the fuzzy mathematics can be relevant in modelling objects in finance, especially when a flexible parametrization is adopted to represent the fuzzy numbers. Fuzzy calculus for financial applications requires a big amount of computations and the LU-fuzzy representation produces good results due to the fact that it is computationally fast and it reproduces the essential quality of the shape of fuzzy numbers involved in computations. The paper considers the Black and Scholes option pricing formula, as long as many other have done in the last few years. We suggest the use of the LU-fuzzy parametric representation for fuzzy numbers, introduced in Guerra and Stefanini and improved in Stefanini, Sorini and Guerra, in the framework of the Black and Scholes model for option pricing, everywhere recognized as a benchmark; the details of the computations by the interval fuzzy arithmetic approach and an illustrative example are also incuded.Fuzzy Operations, Option Pricing, Black and Scholes

An LU-fuzzy calculator for the basic fuzzy calculus

The LU-model for fuzzy numbers has been introduced in [4] and applied to fuzzy calculus in [9]; in this paper we build an LU-fuzzy calculator, in order to explain the use of the LU-fuzzy representation and to show the advantage of the parametrization. The calculator produces the basic fuzzy calculus: the arithmetic operations (scalar multiplication, addition, subtraction, multiplica- tion, division) and the fuzzy extension of many univariate functions (power with integer positive or negative exponent, exponential , logarithm, general power function with numeric or fuzzy exponent, sin, arcsin, cos, arccos, tan, arctan, square root, Gaussian and standard Gaussian functions, hyperbolic sinh, cosh, tanh and inverses, erf error function and complementary erfc error function, cu- mulative standard normal distribution). The use of the calculator is illustrated.Fuzzy Sets, LU-fuzzy Calculator, Fuzzy Calculus

A Simple Approximation of Productivity Scores of Fuzzy Production Plans

This paper suggests a simple approximation procedure for the assessment of productivity scores with respect to fuzzy production plans. The procedure has a clear economic interpretation and all the necessary calculations can be performed in a spreadsheet making it highly operational.rationing; inequality preservation; taxation; manipulation; proportional method

Magnetic operations: a little fuzzy physics?

We examine the behaviour of charged particles in homogeneous, constant and/or oscillating magnetic fields in the non-relativistic approximation. A special role of the geometric center of the particle trajectory is elucidated. In quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an element of non-commutative geometry which enters into the traditional control problems. We show that its application extends beyond the usually considered time independent magnetic fields of the quantum Hall effect. Some simple cases of magnetic control by oscillating fields lead to the stability maps differing from the traditional Strutt diagram.Comment: 28 pages, 8 figure