Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses $alpha$-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence funct...

We compare two established and a new method for the calculation of spectral bounds for Hessian matrices on hyperrectangles by applying them to a large collection of 1522 objective and constraint functions extracted from benchmark global optimization problems. Both the tightness of the spectral bounds and the computational effort of the three methods, which apply to C2 functions φ : R → R that c...

We improve the quantitative estimate for Roth’s theorem on threeterm arithmetic progressions, showing that if A ⊂ {1, . . . , N} contains no nontrivial three-term arithmetic progressions then |A| N(log logN)4/ logN . By the same method we also improve the bounds in the analogous problem over Fq [t] and for the problem of finding long arithmetic progressions in a sumset.

We prove that a nonstandard extension of arithmetic is eeectively conservative over Peano arithmetic by using an internal version of a deenable ultrapower. By the same method we show that a certain extension of the nonstandard theory with a saturation principle has the same proof-theoretic strength as second order arithmetic, where comprehension is restricted to arithmetical formulas.

Interval arithmetic and stochastic arithmetic have been both developed for the same purpose, i. e. to control errors coming from floating point arithmetic of computers and validate the results of numerical algorithms performed on computers. Interval arithmetic delivers guaranteed bounds for numerical results but requires special analysis and algorithms. On the other hand stochastic arithmetic i...

A large number of secret key cryptographic algorithms combine Boolean and arithmetic instructions. To protect such algorithms against first order side channel analysis, it is necessary to perform conversions between Boolean masking and arithmetic masking. Louis Goubin proposed in [7] an efficient method to convert from Boolean to arithmetic masking. However the conversion method he also propose...

This paper is devoted to the analysis of the behaviour, in nite precision arithmetic, of the quasi-minimal residual method without look ahead for the solution of linear systems Ax = b where A is a real or complex matrix of order n. In exact arithmetic, the behaviour of the method as applied to symmetric deenite matrices is well understood; but results about convergence usually suppose that the ...