Abstract The well-known Karush-Kuhn-Tucker theorem can be used, as in the fuzzy case, to find the trapezoidal approximation of a given intuitionistic fuzzy number. The method is quite technical such that obtaining the trapezoidal approximation of an intuitionistic fuzzy numbers from the trapezoidal approximation of a fuzzy number is proposed in the present paper. Among the advantages of this me...

It is generally agreed that of all quadrature formulae, the trapezoidal rule, while being the simplest, is also the least accurate. There is, however, a rather general class of integrals for which the trapezoidal rule can be shown to be a highly accurate means of obtaining numerical values. Specifically, if the integrand is a periodic, even function with all derivatives continuous, then the int...

In this paper, we prove new distance properties between a fuzzy number and its trapezoidal approximation preserving the expected interval. Then, we find the best Lipschitz constant of the trapezoidal approximation operator preserving the expected interval. Finally, we use this result in finding within a reasonable error the trapezoidal approximation of a fuzzy number preserving the expected int...

The effect of the outlet weir height on sieve tray performance is described in this paper. The studies were made to investigate the effect of the outlet weir height on sieve tray mass transfer efficiency and hydraulic performance. Tests were conducted in the 1.22 m diameter section of the Fractionation Research, Inc. (FRI) low-pressure column. Sieve trays with nominal hole areas of 14%, 13%, an...

The purpose of this research is examining the performance rectangular broad and sharp crested weirs in terms cavity index discharge coefficient. For purpose, a computational fluid dynamics CFD code FLUENT applied. Firstly, verified by applies on experiments work Hagre et al 1994 results show excellent agreements between Hager 1994. Secondly applied both weirs. demonstrate that have lower coeffi...

Many authors analyzed triangular and trapezoidal approximation of fuzzy numbers. But, to best of our knowledge, there is no method for symmetric trapezoidal fuzzy number approximation of fuzzy numbers. So, in this paper, we try to convert any fuzzy number into symmetric trapezoidal fuzzy number by using metric distance. This approximation helps us to avoid the computational complexity in the pr...

An experimental campaign is undertaken in order to investigate the hydraulic features of a vertical drop shaft, also considering the influence of a venting system consisting of a coaxial vertical pipe, projecting within the drop shaft with different plunging rates. Three different flow regimes are observed: a “weir flow” for very low head values, where the flow profile is subject to the atmosph...

Discharge behavior at side weirs is significantly influenced by the water surface profile along weir crest. In past century, different approaches were developed to describe this and associated discharge coefficients. However, application of these methods practical problems poses a particular challenge, as complex three-dimensional funnel formed due reduction, leading significant uncertainties i...

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We propose a new approach to assigning distance between fuzzy numbers. A pseudo-metric on the set of fuzzy numbers and a metric on the set of trapezoidal fuzzy numbers are described. The regular reducing functions and the Hausdorff metric are used to define the metric. Using this metric, we can approximate an arbitrary generalized left right fuzzy number with a trapezoidal one. Finally, powers ...