numerous algorithms have been proposed to solve the shortest-pathproblem; many of them consider a single-mode network and crispcosts. other attempts have addressed the problem of fuzzy costs ina single-mode network, the so-called fuzzy shortest-path problem(fspp). the main contribution of the present work is to solve theoptimum path problem in a multimodal transportation network, inwhich the co...

it has been proved that natural frequencies are stationary at the natural modes. also it has been shown that at the first mode it is a minimum and for systems with finite number of degrees of freedom the highest frequency is maximum (reference 1 and 2). beyond these statements nothing more can be said about the behavior of the natural frequencies without defining precisely the manner in which t...