In this paper, an interesting and easy method to solve the multi-dimensional  knapsack problem is presented. Although it belongs to the combinatorial optimization, but the proposed method belongs to the decision making field in mathematics. In order to, initially efficiency values for every item is calculated then items are ranked by using Multiple Criteria Decision Making (MCDA).  Finally, ite...

The size and length effects of an inclusion on multi-pass copper shaped-wire drawing were investigated. For this purpose, an experimental investigation on optimal die half-angle was conducted. Based on experimental data of optimal die half-angle, wire and inclusion deformations, drawing and hydrostatic stress of copper shaped-wires that contain an inclusion were calculated by two-dimensional fi...

Multi-dimensional Fuzzy differential equations driven by multi-dimensional Liu process, have been intensively applied in many fields. However, we can not obtain the analytic solution of every multi-dimensional fuzzy differential equation. Then, it is necessary for us to discuss the numerical results in most situations. This paper focuses on the numerical method of multi-dimensional fuzzy differ...

A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...