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Most of data in a multi attribute decision making (MADM) problem are unstable and changeable, and thus sensitivity analysis can effectively contribute to making proper decisions. Here, we offer a new method for sensitivity analysis of multi-attribute decision making problems so that by changing one element of decision making matrix, we can determine changes in the results of a decision making problem. An analysis is made for simple additive weighting method (SAW) technique, a mostly used multi-attribute decision making techniques, and the corresponding formulas are obtained.

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In the traditional cost-efficiency model, the information about each decision unit includes inputs, outputs, and the input prices are fixed and specific. In practice, the price of the inputs often fluctuates at different times, and these prices for the decision-making unit are time-dependent. By the traditional method, the efficiency of decision units is impossible in the presence of time-dependent input prices. On the other hand, the exact method of cost-efficiency calculation is also difficult and time-consuming. In this study, a new method for calculating cost efficiency of decision making units with time-dependent prices during a period of time using numerical integral is presented. As  the information of the decision-making units varies over time, a method for calculating their cost efficiency accurately is presented. however,  the exact method is difficult or impossible to be solved  in some cases. Therefore, in this study, an approximate method for calculating the cost efficiency in the given state is presented. This is a suitable replacement for the precise method. The efficiency of decision making units at different time is measured and the units are ranked using the proposed method. Finally, a numerical example is provided to indicate the method and compare it with the precise method. This study shows that the efficiency obtained by the approximate method is very close to the efficiency obtained by the exact method, and at the same time, the calculation speed increases.
 

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       A transportation problem involving three constraints: source, destination, and conveyance, where all parameters of the problem are fuzzy is called Fully Fuzzy Solid Transportation Problem (FFSTP). In this paper, a new method is proposed to find an optimal solution of an unbalanced FFSTP which the fuzzy numbers are considered to be k-scale trapezoidal fuzzy numbers. The k-scale trapezoidal fuzzy numbers are a generalization of symmetric trapezoidal fuzzy numbers which are considered recently in the literature. In this method, using a new ranking method, we transform the unbalanced FFSTP into a crisp linear programming formulation and find a fuzzy optimal solution for it. The considered model is not necessary balanced and introduced method will solve that without convert it to a balanced model. The advantages of the proposed method are also discussed.