Abstract: In the context of multi-criteria decision making every individual will act as a decision maker. The decision maker is involved in assigning preferences or weights to the alternatives. Goal programming will also come under the hub of MCDA, where the DM will assign the subjective weights to each goal. By giving so, the weighted sum of deviations will be minimized to some extent but one cannot ascertain whether the weights are consistent or not. In this paper the authors have proposed a simpler way of testing the consistency of weights and demonstrated an easier way to achieve the minimized weighted sum of deviations through AHP. This attempt showed better results and allows the DM to think well before giving the weights to each goal.

Abstract: This paper presents a formulation of a Lacunary approximation for the class ninth of spline function at uniform mesh points and the function values at the end points of the interval. Error bounds for the function and its derivatives are derived. Finally, efficiency estimation and convergence orders are also illustrate errors derivations.