Linear programming and quadratic programming approach for graduation in fuzzy environment

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Sharma, Vivek Narain
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Decision making under uncertainty has become a key issue in the present alternative way of thinking. There is an emerging interest in the use of new techniques to draw definite conclusions from imprecise or vague information in order to take competitive advantage. A critical challenge in decision-making process is not only to find a suitable method to measure and quantify the uncertainty involved in the problem under consideration but also its successful applications. In the present thesis, we consider a graduation problem with imprecise observed values data and imprecise combination of fit and smoothness. The problem is first formulated, solved and analyzed as a fuzzy linear program. Next, a finite iteration technique is developed to solve a fuzzy quadratic programming problem. Significance of this model can be hopefully seen in the light of usage of quadratic program in the field of Finance, Economics, Structural Engineering and Actuarial Sci nces under uncertainty. Furthermore, the graduation problem is revisited using fuzzy quadratic programming model and solutions are obtained both under crisp and fuzzy environment. The results so obtained are shown to be better than the results obtained by using fuzzy linear programming, and the results obtained by Schuette using crisp linear programming. The methods introduced in the present thesis, offer an opportunity to view a graduation problem from a different prospective.