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The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.

Abstract. The traditional single objective mean variance optimization model fails to satisfy the investors with multiple investment objectives. So multi-objective portfolio optimization model is considered in this paper. Since this will help investors to achieve highest expected return among the different financial products of the capital market and to fulfill the expected return objectives simultaneously. Fuzzy Non-Linear Programming (FNLP) and Fuzzy Additive Goal Programming (FAGP) techniques are used to solve this multi-objective model. Since it will fulfill the wanted aspiration level of the investors concerning return and risk objectives. And finally solution procedure is illustrated by numerical examples.

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