Abstract
The goal of an investor is to maximize the required return in an investment by minimizing its risk. With this in mind, a set of securities are chosen according to the experience and knowledge of the investor, which subjective evaluations. Selecting these securities is defined as the portfolio selection problem and it can be classified as convex programming problems. These problems are of utmost importance in a variety of relevant practical fields. In addition, since ambiguity and vagueness are natural and ever-present in real-life situations requiring solutions, it makes perfect sense to attempt to address them using fuzzy convex programming technique. This work presents a fuzzy set based method that solves a class of convex programming problems with vagueness costs in the objective functions and/or order relation in the set of constraints. This method transforms a convex programming problem under fuzzy environment into a parametric convex multi-objective programming problem. The obtained efficient solutions to the transformed problem by satisfying an aspiration level defined by a decision maker. This proposed method is applied in a portfolio selection numerical example by using Bm&fBovespa data of some Brazilian securities.
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