Proceedings

A SELECTION FUZZY MODEL INVOLVING ASSETS
AND PROJECTS
Adrian Victor BĂDESCU 1 ,
Radu Nicolae CRISTEA & Dana-Maria BOLDEANU
Bucharest Academy of Economic Studies, Romania
ABSTRACT
The last decade has brought on an increase and dynamic diversification of the investments,
most of them focused on traditional securities, with an alert orientation towards alternative
means of investment, like private shares, private debt and real estate investments. By
diversifying various types of assets, the overall risk of the portfolio can be reduced, while the
medium and long term potential benefits may increase. If we consider the transaction costs as
being proportional, we shall use the expected net return and standard deviation as objective
functions. We propose a bi-objective programming model for solving the mixed assets
portfolio selection problem within developed research, by resorting to a series of remarkable
results of the fuzzy theory.
KEYWORDS: Fuzzy model, securities portfolio, expected net return, investment decision
INTRODUCTION
The fuzzy approaches are used frequently for describing and treating uncertain and
imprecise elements from a decision problem. Similarly, fuzzy theory facilitates the
uncertainty analysis of systems in which it is caused by elements of unclear origin,
rather than its random nature, and may be applied in order to mathematically quantify
imprecise observation values, linguistically data or verbal decisions. The group
membership function, a central model of any fuzzy model, is thought as being the
strongest landmark of fuzzy set theory (Munda et al., 1992). In practical applications
concerning set theory, the construction of membership functions is usually
accomplished thru iterations (McNeil and Freiberger, 1994), (Bardossy and
Duckstein, 1995), (Klir and Yuan, 1996).
Together with fuzzy theory and probability analysis, the existing approach methods
for uncertainty and imprecision also include another version, based on using interval
mathematics. In many cases, using intervals for expressing the variation of certain
coefficients may serve the purpose of research to a greater extent. (Alefeld and Mayer,
1996)
It has been frequently suggested that the origin of modern mathematical models in
finances resides in Louis Bachelier’s dissertation over speculation theory. However
true that may be, there is no doubt that Markowitz’s research regarding portfolio
1 Correspondence address: Adrian Victor BĂDESCU, Bucharest Academy of Economic Studies,
Romania; email: badescuadi@gmail.com
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