Fuzzy Investment Decision Making

Recent literature on fuzzy numbers is rich of several approaches to approximate operations between fuzzy numbers. The desirable feature is to preserve the real shape of the fuzzy numbers resulting from the operations, without loosing in simplicity and applicability and in goodness of the approximations. In some recent papers we introduce a representation of the fuzzy numbers, based on the use of parametrized monotonic functions to model the alfa-cuts (or the membership functions) of the fuzzy numbers. We call it the LU representation, as it models directly the Lower and the Upper branches of the fuzzy numbers and it uses the parametrization to perform the arithmetic operations and more generally the fuzzy calculus. It is well known that economic and financial applications are strongly dependent on the precision of the input data and that in many cases the quality of the information becomes critical to the validity of the results. A suitable methodology to approach this problems can be based of the fuzzy calculus as it allows the description of uncertain or imprecise interest rates, volatility or prices in combination with the stochastic (risky) characters of the real world. We develop here a fuzzy investment choice process taking advantage of the good qualities of the LU parametric representation.