A Multi-Objective Investment Selection Problem Using Fuzzy and Intuitionistic Fuzzy Approach

Investment refers to allocating funds in the expectation of some benefit in the future which in financial terms is the return. In the presence of various investment alternatives, the decision maker stands confused as to which option would offer him the highest return. Thus, the problem of appropriate investment selection can be treated as a multi-objective decision-making (MODM) problem that involves optimization of return on investment, time, risk, etc. However, the time, return, and risk involved in such problems cannot be defined in precise units and are fuzzy in nature. Amidst such a scenario in addition to fuzzy set (FS) theory, intuitionistic fuzzy sets (IFSs) which provide a mathematical framework to deal with imprecise information of the real world can be of much help. It can be seen as an alternative to describe a FS-in situation when the existing data is not enough to define a usual FS. Against this backdrop, this paper is an attempt to develop an IF multi-objective linear model (MOLM) for the investment selection problem where the coefficients of the objective functions (OFs) are represented by IF linear membership (MM) and non-membership (N-MM) functions. The constraints in the problem are treated as crisp. The application of the methodology is explained with the help of a numerical example. Comparing the fuzzy and intuitionistic models it is seen that the IFO model gives optimal results in selection and order allocations to the investors. Also, a Pareto optimality test is performed to test the strength of the solution.