Portfolio selection can be regarded as a type of multi-objective decision problem. However, traditional solution methods rarely discussed the decision maker’s nonsatisfaction and hesitation degrees with regard to multiple objectives and they require many extra binary variables, which lead to tedious computational burden. Based on the above, the aim of this paper is to develop a new and unified intuitionistic fuzzy multi-objective linear programming (IFMOLP) model for such portfolio selection problems. The nonmembership functions are constructed by the pessimistic, optimistic, and mixed approaches so as to perfect the traditional intuitionistic fizzy (IF) inequalities and IF theory. The decision maker’s hesitation degrees with regard to multiple objectives are represented by using IF inequalities, and the new IFMOLP model based on IF inequalities is proposed. The IFMOLP problems are solved by the S-shaped membership functions without extra binary variables required by the piecewise-linear method. Finally, the portfolio selection model under IF environments based on IFMOLP is established, and a real example is analyzed to demonstrate its validity and superiority. The developed unified IFMOLP model and method can not only effectively solve multi-objective decision problems with nonsatisfaction and hesitation degrees but also remarkably reduce the complexity of the nondeterministic polynomial-hard problems.
Symbolic Dynamic Programming for Continuous State MDPs with Linear Program Transitions
