In this study, the authors consider a multiple objective decision-making problem whose objectives involve imprecise/fuzzy coefficients. Triangular possibility distributions are used to quantify the imprecise nature. By using the concept of the most possible α-efficient solution, the authors propose a computationally efficient auxiliary model to resolve imprecise objectives. The present model effectively uses all the information provided by the possibility distributions. Furthermore, the authors develop an interactive decision support system ISGP-II to solve a (crisp) multiple objective decision-making problem. ISGP-II provides a process of psychological convergence for the decision maker, whereby (s)he learns to recognize good solutions and their importance in the system, and to design an optimal system, instead of optimizing a given system. For illustrating the proposed approach, the authors solve a practical bank balance sheet problem with three objectives: maximizing after-tax profit, minimizing capital-adequacy ratio and minimizing risk-asset ratio, where after-tax profit (or cost of fund), relative need for capital, and relative risk of assets are imprecise under dynamic economic conditions and decision makers’ subjective judgments.
