Fuzzy Multiobjective Evaluation of Investments with Applications

The methods for Multiobjective Decision Making in the fuzzy setting in context of Investment Evaluation Problem are analyzed. The problems typical for Multiobjective Decision Making are indicated and new solutions of them are proposed as well. The problem of appropriate common scale for representation of objective and subjective criteria is solved using the simple subsethood measure based on alpha-cut representation of fuzzy values. To elaborate an appropriate method for aggregation of aggregating modes, we use the synthesis of the tools of Type 2 and Level 2 Fuzzy Sets. As the result the final assessments of compared alternatives are presented in form of fuzzy valued membership function defined on the support composed of considered alternatives. To compare obtained fuzzy assessments we use the probabilistic approach to fuzzy values comparison. In is shown that Investment Evaluation Problem is frequently a hierarchical one and a new method for solving such problems, different from commonly used fuzzy AHP method, is proposed. To make the presentation more transparent, it is illustrated throughout the chapter with use of two examples. The first of them is well known Tool Steel Material Selection problem which can be considered as the typical investment problem and relevant test charged by all difficulties concerned with the problems of Multiobjective Decision Making. The next example is a simplified investment project evaluation problem we have used to show that even when project's estimation is based on the budgeting, i.e., only financial parameters are taking into account, we are dealing with multiple-criteria task in the fuzzy setting.