Relative Membership Degree Method for Fuzzy Multi-attribute Decision-making with Preference Information on Alternatives

Abstract

The fuzzy multi-attribute decision-making (FMADM) problem that the attribute weights are interval numbers and the decision maker (DM) has avail preference information on alternatives is investigated. Firstly, a quadratic programming model based on the minimum sum of deviation squares between the subjective and objective decision-making preference information on alternatives is established, the attribute weights are obtained by solving the model and thus the overall values of every alternative are gained by using the additive weighting method. Secondly, The fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS) of alternatives are introduced. Based on fuzzy sets theory, the relative membership degree of every alternative is obtained by means of the distance to which an alternative corresponds to the FPIS and FNIS, the alternatives are ranked by using the relative membership. The method not only avoids comparing for fuzzy numbers, but also has the advantages of simple operation and easy calculation. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.