Fuzzy linear programming technique for multiattribute group decision making in fuzzy environments

The aim of this paper is to develop a linear programming technique for multidimensional analysis of preferences in multiattribute group decision making under fuzzy environments. Fuzziness is inherent in decision data and group decision making processes, and linguistic variables are well suited to assessing an alternative on qualitative attributes using fuzzy ratings. A crisp decision matrix can be converted into a fuzzy decision matrix once the decision makers' fuzzy ratings have been extracted. In this paper, we first define group consistency and inconsistency indices based on preferences to alternatives given by decision makers and construct a linear programming decision model based on the distance of each alternative to a fuzzy positive ideal solution which is unknown. Then the fuzzy positive ideal solution and the weights of attributes are estimated using the new decision model based on the group consistency and inconsistency indices. Finally, the distance of each alternative to the fuzzy positive ideal solution is calculated to determine the ranking order of all alternatives. A numerical example is examined to demonstrate the implementation process of the technique. (C) 2003 Elsevier Inc. All rights reserved.