Fuzzy Linear Programming Approach to Multi-Attribute Decision-Making with Linguistic Variables and Incomplete Information

The aim of this paper is to develop a new fuzzy linear programming technique for solving multi-attribute decision-making (MADM) problems with incomplete weight preference information under fuzzy environments. In this methodology, linguistic variables are used to capture fuzziness in decision information and decision-making processes by means of a fuzzy decision matrix. Consistency and inconsistency indices are defined on the basis of preference relations between alternatives given by the decision maker under uncertain environments. Each alternative is assessed on the basis of its distance to a fuzzy ideal solution (FIS) which is unknown a priori. Then the FIS and the weights of attributes are estimated using a new linear programming model based upon the consistency and inconsistency indices defined. The fuzzy distance of each alternative to the FIS can be calculated to determine the ranking order of all alternatives. An extended illustrative example on the selection of air-fighters is presented to demonstrate the implementation process of this methodology. The methodology proposed in this paper can deal with MADM problems under not only fuzzy environments but also crisp environments. Also it has been proven that different weight information structures may result in different final decision results.