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An approach based on relative optimal membership degree is proposed to deal with multiple attribute decisionmaking (MADM) problems under risk with weight information unknown and attribute value as linguistic variable. Firstly, the operational laws of linguistic variable are introduced, and risk linguistic decision matrix is transformed into certain linguistic decision matrix by expectation value. Then, the ideal solution and negative ideal solution with linguistic variable are defined, and the attribute weight model is developed by relative optimal membership degree between alternatives and ideal solutions. In addition, the alternatives are ranked by relative optimal membership degree. Finally, illustrative example is provided to demonstrate the steps and effectiveness of the proposed approach.

The Study on Multi-Attribute Decision-Making with Risk Based on Linguistic Variable