Abstract
An approach based on relative optimal membership degree is proposed to deal with multiple attribute decision-making (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.
Highlights
Multiple attribute decision making (MADM) has been extensively applied to various areas such as society, economics, management, military and engineering technology
The attribute weights are determined and the alternatives are ranked by relative optimal membership degree
The attribute weight model is developed by relative optimal membership degree between alternatives and ideal solutions, and the alternatives are ranked by relative optimal membership degree
Summary
Multiple attribute decision making (MADM) has been extensively applied to various areas such as society, economics, management, military and engineering technology. 27) proposed the method of dynamic hybrid multiple attribute decision making under risk, based on the unknown weight information and the attribute values which integrates with the precision number, interval number and linguistic fuzzy number. 27) proposed a rank approach based on projection model to deal with multiple attribute decision-making problems under risk and with attribute value as continuous random variable on bounded intervals. 28) proposed a grey correlation rank method to solve the problems of multiple attribute continuous decisionmaking under risk with weight unknown and attribute value as continuous random variable on bounded intervals. The research above is not studied the MADMR problems with weight information unknown and attribute value as linguistic variable With respect to these decision making problems, firstly, we transformed the risk linguistic decision matrix into certain linguistic decision matrix by expectation value.
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