A novel multiple attribute material selection approach with uncertain membership linguistic information

• The definition of uncertain membership linguistic variable (UMLV) is proposed.
• The operational laws, score function and comparison rules of the UMLV are defined.
• Four uncertain membership linguistic aggregation operators are proposed.
• A novel decision making approach for material selection is presented.

In engineering design, the decision to select an optimal material has become a challenging task for the designers, and the evaluation of alternative materials may be based on some multiple attribute decision making (MADM) methods. However, the current methods for material selection may induce the information losing and cannot represent the real preference of decision maker precisely. Therefore, in this paper, inspired by the idea of the intuitionistic linguistic variables, we define a new fuzzy variable called uncertain membership linguistic variable (UMLV) which composes two linguistic variables and membership degrees of elements to the linguistic variables. Meanwhile, the operational laws, score function, accuracy function and comparison rules of the UMLV are defined. Then, some aggregation operators are developed for aggregating the uncertain membership linguistic information such as the uncertain membership linguistic weighted average (UMLWA) operator, the uncertain membership linguistic weighted geometric (UMLWG) operator, the uncertain membership linguistic ordered weighted average (UMLOWA) operator and the uncertain membership linguistic ordered weighted geometric (UMLOWG) operator, and some desirable properties of these operators are discussed. Based on the proposed operators, an approach is proposed for material selection problems under uncertain membership linguistic environment. Finally, two numerical examples for material selection are given to illustrate the application of the proposed approach.