Novel multi-attribute decision-making method based on Z-number grey relational degree

In practical multi-attribute decision-making, due to the complexity of decision-making environment and the fuzziness of human thinking, the fuzzy index values given by experts are not necessarily completely reliable, that is, it is more reasonable to measure the reliability degree of fuzzy index values. The Z-number proposed by Zadeh can effectively meet the requirement of describing this kind of decision information. This paper considers a kind of multi-attribute decision-making problems under the information environment of Z-numbers and proposes a new multi-attribute decision-making method based on Z-number grey relational degree (ZNGRD-MADM). Specifically, in ZNGRD-MADM, some comparative relations of Z-numbers and a new definition of generalized distance of Z-numbers are proposed firstly. Then, a new concept of Z-number grey relational degree (ZNGRD) is proposed based on the generalized distance of Z-numbers and its properties are proved. Thirdly, a new alternative ranking method is proposed based on the Z-numbers comparative relations and ZNGRD. Finally, the proposed ZNGRD-MADM method is applied to the problem of Web service selection, and its feasibility and effectiveness are verified through sensitivity analysis and comparative analysis.