关键词: q-ROUL集, Acezl-Asina t-norms, WASPAS方法, Hamy均值算子, 多准则决策

Abstract: Due to the rapid development of economy and society, decision-making problems have become more and more complex. The evaluation of alternatives to different criteria contains more vague and uncertain information. Complex practical decision-making problems contain a lot of uncertain information. Decision-makers can hardly rely on accurate data to depict uncertainty. Linguistic evaluation is favored by decision-makers. q-Rung orthopair uncertain linguistic set is composed of uncertain linguistic part and q-rung orthopair fuzzy part. It is an effective and novel expression tool for uncertain and vague information. WASPAS method is a simple decision-making technique which combines the weighted sum model (WSM) with the weighted product model (WPM) and makes the alternatives rank accurately and the results stable.
   Although this method has been extended and applied in various decision-making environments, such as intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, rough sets and so on, there are still rooms for extension and improvement. Therefore, there are some issues that need to be solved: (1)The existing WASPAS methods have not been extended in the q-ROUL settings. (2)In many methods, the WSM and WPM often use basic algebraic operation rules, but rarely can flexibly adjust the decision results to the decision scenarios. (3)Most of the existing studies on the WASPAS method ignore the interrelationship between any two criteria, but do not consider the interrelationship among multiple criteria. (4)The score function or expectation function is a de-fuzzification method often used by the WASPAS method, but the decision result may be inaccurate due to the loss of some decision information.
   To solve these problems, a novel q-ROUL multi-criteria decision-making method based on the improved WASPAS is proposed in this paper. The Acezl-Asina (AA) operational laws of q-ROUL numbers are introduced based on the concepts of q-ROUL set and AA t-norm and s-norm. The q-ROUL Acezl-Asina Hamy mean (q-ROULAAHM) and q-ROUL Acezl-Asina dual Hamy mean (q-ROULAADHM) operators and their weighted forms (i.e., q-ROULAAWHM, q-ROULAAWDHM) are developed. Then, the maximum deviation model is constructed on the q-ROUL Hamming distance measure to determine the weight vector of criteria. Thirdly, the above aggregation operators and Hamming distance are employed to improve the WASPAS method, so that the decision-making process of this method is more flexible, this method can capture the interrelationship among multiple criteria and the information of decision results is complete and accurate. Finally, the effectiveness and rationality of the improved WASPAS method are verified by a numerical example.

Key words: q-ROULS, Acezl-Asina t-norms, WASPAS method, Hamy mean, multi-criteria decision-making