Neighborhood-related q-rung orthopair fuzzy covering-based rough set models and their applications for multi-attribute decision making

In the current intelligent era, with the increasing complexity and diversification of productive practices, it is usually necessary to get a balanced consideration of many aspects of the decision-making problem. One of the most important and popular methods to solve decision problems is multi-attribute decision making (MADM). Traditional MADM problems in q-rung orthopair fuzzy (q-ROF) environment aggregate evaluation information by means of aggregation operators. However, aggregation operators are improper to effectively solve some complicated problems. To settle this problem, we come up with a new method based on neighborhood-related q-ROF covering-based rough set (NRq-ROFCRS) models for MADM problem in this paper. To define these models, several q-ROF logical operators are firstly defined. Next the concepts of q-ROF neighborhood systems of an object, q-ROF minimal and maximal description of an object and q-ROF covering are defined. On this basis, four t-norm-based q-ROF neighborhood operators (Tq-ROFNOs) and four overlap function-based q-ROF neighborhood operators (Oq-ROFNOs) are proposed. For a finite q-ROF covering, combining four Tq-ROFNOs and six q-ROF coverings results in 24 Tq-ROFNOs and only sixteen groups of Tq-ROFNOs are obtained. We also combine four Oq-ROFNOs and six q-ROF coverings and prove that only seventeen groups of Oq-ROFNOs are obtained. Then partial order relations among 16 groups of Tq-ROFNOs and 17 groups of Oq-ROFNOs are discussed, respectively. Moreover, four types of NRq-ROFCRS models are defined based on q-ROF neighborhood operators and the groups and partial order relations of neighborhood-related q-ROF approximate operators are discussed. Finally, a novel method for MADM problems by integrating NRq-ROFCRS models with TOPSIS method is put forward and the effectiveness and the reasonableness of our method are verified by experiments.