Improved q-rung orthopair fuzzy line integral aggregation operators and their applications for multiple attribute decision making

The q-rung orthopair fuzzy line integral (q-ROFLI) operator is a potent mathematical tool to aggregate non-standard fuzzy information in the process of Decision Making. To overcome some disadvantages of the q-rung orthopair fuzzy integral curves (q-ROFICs) which was proposed by Gao et al. (IEEE Trans Cybern, https://doi.org/10.1109/TCYB.2019.290865, 2019), in this paper, we present a novel definition of q-ROFICs. Based on this notion, we give a completed definition for q-ROFLI. Furthermore, we give a Newton–Leibniz formula through the q-rung orthopair fuzzy function with the variable upper limit (VUL-q-ROFF), and investigate the intermediate value theorem which can be utilized to solve generalized mean value theorem. Moreover, we propose the q-rung orthopair fuzzy line integral aggregation (q-ROFLIA) operator, and an improved q-ROFLIA with reliability (R-q-ROFLIA) operator. As their applications, we give several examples to show the process for aggregating q-rung orthopair fuzzy data by these operators. At last, the validity and flexibility of the above operators are verified through a practical example, especially the superiority of R-q-ROFLIA can avoid losing important extreme data, and make the results more suitable for the practical Decision Making.