q-Rung orthopair fuzzy frank power point aggregation operators with new multi-parametric distance measures

The recently proposed q-rung orthopair fuzzy set (q-ROFS) whose main feature is that the qth power of membership degree (MD) and the qth power of non-membership degree (NMD) is equal to or less than 1, is a powerful tool to describe uncertainty. The major contribution of this paper lies to investigate power point average (PPA) aggregation operators with q-rung orthopair fuzzy information based on Frank t-conorm and t-norm. Since the existing power average (PA) operators all rely on the traditional distance measures to measure support degree between the input values, it cannot reflect decision makers’ attitude. In response, this paper introduces firstly a series of distance measures for q-rung orthopair fuzzy numbers (q-ROFNs) based on point operators, from which the corresponding support measures can be obtained. Secondly, based on the proposed point distance measures, new Frank power point average aggregation operators are proposed to aggregate q-rung orthopair fuzzy information. Finally, a novel multiple attribute decision making (MADM) technique is presented based on the proposed Frank power point average aggregation operators. The developed MADM method not only can get more objective information, but also avoid the influence of unduly high or low attribute values on the decision result, providing a new way for decision makers (DMs) under q-rung orthopair fuzzy environment.