Ranking intuitionistic fuzzy numbers by relative preference relation

Ranking fuzzy numbers(FNs) was a critical issue in fuzzy computing field. Generally, triangular FNs, trapezoidal FNs, and even interval-valued FNs(IVFNs) were often expressed in ranking. However, ranking intuitionistic FNs(IFNs) were less mentioned due to the complicated components in membership functions. Herein, we will develop fuzzy binary relation that is an extended fuzzy preference relation(EFPR) to express the preference degree of two IFNs, and then the relation is improved to be a relative preference relation(RPR) used to rank a set of IFNs. Since EFPR on IFNs is a total ordering relation, RPR will be also a total ordering relation. Based on belonging and non-belonging components of membership functions in IFNs, using EFPR being also fuzzy preference relation(FPR) is suitable to compare FNs on pairwise, but time complexity on fuzzy operation of comparison computing is complicated. Hence, RPR is developed to avoid comparing on pairwise. Through yielding RPR values for a set of IFNs, IFNs are effectively and efficiently ranked to utilize related decision-making problems.