模糊排序的次序逆轉機率之衡量

Fuzzy Ranking: The Measurement of Rank Reversal Probabilities

本文主要貢獻在於提出模糊排序的次序逆轉機率（Rak Reversal Probabilities）衡量方法，解決評估結果排序穩定度（Ranking Stability）的衡量問題。針對三角模糊數（Trangular Fuzzy Numbers，TFN嘗試利用g-cut排序法推導出次序逆轉機率的衡量公式，並建立次序穩定矩陣（Rank Stable Matrix），用以衡量評估排序結果的穩定程度。本研究發現三角模糊數的成對比較有27種可能的排列組合，其中僅有10種組合會發生次序逆轉現象，並依其特性將之區分為左海逆轉型（left-side rank reversal type）、右邊逆轉型（right-side rank reversal type）及雙邊逆轉型（both-side rank reversal type）三種類型，且其次序逆轉機率衡量公式各異。最後，本研究再以實例分析，以應證本方法確具一般性及可應用性。

The contribution of this study is presenting the measurement of the rank reversal possibilities on the fuzzy ranking, and solving the results of assessment on the measurement of ranking stability. Based on the triangular fuzzy number, we use the a-cut to derive the measurement formula of rank reversal probabilities, and besides, build up the rank stable matrix, for measuring the stability of rank results. This research finds that there are 27 possibilities for the comparatives on the pairs of triangular fuzzy numbers; only 10 pairs among them will form the rank reversal situation. This research classifies all pairs into three different types as left side rank reversal type, right-side rank reversal type and both-side rank reversal type by the characteristics, and that the formula of measure of rank reversal possibilities also varies. Finally, which also bring the case study to verify the generalization and applicability of this method of measurement.