最小化資訊損失的模糊權重正規化方法

Fuzzy Weights Normalization Methods with Minimal Information Loss

本文首先指出良好的模糊權重正規化方法，除能消除權重衡量尺度不一的情況外，還應盡可能保留原始權重所含的資訊，以免喪失以模糊數進行分析的意義。而為消除衡量尺度不一的情況，應先進行權重的約化，再進行正規化。接著，以Wang and Elhag (2006)的正規化區間權重定義為基礎，採用互相對應的權重係數隸屬函數所夾區域面積衡量正規化過程之資訊損失，提出三角模糊權重正規化的相關方法。新方法所得問題求解模式為線性規劃或具線性限制式之凸二次規劃。

In this paper, at first, it is pointed out that a good method for fuzzy weights normalization should not only be able to eliminate the difference in the measurement scales, but also preserve the information contained in the original weights as much as possible so as not to lose the meaning of analyzing with fuzzy numbers. To eliminate the difference in the measurement scales, the weights should be scaled before normalization. Then, based on Wang and Elhag’s (2006) definition of normalized weights, methods for normalizing triangular fuzzy weights are proposed, when the information loss in normalization is measured by the area between the corresponding membership functions of the weights. The mathematical models for the new methods are linear program or convex quadratic program with linear constraints.