凸和與模糊決策樹分析

Convex Sum and Fuzzy Decision Tree Analysis

本文在探討模糊決策樹合理的模式與分析方法。在模式方面，因機率值的取值範圍為實數區間 [0, 1]，是個連通的集合，故應採用連續型模糊數描述事件機率值而非離散型模糊數。除較合理外，這同時可使語意期望值的求解簡化成線性規劃問題，甚至可進一步轉成更容易求解的連續型背包問題。而在分析方法方面，為符合決策的意涵，本研究認為對所有決策結點都應該利用比序函數比較其所有分支的期望收益，以找出該結點的期望收益與最佳決策方案。

We discuss the modeling and analysis of a fuzzy decision tree. Since the parameter space of a probability value, i.e. the interval [0, 1], is connected, using continuous fuzzy numbers to represent the event probabilities in a decision tree is more reasonable than using discrete ones. Moreover, this assumption of continuity makes the computation of linguistic expectation easier, the related mathematical programming models become simple linear programs which can be transformed into fractional knapsack problems. In the analysis of fuzzy decision tree, to find the optimal decision and the expected revenue associate with a decision node, a ranking function should be used, not a set-union operation.