Abstract
The Choquet capacity and integral is an eminent scheme to represent the interaction knowledge among multiple decision criteria and deal with the independent multiple sources preference information. In this paper, we enhance this scheme’s decision pattern learning ability by combining it with another powerful machine learning tool, the random forest of decision trees. We first use the capacity fitting method to train the Choquet capacity and integral-based decision trees and then compose them into the capacity random forest (CRF) to better learn and explain the given decision pattern. The CRF algorithms of solving the correlative multiple criteria based ranking and sorting decision problems are both constructed and discussed. Two illustrative examples are given to show the feasibilities of the proposed algorithms. It is shown that on the one hand, CRF method can provide more detailed explanation information and a more reliable collective prediction result than the main existing capacity fitting methods; on the other hand, CRF extends the applicability of the traditional random forest method into solving the multiple criteria ranking and sorting problems with a relatively small pool of decision learning data.
Highlights
IntroductionThe multiple criteria involved in most decision or evaluation problems are usually not independent, and a variety of interactions, from negative to positive, can exist among them [1,2,3]
In capacity random forest (CRF) Algorithm 1, the performance of each capacity based DTs (CDTs) about S, or of the optimal capacity μS, should deeply depend on the objective function value of the adopted capacity identification method, which is denoted as zμ
{2, 1, 0} and {0.5, 0.3, 0.1} as their targeted evaluations; the corresponding results by the capacity random forest algorithm are given in Table 8, wherein first three rows of the "Intervals" columns are the allowable values that belong to the three classes; e.g., the element of first row and third column, [0.6, 1], means if the prediction value falls in this interval, the alternative will belong to "good." these intervals are given empirically
Summary
The multiple criteria involved in most decision or evaluation problems are usually not independent, and a variety of interactions, from negative to positive, can exist among them [1,2,3]. Generally not a very lot of data, and their overall evaluations, ranking orders, or classifications as the learning set, the scheme of capacity plus Choquet integral can learn, simulate, and explain the correlative multiple criteria decision pattern, wherein the decision and explanation knowledge will be stored in the power set of decision criteria as the capacity values of all decision subsets.
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