Abstract
A novel generalized grey target decision method for mixed attributes based on Kullback-Leibler (K-L) distance is proposed. The proposed approach involves the following steps: first, all indices are converted into index binary connection number vectors; second, the two-tuple (determinacy, uncertainty) numbers originated from index binary connection number vectors are obtained; third, the positive and negative target centers of two-tuple (determinacy, uncertainty) numbers are calculated; then the K-L distances of all alternatives to their positive and negative target centers are integrated by the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method; the final decision is based on the integrated value on a bigger the better basis. A case study exemplifies the proposed approach.
Highlights
The grey target decision method has been studied by many scholars since it was proposed by Deng [1]
The reported mixed attribute grey target decision method deals with target center distance in two ways: one is by distance including mainly Euclidean distance and other similar distances [4,5,6,7,8,9]; the other method is by vector-based distance, such as the generalized grey target decision method [10,11]
The K-L distances of all alternatives to their positive and negative target centers are integrated by using the TOPSIS method: the final decision is based on the integrated value for which the bigger is the better
Summary
The grey target decision method has been studied by many scholars since it was proposed by Deng [1]. Following the further research on decision-making, the indices of alternatives are extended from pure real values to mixed attribute values This mixed attribute based grey target decision method is proposed to make it more applicable. The tool for measuring the uncertainty of fuzzy numbers in mixed attribute based grey target decision method is needed to make decision-making more valuable in terms of its theoretical significance and practical application. Entropy is often used to measure uncertainty; it is sure to be applied to the generalized grey target decision method involving fuzzy numbers. Proposed an optimization algorithm based on cross-entropy [19] The principle of this proposed approach goes as follows: all indices of alternatives are first converted into binary connection number vectors and divided into those of deterministic terms and uncertain terms based on the previous method. The K-L distances of all alternatives to their positive and negative target centers are integrated by using the TOPSIS method: the final decision is based on the integrated value for which the bigger is the better
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