Symmetric Kullback–Leibler distance based generalized grey target decision method for mixed attributes

Abstract

Purpose

The reported Kullback–Leibler (K–L) distance-based generalized grey target decision method (GGTDM) for mixed attributes is an asymmetric decision-making basis (DMB) that does not have the symmetric characteristic of distance in common sense, which may affect the decision-making result. To overcome the deficiency of the asymmetric K–L distance, the symmetric K–L distance is investigated to act as the DMB of GGTDM for mixed attributes.

Design/methodology/approach

The decision-making steps of the proposed approach are as follows: First, all mixed attribute values are transformed into binary connection numbers, and the target centre indices of all attributes are determined. Second, all the binary connection numbers (including the target centre indices) are divided into deterministic and uncertain terms and converted into two-tuple (determinacy and uncertainty) numbers. Third, the comprehensive weighted symmetric K–L distance can be computed, as can the alternative index of normalized two-tuple (deterministic degree and uncertainty degree) number and that of the target centre. Finally, the decision-making is made by the comprehensive weighted symmetric K–L distance according to the rule that the smaller the value, the better the alternative.

Findings

The case study verifies the proposed approach with its sufficient theoretical basis for decision-making and reflects the preferences of decision-makers to address the uncertainty of an uncertain number.

Originality/value

This work compares the single-direction-based K–L distance to the symmetric one and uses the symmetric K–L distance as the DMB of GGTDM. At the same time, different coefficients are assigned to an uncertain number’s deterministic term and uncertain term in the calculation process, as this reflects the preference of the decision-maker.

Citation

Ma, J. and Zhu, H. (2024), "Symmetric Kullback–Leibler distance based generalized grey target decision method for mixed attributes", Grey Systems: Theory and Application, Vol. 14 No. 4, pp. 754-769. https://doi.org/10.1108/GS-01-2024-0001