Generalised grey target decision method based on the Gini–Simpson index involving mixed attributes and uncertain numbers

Abstract

Purpose

The purpose of this paper is to investigate a novel generalised grey target decision method (GGTDM) with index and weight involving mixed attribute values.

Design/methodology/approach

The mixed attribute values are transformed into binary connection numbers and also comprised of two-tuple (determinacy, uncertainty) numbers to fulfil the decision-making task. The proposed method constructs the weight function to convert the mixed attribute-based weights into the certain number-based weights and determines the alternatives ranking by the comprehensive weighted Gini–Simpson indices (CWGSIs).

Findings

The result of decision making regarding the numerical example by the proposed approach is somewhat different from that obtained by the reported vector-based method. The reasons for this are threefold: the decision-making bases are different, the target centre indices are determined by different mechanisms and certain number-based weights are calculated in different ways.

Research limitations/implications

The proposed method ranks an alternative based on the Gini–Simpson index, as derived from the viewpoint of measuring the uncertainty (heterogeneity): however, the vector-based GGTDM makes a decision based on proximity, as is the case when measuring the similarities between index vectors.

Practical implications

The proposed approach is admissible to solving mixed attribute-based decision making especially for alternative indices and attribute weights containing both uncertain numbers.

Originality/value

The proposed method provides a new perspective on measuring the difference of alternatives to the target centre via the CWGSI: the CWGSI is obtained by relying on the pseudo-probabilities achieved by the ratios of the alternative indices to the target centre indices. It also builds a weight function converting the mixed attribute-based weights into certain number-based weights. This method provides a framework that should be tested in terms of its effective decision making using real data and an actual problem.

Citation

Ma, J. (2019), "Generalised grey target decision method based on the Gini–Simpson index involving mixed attributes and uncertain numbers", Data Technologies and Applications, Vol. 53 No. 4, pp. 484-500. https://doi.org/10.1108/DTA-02-2019-0019