Generalised grey target decision method based on the Gini–Simpson index involving mixed attributes and uncertain numbers. (3rd September 2019) - Ma, Jinshan
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.