Kullback-Leibler Distance Based Generalized Grey Target Decision Method With Index and Weight Both Containing Mixed Attribute Values

Abstract

This paper proposes a generalized grey target decision method (GGTDM) with index and weight both containing mixed attribute values based on Kullback-Leibler (K-L) distance. The proposed approach builds the weight function converting the mixed attribute-based weights into the certain numberbased weights and takes the comprehensive weighted K-L distance as the decision-making basis (DMB). The proposed approach conducts its task in the following steps. First, all indices of alternatives are converted into binary connection numbers. Second, the two-tuple (determinacy, uncertainty) numbers originated from index binary connection numbers are obtained. Third, the two-tuple (determinacy, uncertainty) numbers of target center are calculated. Following that the certain number-based weights are obtained by the weight function. Then the comprehensive weighted K-L distance of each alternative and its target center is calculated. And the final decision making is based on the value of comprehensive weighted K-L distance with which the smaller the better. A case study illustrates the proposed approach with its effectiveness of converting the uncertain weights into the certain weights and the accurate results comparing with other decision-making methods.

Confidence relative off-targets distance-based multi-dimensional transparency evaluation of distribution station area

“…The gray target model can comprehensively integrate the multi-layer decision information to provide the low-complexity and accurate evaluation of numerous distribution station areas in complex decision-making (Zhengxin et al, 2009;Ma et al, 2020;Sun and Fang, 2021). It constructs a standard ideal vector by searching for the optimal value in the evaluation index vector.…”

A novel generalized grey target decision method with index and weight both containing mixed types of data

“…The decision-making by the comprehensive-weighted proximity (CWP) converts uncertain weights into certain weights by the proximity based method (Ma, 2018b) or the module based method (Ma, 2018c). While different weight functions can also be constructed to obtain the certain weights with comprehensive-weighted Gini-Simpson index (CWGSI) or comprehensive-weighted Kullback-Leibler distance (CWKLD) as the DMB (Ma, 2019c, e;Ma et al, 2020). The previous research studies indeed solve the problem of transforming uncertain weights into certain weights.…”