A heterogeneous picture fuzzy SWARA-MARCOS evaluation framework based on a novel cross-entropy measure

Abstract

Multi-criteria decision-making (MCDM) entails a heterogeneous decision-making problem, which poses challenges for decision-makers (DMs) in generating an optimal solution. To address this, we have proposed a heterogeneous evaluation framework. First, a novel picture fuzzy cross-entropy measure was defined with the simultaneous consideration of uncertainty and hesitancy of picture fuzzy information, overcoming the shortcomings of the existing cross-entropy measure in relation to its validity and properties. Next, an optimisation-model for determining the objective weights of criteria was constructed based on the proposed closeness measurement and the step-wise weight assessment ratio analysis (SWARA) method. This model was constituted from both objective and subjective perspectives under the circumstance of completely unknown criterion information. Additionally, the conventional Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method was extended to the picture fuzzy environment, and a normalisation method was developed to transform heterogeneous judgments, including linguistic terms, interval numbers, and picture fuzzy numbers, into a unified representation form. A heterogeneous picture fuzzy SWARA-MARCOS evaluation framework was then established and used to solve a military equipment supplier selection problem. The results demonstrated the validity and feasibility of the proposed evaluation framework, while sensitivity, comparative, and complexity analyses demonstrated the robustness and superiority of it.

KEYWORDS:

• Multi-criteria decision-making
• Cross-entropy
• Picture fuzzy sets
• MARCOS
• SWARA

Acknowledgement

The authors would like to thank the anonymous reviewers and Editors for their helpful suggestions that improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

This paper contains no data.

Additional information

Funding

This work was supported by Zhejiang Provincial Natural Science Foundation of China [grant number Y24G010019], the National Natural Science Foundation of China [grant numbers 72171208 and 71771195], and Open Research Projects of Zhejiang Lab [grant number 2021KG0AB04].