Geometric linguistic scale and its application in multi-attribute decision-making for green agricultural product supplier selection

Abstract

Establishing long-term cooperative relationships with reliable suppliers of green agricultural products is essential to the sustainable development of fresh supermarkets. Qualitative attributes in such a multi-attribute decision-making problem have spawned the analyses on linguistic evaluations that are close to people's cognition and expression habits. There is still a challenge to capture the mathematical implications of linguistic evaluations and link them with decision-maker's psychology. To address this issue, this paper introduces a geometric linguistic scale which is characterized by the proportional relations between progressive grades and their corresponding fuzzy implications. Aggregation methods based on the geometric linguistic scale are developed to handle decision matrices with direct linguistic evaluations, full pairwise comparisons and partial pairwise comparisons, respectively. A consistency repairing process is presented to improve the reliability of pairwise comparisons. We further investigate a real-world problem concerning green agricultural supplier selection to illustrate the proposed method. The rational range of the scale parameter and consistency index are analysed through a sensitivity analysis.