A linguistic Z-number-based sorting method for three-way multi-criterion decision-making in ecological function zoning

Traditional multi-criterion decision-making methods can help decision-makers decide whether to accept or reject an alternative, but they cannot ensure these results fully meet decision-makers' requirements. Three-way decision methods overcome this limitation by dividing alternatives into three regions. However, traditional three-way decision methods rarely considered the reliability of evaluation information and individual regrets under some criteria. Moreover, most weighting methods in three-way decisions ignored the influence of abnormal values. To fill the above gaps, this paper develops a linguistic Z-number-based sorting method combining the three-way decision with the gain and lost dominance score (GLDS) method that reflects individual regrets under some criteria. Firstly, to avoid individual regrets, we introduce the linguistic Z-number-based GLDS sorting (LZ-GLDS-Sort) method, which obtains two states of alternatives that will be used in the three-way decision. Linguistic Z-numbers can express linguistic evaluation and credibility. Two parameters are introduced in the LZ-GLDS-Sorting method to reflect the relative importance of evaluation information and credibility. Then, a three-way decision method is introduced to divide alternatives into three regions, in which the variation-coefficient weighting method is introduced to avoid the effect of abnormal values. Finally, the ecological function zoning as an example is provided to validate the applicability of this model.