Quality Evaluation of Urban Low-carbon Development based on Fermatean Fuzzy Regret Theory Model

In response to the complexity and fuzziness of the evaluation environment for urban low-carbon development quality, and by integrating the regret avoidance psychology of experts in the evaluation process, this paper proposes a Fermatean fuzzy regret-theory multi-index decision-making model incorporating bidirectional projection. Firstly, considering the defects of misjudgment of similarity and unlimited range of projection values in the projection, a novel Fermatean fuzzy bidirectional projection method is proposed. Secondly, since the conflictiveness of indexes should only be related to the degree of association of the indexes, independent of the positive and negative signs, a CRITIC (CRiteria Importance Through Intercriteria Correlation) weight assignment method harmonizing with Fermatean fuzzy bidirectional projection is proposed to eliminate the influence of the positive and negative signs of similarity on the weighting results. Finally, the viability of the presented model is verified by urban low-carbon development quality cases, and a comparison analysis is also conducted to show the superiority of the presented method.