Aiming at the multi-attribute bilateral matching problem with unknown attribute weights under a linguistic intuitionistic fuzzy environment, a decision method based on TODIM considering satisfaction and fairness degrees is proposed. First, the theories of linguistic intuitionistic fuzzy sets and bilateral matching are given, and the multi-attribute bilateral matching problem under a linguistic intuitionistic fuzzy environment is described. To solve this problem, according to linguistic intuitionistic fuzzy preference matrices, the overall attribute dominances are calculated based on TODIM; considering group consensus, a new method is proposed to calculate attribute weights based on linguistic intuitionistic fuzzy induced ordered weighted averaging (LIFIOWA) operator; then, the overall dominances of bilateral subjects are obtained by aggregating the overall attribute dominances and attribute weights. Furthermore, the overall dominances are standardized to calculate the satisfaction degrees of bilateral subjects; the fairness degrees of bilateral subjects are calculated considering the loss attenuation coefficient. Based on satisfaction degree matrices, fairness degree matrices and bilateral matching matrices, multiple bilateral matching models are established and then solved to obtain the optimal bilateral matching scheme. Finally, an example shows the effectiveness, reliability and accuracy of the proposed method. The research results indicate the following main characteristics of the proposed method: (1) A new method for calculating the unknown attribute weights using LIFIOWA operator is proposed. (2) According to the TODIM idea, a calculation method for fairness degree considering the loss attenuation coefficient is proposed. (3) Considering satisfaction and fairness degrees, multiple bilateral matching models under a linguistic intuitionistic fuzzy environment are established.
Keywords: Bilateral matching model; Fairness degree; Linguistic intuitionistic fuzzy number; Multi-attribute bilateral matching; Satisfaction degree.
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