Probabilistic linguistic hesitant fuzzy multi-attribute decision making for rural revitalization project selection of China

Rural revitalization strategy has pointed out the right direction for solving Chinese "three rural" problems. Selecting the most suitable rural revitalization project can be regarded as a multi-attribute decision making (MADM) problem. This paper utilizes the probabilistic linguistic (PL) hesitant fuzzy sets (PLHFSs) to characterize the uncertain information of evaluating rural revitalization projects. PLHFS introduces the characteristics of linguistic hesitant fuzzy set (LHFS) into probabilistic linguistic term set (PLTS), which can represent the membership degrees of linguistic terms (LTs) and the associated probabilities to the set, simultaneously. The normalized and ordered PLHFS is proposed. Some new operation laws for PLHFSs are defined by using Archimedean T-norm and T-conorm (ATT) functions. By employing the Maclaurin symmetric mean (MSM) operator and power average (PA) operator, this paper develops a probabilistic linguistic hesitant fuzzy Archimedean power Maclaurin symmetric mean (PLHFAPMSM) operator and a probabilistic linguistic hesitant fuzzy Archimedean power weighted Maclaurin symmetric mean (PLHFAPWMSM) operator. Some desirable properties of the PLHFAPMSM and PLHFAPWMSM operators are discussed deeply. For MADM with PLHFSs, the individual attribute weight vector for each alternative is derived by data envelopment analysis (DEA). Further, the comprehensive attribute weight vector is determined by a linear goal programming model. Thereby, using the PLHFAPWMSM operator, a new method for MADM with PLHFSs is proposed. Finally, a practical example of rural revitalization project selection is analyzed to illustrate the effectiveness and feasibility of the proposed method.