Improvement of full consistency multiple objective optimization based on concept of stratification theory and PageRank and linguistic polytopic hesitant fuzzy sets

Innovative, Resilient, and Green Supplier Selection (IRGSS) is an emerging need often viewed as a complex multi-criteria decision-making problem. However, overly stringent restrictions on the assessed values, such as q-rung ortho-pair hesitant fuzzy uncertain linguistic sets, and dependent uncertainty events affecting criterion weights threaten the decision's reliability. Thus, LPHFSSPFUCOM-MULTIMOORA is proposed to address these challenges. First, the paper proposes novel Linguistic Polytopic Hesitant Fuzzy sets (LPHFSs), which assume the sum of the qth power of the three types of memberships is not greater than 1 and relax the constraints on the assessed values. Second, the Full Consistency Method (FUCOM) is improved to find weights by integrating the Concept of Stratification Theory (CST) and PageRank, named SPFUCOM. CST depicts the occurrence process of uncertain events and PageRank finds their occurrence probabilities considering dependency. Third, the multiplicative Multi-objective Optimization by Ratio Analysis (MULTIMOORA) is novelly applied with SPFUCOM and LPHFSs to rank suppliers. Finally, a case from an electric vehicle manufacturer is studied to illustrate the applicability of the proposed method. Through sensitivity and comparative analyses, the rationality and advantages of the proposed method are verified. This study can provide insights for managers to solve the IRGSS problem.