Decision Analysis Approach Based on 2-Tuple Linguistic \(m\)-Polar Fuzzy Hamacher Aggregation Operators

Abstract

This research article is devoted to presenting the concept of 2-tuple linguistic $m$ -polar fuzzy sets (2 TL $m$ FSs) and introducing some fundamental operations on them. With 2 TL $m$ FSs, we shall be able to capture imprecise information with high generality. With the appropriate operators, we shall be able to apply 2 TL $m$ FSs in decision-making efficiently. The aggregation operators that we propose are the 2 TL $m$ F Hamacher weighted average (2 TL $m$ FHWA) operator, 2 TL $m$ F Hamacher ordered weighted average (2 TL $m$ FHOWA) operator, 2 TL $m$ Hamacher hybrid average (2 TL $m$ FHHA) operator, 2 TL $m$ F Hamacher weighted geometric (2 TL $m$ HWG) operator, 2 TL $m$ Hamacher ordered weighted geometric (2 TL $m$ HOWG) operator, and 2 TL $m$ F Hamacher hybrid geometric (2 TL $m$ FHHG) operator. We investigate their properties, including the standard cases of monotonicity, boundedness, and idempotency. Then we develop an algorithm to solve multicriteria decision-making problems formulated with 2 TL $m$ F information. The 2 TL $m$ F data in multiattribute decision-making are merged with the help of aggregation operators, and we consider the particular instances of the 2 TL $m$ FHA and 2 TL $m$ FHG operators. The influence of the parameters on the outputs is explored with a numerical simulation. Moreover, a comparative study with existing methods was performed in order to show the applicability of the proposed model and motivate the discussion about its virtues and advantages. The results confirm that the model here developed is reliable for decision-making purposes.