Extensions of Dombi Aggregation Operators for Decision Making under m -Polar Fuzzy Information
Muhammad Akram, Naveed Yaqoob, Ghous Ali, Wathek Chammam
Source abstract
An m -polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The m -polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under the m -polar fuzzy environment with the help of Dombi norm operations. In this article, we develop some averaging and geometric aggregation operators using Dombi t -norm and t -conorm to handle uncertainty in m -polar fuzzy ( m F , henceforth) information, which are m F Dombi weighted averaging ( m FDWA ) operator, m F Dombi ordered weighted averaging ( m FDOWA ) operator, m F Dombi hybrid averaging ( m FDHA ) operator, m F Dombi weighted geometric ( m FDWG ) operator, m F Dombi weighted ordered geometric operator, and m F Dombi hybrid geometric ( m FDHG ) operator. We investigate properties, namely, idempotency, monotonicity, and boundedness, for the proposed operators. Moreover, we give an algorithm to solve multicriteria decision-making issues which involve m F information with m FDWA and m FDWG operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with m F -ELECTRE-I approach (Akram et al. 2019) and m F Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test.
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