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 (mF, henceforth) information, which are mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid averaging (mFDHA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi weighted ordered geometric operator, and mF Dombi hybrid geometric (mFDHG) 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 mF information with mFDWA and mFDWG operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with mF-ELECTRE-I approach (Akram et al. 2019) and mF Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test.
Highlights
Multicriteria decision making (MCDM) is performing a vital role in different areas, including social, physical, medical, and environmental sciences
We develop a novel operator called mF Dombi hybrid averaging (mFDHA) operator, which obtains the properties of both mF Dombi weighted averaging (mFDWA) and mF Dombi ordered weighted averaging (mFDOWA) operators
Motivated by Dombi operations, we have proposed certain mF Dombi Aggregation operators (AOs), namely, mFDWA, mFDOWA, mFDHA, mF Dombi weighted geometric (mFDWG), mFDOWG, and mF Dombi hybrid geometric (mFDHG) operators
Summary
Multicriteria decision making (MCDM) is performing a vital role in different areas, including social, physical, medical, and environmental sciences. MCDM methods are used to determine a suitable object and used to rank the objects in an appointed problem. To solve different uncertain problems for decision making, Atanassov [1] presented the concept of intuitionistic fuzzy set (IFS) which considers both membership and nonmembership parts, an extension of fuzzy set [2] in which simple membership part is characterized. Aggregation operators (AOs) perform an important role in order to combine data into a single form and solve MCDM problems. Yager [3] introduced weighted AOs. Xu [4] proposed some new AOs under
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