Multi-Attribute Decision-Making Based on m-Polar Fuzzy Hamacher Aggregation Operators
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Department of Mathematics, University of the Punjab, New Campus, Lahore 4590, Pakistan
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BORDA Research Unit and IME, University of Salamanca, 37007 Salamanca, Spain
*
Authors to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1498; https://doi.org/10.3390/sym11121498
Received: 27 November 2019
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Revised: 5 December 2019
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Accepted: 9 December 2019
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Published: 10 December 2019
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems – part II)
In this paper, we introduce certain aggregation operators, namely, the m-polar fuzzy (mF) Hamacher weighted average operator, mF Hamacher ordered weighted average (mFHOWA) operator, mF Hamacher hybrid average (mFHHA) operator, mF Hamacher weighted geometric (mFHWG) operator, mF Hamacher weighted ordered geometric operator, and mF Hamacher hybrid geometric (mFHHG) operator. We discuss some properties of these operators, inclusive of their ability to implement both symmetric and asymmetric treatments of the items. We develop an algorithmic model to solve multi-attribute decision-making (MADM) problems in mF environment using mF Hamacher weighted average operator (mFHWA) and mFHWG operators. They can compensate for the possible asymmetric roles of the attributes that describe the problem. In the end, to prove the validity and feasibility of the proposed work, we give applications for selecting the most affected country regarding human trafficking, selecting health care waste treatment methods and selecting the best company for investment. We also solve practical MADM problems by using ELECTRE-I method, and give a comparative analysis.
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MDPI and ACS Style
Waseem, N.; Akram, M.; Alcantud, J.C.R. Multi-Attribute Decision-Making Based on m-Polar Fuzzy Hamacher Aggregation Operators. Symmetry 2019, 11, 1498. https://doi.org/10.3390/sym11121498
AMA Style
Waseem N, Akram M, Alcantud JCR. Multi-Attribute Decision-Making Based on m-Polar Fuzzy Hamacher Aggregation Operators. Symmetry. 2019; 11(12):1498. https://doi.org/10.3390/sym11121498
Chicago/Turabian StyleWaseem, Neha, Muhammad Akram, and José Carlos R. Alcantud. 2019. "Multi-Attribute Decision-Making Based on m-Polar Fuzzy Hamacher Aggregation Operators" Symmetry 11, no. 12: 1498. https://doi.org/10.3390/sym11121498
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