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Open AccessArticle

Multi-Criteria Group Decision-Making Using an m-Polar Hesitant Fuzzy TOPSIS Approach

1
Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
2
BORDA Research Unit and IME, Universidad de Salamanca, Salamanca 37008, Spain
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(6), 795; https://doi.org/10.3390/sym11060795
Received: 21 May 2019 / Revised: 7 June 2019 / Accepted: 12 June 2019 / Published: 14 June 2019
The m-polar fuzzy sets (mF sets) have a representative and fundamental role in several fields of science and decision-making. The fusion of mF sets with several other theories of mathematics has become a favorable practice for depicting numerous types of uncertainties under multi-polar information. In this article, we introduce an innovative hybrid model, called m-polar hesitant fuzzy sets (mHF-sets), a hybridization of hesitancy and mF sets, which enables us to tackle multi-polar information with hesitancy. Hesitancy incorporates symmetry into the treatment of the data, whereas the m-polar fuzzy format allows for differentiated or asymmetric sources of information. We highlight and explore basic key properties of mHF-sets and formulate intrinsic operations. Moreover, we develop an m-polar hesitant fuzzy TOPSIS (mHF-TOPSIS) approach for multi-criteria group decision-making (MCGDM), which is a natural extension of the TOPSIS method to this framework. We describe applications of mHF-sets in group decision-making. Further, we show the efficiency of our proposed approach by applying it to the industrial field. Finally, we generate a computer programming code that implements our decision-making procedure for ease of lengthy calculations. View Full-Text
Keywords: m-Polar fuzzy set; hesitant fuzzy set; m-polar hesitant fuzzy set; decision-making; TOPSIS m-Polar fuzzy set; hesitant fuzzy set; m-polar hesitant fuzzy set; decision-making; TOPSIS
MDPI and ACS Style

Akram, M.; Adeel, A.; Alcantud, J.C.R. Multi-Criteria Group Decision-Making Using an m-Polar Hesitant Fuzzy TOPSIS Approach. Symmetry 2019, 11, 795. https://doi.org/10.3390/sym11060795

AMA Style

Akram M, Adeel A, Alcantud JCR. Multi-Criteria Group Decision-Making Using an m-Polar Hesitant Fuzzy TOPSIS Approach. Symmetry. 2019; 11(6):795. https://doi.org/10.3390/sym11060795

Chicago/Turabian Style

Akram, Muhammad; Adeel, Arooj; Alcantud, José C.R. 2019. "Multi-Criteria Group Decision-Making Using an m-Polar Hesitant Fuzzy TOPSIS Approach" Symmetry 11, no. 6: 795. https://doi.org/10.3390/sym11060795

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Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

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