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Mathematics 2019, 7(2), 185; https://doi.org/10.3390/math7020185

Consensus-Based Multi-Person Decision Making with Incomplete Fuzzy Preference Relations Using Product Transitivity

1
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Punjab 54000, Pakistan
2
Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan
*
Author to whom correspondence should be addressed.
Received: 27 December 2018 / Revised: 13 February 2019 / Accepted: 14 February 2019 / Published: 16 February 2019
(This article belongs to the Special Issue Nonlinear Analysis Using Fuzzy Mathematics)
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Abstract

In this paper, a consensus-based method for multi-person decision making (MPDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the complete fuzzy preference relation (FPR). Then it is confirmed to be product consistent by using the transitive closure formula. Following this, weights of decision makers (DMs) are evaluated by merging consistency weights and predefined priority weights (if any). The consistency weights for the DMs are estimated through product consistency investigation of the information provided by each DM. The consensus process determines whether the selection procedure should be initiated or not. The hybrid comprises of a quitting process and feedback mechanism, and is used to enhance the consensus level amongst DMs in case of an inadequate state. The quitting process arises when some DMs decided to leave the course, and is common in MPDM while dealing with a large number of alternatives. The feedback mechanism is the main novelty of the proposed technique which helps the DMs to improve their given preferences based on this consistency. At the end, a numerical example is deliberated to measure the efficiency and applicability of the proposed method after the comparison with some existing models under the same assumptions. The results show that proposed method can offer useful comprehension into the MPDM process. View Full-Text
Keywords: fuzzy set; multi-person decision making (MPDM); fuzzy preference relation (FPR); incomplete fuzzy preference relation (IFPR); product transitivity fuzzy set; multi-person decision making (MPDM); fuzzy preference relation (FPR); incomplete fuzzy preference relation (IFPR); product transitivity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Rehman, A.-U.; Hussain, M.; Farooq, A.; Akram, M. Consensus-Based Multi-Person Decision Making with Incomplete Fuzzy Preference Relations Using Product Transitivity. Mathematics 2019, 7, 185.

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