A Multi-Criteria Decision-Making Method Based on Heronian Mean Operators Under a Linguistic Hesitant Fuzzy Environment

Su-Min Yu (), Huan Zhou (), Xiao-Hong Chen () and Jian-Qiang Wang ()
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Su-Min Yu: Business School, Central South University, Lushan South Road, Changsha 410083, P. R. China
Huan Zhou: Business School, Central South University, Lushan South Road, Changsha 410083, P. R. China
Xiao-Hong Chen: Business School, Central South University, Lushan South Road, Changsha, 410083, P. R. China
Jian-Qiang Wang: Business School, Central South University, Lushan South Road, Changsha 410083, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2015, vol. 32, issue 05, 1-35

Abstract: Linguistic hesitant fuzzy sets (LHFSs) are a very useful and appropriate means of expressing preferences of decision-makers; moreover their basic operations and comparison methods have been defined and applied to the solving of MCDM problems. However, there are a number of limitations in the related studies. In this paper, using information from existing studies, several new operations and a new order relationship are defined; moreover four linguistic hesitant fuzzy Heronian mean operators are proposed: the linguistic hesitant fuzzy arithmetic Heronian mean (LHFAHM) operator; the linguistic hesitant fuzzy weighted arithmetic Heronian mean (LHFWAHM) operator; the linguistic hesitant fuzzy geometric Heronian mean (LHFGHM) operator; and the linguistic hesitant fuzzy weighted geometric Heronian mean (LHFWGHM) operator. Furthermore, some useful and desirable properties of these operators are analyzed in some special cases, with respect to the different parameter values in these operators, are discussed. Additionally, an approach based on the LHFWAHM and LHFWGHM operators for solving MCDM problems is proposed. Finally, an illustrative example is provided to verify the validity and feasibility of the proposed approaches, and a comparison analysis is also presented to demonstrate the influences of different parameters on the results of decision-making.

Keywords: Multi-criteria decision-making; linguistic hesitant fuzzy sets; arithmetic Heronian mean operator; geometric Heronian mean operator (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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DOI: 10.1142/S0217595915500359

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