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Algorithms 2018, 11(10), 154; https://doi.org/10.3390/a11100154

Two Hesitant Multiplicative Decision-Making Algorithms and Their Application to Fog-Haze Factor Assessment Problem

1,2,* and 3,4
1
School of Mathematics and Statistics, Hefei Normal University, Hefei 230601, Anhui, China
2
School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, China
3
School of Management, Hefei University of Technology, Hefei 230009, Anhui, China
4
School Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
*
Author to whom correspondence should be addressed.
Received: 29 August 2018 / Revised: 28 September 2018 / Accepted: 2 October 2018 / Published: 10 October 2018
(This article belongs to the Special Issue Algorithms for Decision Making)
Full-Text   |   PDF [255 KB, uploaded 10 October 2018]

Abstract

Hesitant multiplicative preference relation (HMPR) is a useful tool to cope with the problems in which the experts utilize Saaty’s 1–9 scale to express their preference information over paired comparisons of alternatives. It is known that the lack of acceptable consistency easily leads to inconsistent conclusions, therefore consistency improvement processes and deriving the reliable priority weight vector for alternatives are two significant and challenging issues for hesitant multiplicative information decision-making problems. In this paper, some new concepts are first introduced, including HMPR, consistent HMPR and the consistency index of HMPR. Then, based on the logarithmic least squares model and linear optimization model, two novel automatic iterative algorithms are proposed to enhance the consistency of HMPR and generate the priority weights of HMPR, which are proved to be convergent. In the end, the proposed algorithms are applied to the factors affecting selection of fog-haze weather. The comparative analysis shows that the decision-making process in our algorithms would be more straight-forward and efficient. View Full-Text
Keywords: automatic iterative algorithms; hesitant multiplicative preference relation; consistency; group decision making automatic iterative algorithms; hesitant multiplicative preference relation; consistency; group decision making
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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Pei, L.; Jin, F. Two Hesitant Multiplicative Decision-Making Algorithms and Their Application to Fog-Haze Factor Assessment Problem. Algorithms 2018, 11, 154.

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