Next Article in Journal
Adaptive and Blind Audio Watermarking Algorithm Based on Chaotic Encryption in Hybrid Domain
Next Article in Special Issue
Picture Hesitant Fuzzy Set and Its Application to Multiple Criteria Decision-Making
Previous Article in Journal
Numerical Study of Dynamic Properties of Fractional Viscoplasticity Model
Previous Article in Special Issue
Intuitionistic Fuzzy Multiple Attribute Decision-Making Model Based on Weighted Induced Distance Measure and Its Application to Investment Selection
Article Menu
Issue 7 (July) cover image

Export Article

Open AccessArticle
Symmetry 2018, 10(7), 283;

Selecting the Optimal Mine Ventilation System via a Decision Making Framework under Hesitant Linguistic Environment

School of Resources and Safety Engineering, Central South University, Changsha 410083, China
School of Systems Engineering, National University of Defense Technology, Changsha 410073, China
Author to whom correspondence should be addressed.
Received: 15 June 2018 / Revised: 10 July 2018 / Accepted: 10 July 2018 / Published: 13 July 2018
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
Full-Text   |   PDF [345 KB, uploaded 16 July 2018]


Ventilation systems are amongst the most essential components of a mine. As the indicators of ventilation systems are in general of ambiguity or uncertainty, the selection of ventilation systems can therefore be regarded as a complex fuzzy decision making problem. In order to solve such problems, a decision making framework based on a new concept, the hesitant linguistic preference relation (HLPR), is constructed. The basic elements in the HLPR are hesitant fuzzy linguistic numbers (HFLNs). At first, new operational laws and aggregation operators of HFLNs are defined to overcome the limitations in existing literature. Subsequently, a novel comparison method based on likelihood is proposed to obtain the order relationship of two HFLNs. Then, a likelihood-based consistency index is introduced to represent the difference between two hesitant linguistic preference relations (HLPRs). It is a new way to express the consistency degree for the reason that the traditional consistency indices are almost exclusively based on distance measures. Meanwhile, a consistency-improving model is suggested to attain acceptable consistent HLPRs. In addition, a method to receive reasonable ranking results from HLPRs with acceptable consistency is presented. At last, this method is used to pick out the best mine ventilation system under uncertain linguistic decision conditions. A comparison and a discussion are conducted to demonstrate the validity of the presented approach. The results show that the proposed method is effective for selecting the optimal mine ventilation system, and provides references for the construction and management of mines. View Full-Text
Keywords: mine ventilation systems; hesitant linguistic environment; likelihood; preference relations mine ventilation systems; hesitant linguistic environment; likelihood; preference relations
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).

Share & Cite This Article

MDPI and ACS Style

Liang, W.; Zhao, G.; Luo, S. Selecting the Optimal Mine Ventilation System via a Decision Making Framework under Hesitant Linguistic Environment. Symmetry 2018, 10, 283.

Show more citation formats Show less citations formats

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

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top