Linguistic neutrosophic power Muirhead mean operators for safety evaluation of mines

Autoři: Suizhi Luo aff001;  Weizhang Liang aff002;  Guoyan Zhao aff002
Působiště autorů: College of Systems Engineering, National University of Defense Technology, Changsha, Hunan, China aff001;  School of Resources and Safety Engineering, Central South University, Changsha, Hunan, China aff002
Vyšlo v časopise: PLoS ONE 14(10)
Kategorie: Research Article
doi: 10.1371/journal.pone.0224090


Safety is the fundamental guarantee for the sustainable development of mining enterprises. As the safety evaluation of mines is a complex system engineering project, consistent and inconsistent, even hesitant evaluation information may be contained simultaneously. Linguistic neutrosophic numbers (LNNs), as the extensions of linguistic terms, are effective means to entirely and qualitatively convey such evaluation information with three independent linguistic membership functions. The aim of our work is to investigate several mean operators so that the safety evaluation issues of mines are addressed under linguistic neutrosophic environment. During the safety evaluation process of mines, many influence factors should be considered, and some of them may interact with each other. To this end, the Muirhead mean (MM) operators are adopted as they are powerful tools to deal with such situation. On the other hand, to diminish the impacts of irrational data provided by evaluators, the power average (PA) operators are under consideration. Thus, with the combination of MM and PA, the power MM operators and weighted power MM operators are proposed to aggregate linguistic neutrosophic information. Meanwhile, some key points and special cases are studied. The advantages of these operators are that not only the interrelations among any number of inputs can be reflected, but also the effects of unreasonable information can be reduced. Thereafter, a new linguistic neutrosophic ranking technique based on these operators is developed to evaluate the mine safety. Moreover, in-depth discussions are made to show the robust and flexible abilities of our method. Results manifest that the proposed method is successful in dealing with mine safety evaluation issues within linguistic neutrosophic circumstances.

Klíčová slova:

Cognitive linguistics – Decision making – Distance measurement – Equipment – Fire safety – Minerals – Permutation – Mining engineering


1. Badri A, Nadeau S, Gbodossou A. A new practical approach to risk management for underground mining project in Quebec. Journal of Loss Prevention in the Process Industries 2013; 26: 1145–1158

2. Liang WZ, Luo SZ, Zhao GY. Evaluation of cleaner production for gold mines employing a hybrid multi-criteria decision making approach. Sustainability 2019; 11(1): 146. doi: 10.3390/su11010146

3. Wang QX, Wang H, Qi ZQ. An application of nonlinear fuzzy analytic hierarchy process in safety evaluation of coal mine. Safety Science 2016; 86: 78–87.

4. Liang WZ, Zhao GY, Wu H, Chen Y. Assessing the risk degree of goafs by employing hybrid TODIM method under uncertainty. Bulletin of Engineering Geology & the Environment 2018; 78(5): 3767–3782. doi: 10.1016/j.ijmst.2015.11.014

5. Liu H, Zeng LH. Statistical analysis of national coal mine safety accidents in 2018. Inner Mongolia Coal Economy 2019; 6: 92–93.

6. Wei CF, Pei Z, Li HM. An induced OWA operator in coal mine safety evaluation. Journal of Computer and System Sciences 2012; 78(4): 997–1005.

7. Peng HG, Wang JQ, Cheng PF. A linguistic intuitionistic multi-criteria decision-making method based on the frank heronian mean operator and its application in evaluating coal mine safety. International Journal of Machine Learning and Cybernetics 2017; 9: 1053–1068.

8. Liang WZ, Zhao GY, Wang X, Zhao J, Ma CD, Assessing the rockburst risk for deep shafts via distance-based multi-criteria decision making approaches with hesitant fuzzy information. Engineering Geology 2019; doi: 10.1016/j.enggeo.2019.105211

9. Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning—I. Information Sciences 1975; 8(3): 199–249.

10. Liu PD. Two-dimensional uncertain linguistic generalized normalized weighted geometric Bonferroni mean and its application to multiple-attribute decision making. Scientia Iranica. Transaction E, Industrial Engineering 2018; 25(1): 450–465.

11. Mendoza-Sanchez J, Silva F, Rangel L, Jaramillo L, Mendoza L, Garzon J, Quiroga A. Benefit, risk and cost of new oral anticoagulants and warfarin in atrial fibrillation; A multicriteria decision analysis. PlOS One 2018; 13(5): e0196361. doi: 10.1371/journal.pone.0196361 29723207

12. Liang WZ, Zhao GY, Wu H, Dai B. Risk assessment of rockburst via an extended MABAC method under fuzzy environment. Tunnelling and Underground Space Technology 2019; 83: 533–544.

13. Chang KH, Chang YC, Chain K, Chung HY. Integrating soft set theory and fuzzy linguistic model to evaluate the performance of training simulation systems. PlOS One 2016; 11(9): e0162092. doi: 10.1371/journal.pone.0162092 27598390

14. Liu PD, Zhang XH. Approach to multi-attributes decision making with intuitionistic linguistic information based on Dempster-shafer evidence theory. IEEE Access 2018; 6: 52969–52981.

15. Luo SZ, Zhang HY, Wang JQ, Li L. Group decision-making approach for evaluating the sustainability of constructed wetlands with probabilistic linguistic preference relations. Journal of the Operational Research Society 2019; 1–17. doi: 10.1080/01605682.2018.1510806

16. Chen ZC, Liu PH, Pei Z. An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers. International Journal of Computational Intelligence Systems 2015; 8(4): 747–760.

17. Liu PD, Tang GL. Some intuitionistic fuzzy prioritized interactive Einstein choquet operators and their application in decision making. IEEE Access 2018; 6: 72357–72371.

18. Liu PD, Li DF. Some Muirhead mean operators for intuitionistic fuzzy numbers and their applications to group decision making. PlOS One 2017; 12(1): e0168767. doi: 10.1371/journal.pone.0168767 28103244

19. Smarandache F. Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis. 1st ed. Rehoboth: American Research Press; 1998.

20. Biswas P, Pramanik S, Giri BC. TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment. Neural Computing and Applications 2016; 27(3): 727–737.

21. Garg H, Nancy. New logarithmic operational laws and their applications to multiattribute decision making for single-valued neutrosophic numbers. Cognitive Systems Research 2018; 52: 931–946.

22. Rashno A, Nazari B, Koozekanani DD, Drayna PM, Sadri S, Rabbani H, Parhi KK. Fully-automated segmentation of fluid regions in exudative age-related macular degeneration subjects: Kernel graph cut in neutrosophic domain. PlOS One 2017; 12(10): e0186949. doi: 10.1371/journal.pone.0186949 29059257

23. Pramanik S, Biswas P, Giri BC. Hybrid vector similarity measures and their applications to multi-attribute decision making under neutrosophic environment. Neural Computing and Applications 2017; 28(5): 1163–1176.

24. Garg H, Nancy. Some hybrid weighted aggregation operators under neutrosophic set environment and their applications to multicriteria decision-making. Applied Intelligence 2018; 48(12): 4871–4888.

25. Li DP, Cheng SJ, Cheng PF, Wang JQ, Zhang HY. A novel financial risk assessment model for companies based on heterogeneous information and aggregated historical data. PlOS One 2018; 13(12): e0208166. doi: 10.1371/journal.pone.0208166 30586437

26. Nancy, Garg H. A novel divergence measure and its based TOPSIS method for multi criteria decision-making under single-valued neutrosophic environment. Journal of Intelligent & Fuzzy Systems 2019; 36(1): 101–115.

27. Dey PP, Pramanik S, Giri BC. An extended grey relational analysis based multiple attribute decision making in interval neutrosophic uncertain linguistic setting. Neutrosophic Sets and Systems 2016; 11: 21–30.

28. Garg H, Nancy. Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment. Applied Intelligence 2018; 48(8): 2199–2213.

29. Abdel-Basset M, Saleh M, Gamal A, Smarandache F. An approach of TOPSIS technique for developing supplier selection with group decision making under type-2 neutrosophic number. Applied Soft Computing 2019; 77: 438–452.

30. Ji P, Zhang HY, Wang JQ. Selecting an outsourcing provider based on the combined MABAC–ELECTRE method using single-valued neutrosophic linguistic sets. Computers & Industrial Engineering 2018; 120: 429–441.

31. Liu PD, Khan Q, Mahmood T, Smarandache F, Li Y. Multiple attribute group decision making based on 2-tuple linguistic neutrosophic Dombi power Heronian mean operators. IEEE Access 2019; 1–1. doi: 10.1109/ACCESS.2019.2925344

32. Abdel-Basset M, Saleh M, Gamal A, Smarandache F. An approach of TOPSIS technique for developing supplier selection with group decision making under type-2 neutrosophic number. Applied Soft Computing 2019; 77: 438–452.

33. Wang J, Lu JP, Wei GW, Lin R, Wei C. Models for MADM with single-valued neutrosophic 2-tuple linguistic Muirhead mean operators. Mathematics 2019; 7(5): 442. doi: 10.3390/math7050442

34. Dat LQ, Thong NT, Ali M, Smarandache F, Abdel-Basset M, Long HV. Linguistic approaches to interval complex neutrosophic sets in decision making. IEEE Access 2019; 7: 38902–38917.

35. Fang ZB, Ye J. Multiple attribute group decision-making method based on linguistic neutrosophic numbers. Symmetry 2017; 9(7): 111. doi: 10.3390/sym9070111

36. Luo SZ, Liang WZ, Xing LN. Selection of mine development scheme based on similarity measure under fuzzy environment. Neural Computing and Applications 2019; 1–12. doi: 10.1007/s00521-019-04026-x

37. Liang WZ, Zhao GY, Hong CS. Performance assessment of circular economy for phosphorus chemical firms based on VIKOR-QUALIFLEX method. Journal of Cleaner Production 2018; 196: 1365–1378.

38. Mondal K, Pramanik S, Giri BC. Multi-criteria group decision making based on linguistic refined neutrosophic strategy. In: Smarandache F, Pramanik S, editors. New Trends in Neutrosophic Theory and Applications. Brussels: Pons Editions; 2018. pp. 125–139.

39. Luo SZ, Liang WZ. Optimization of roadway support schemes with likelihood–based MABAC method. Applied Soft Computing 2019; 80: 80–92.

40. Shi LL, Ye J. Cosine measures of linguistic neutrosophic numbers and their application in multiple attribute group decision-making. Information 2017; 8(4): 117. doi: 10.3390/info8040117

41. Liang WZ, Zhao GY, Wu H. Evaluating investment risks of metallic mines using an extended TOPSIS method with linguistic neutrosophic numbers. Symmetry 2017; 9(8): 149. doi: 10.3390/sym9080149

42. Pamučar D, Badi I, Sanja K, Obradović R. A novel approach for the selection of power-generation technology using a linguistic neutrosophic CODAS method: A case study in Libya. Energies 2018; 11(9): 2489. doi: 10.3390/en11092489

43. Liang WZ, Zhao GY, Hong CS. Selecting the optimal mining method with extended multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) approach. Neural Computing and Applications 2018; doi: 10.1007/s00521-018-3405-5

44. Garg H, Nancy. Algorithms for possibility linguistic single-valued neutrosophic decision-making based on COPRAS and aggregation operators with new information measures. Measurement 2019; 138: 278–290.

45. Wang J, Gao H, Wei GW. Some 2-tuple linguistic neutrosophic number Muirhead mean operators and their applications to multiple attribute decision making. Journal of Experimental & Theoretical Artificial Intelligence 2019; 31(3): 409–439.

46. Liu PD, You XL. Bidirectional projection measure of linguistic neutrosophic numbers and their application to multi-criteria group decision making. Computers & Industrial Engineering 2019; 128: 447–457.

47. Li YY, Wang JQ, Wang TL. A linguistic neutrosophic multi-criteria group decision-making approach with EDAS method. Arabian Journal for Science and Engineering 2019; 44(3): 2737–2749.

48. Wang XG, Geng YS, Yao PP, Yang MJ. Multiple attribute group decision making approach based on extended VIKOR and linguistic neutrosophic set. Journal of Intelligent & Fuzzy Systems 2019; 36(1): 149–160.

49. Liu PD, Wang P. Some q-Rung Orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. International Journal of Intelligent Systems 2018; 33(2): 259–280.

50. Liu S, Yu W, Liu L, Hu YA. Variable weights theory and its application to multi-attribute group decision making with intuitionistic fuzzy numbers on determining decision maker’s weights. PlOS One 2019; 14(3): e0212636. doi: 10.1371/journal.pone.0212636 30840647

51. Garg H, Nancy. Linguistic single-valued neutrosophic prioritized aggregation operators and their applications to multiple-attribute group decision-making. Journal of Ambient Intelligence and Humanized Computing 2018; 9(6): 1975–1997.

52. Liu PD, Liu JL. Some q-Rung Orthopai fuzzy Bonferroni mean operators and their application to multi-attribute group decision making. International Journal of Intelligent Systems 2018; 33(2): 315–347.

53. Liu PD, Wang P. Multiple-attribute decision making based on Archimedean Bonferroni operators of q-Rung Orthopair fuzzy numbers. IEEE Transactions on Fuzzy Systems 2018; doi: 10.1109/TFUZZ.2018.2826452

54. Fan CX, Ye J, Hu KL, Fan E. Bonferroni mean operators of linguistic neutrosophic numbers and their multiple attribute group decision-making methods. Information 2017; 8(3): 107. doi: 10.3390/info8030107

55. Wang YM, Liu P. Linguistic neutrosophic generalized partitioned Bonferroni mean operators and their application to multi-attribute group decision making. Symmetry 2018; 10(5), 160. doi: 10.3390/sym10050160

56. Liu PD, You XL. Some linguistic neutrosophic Hamy mean operators and their application to multi-attribute group decision making. PlOS One 2018; 13(3): e0193027. doi: 10.1371/journal.pone.0193027 29513697

57. Liang WZ, Zhao GY, Luo SZ. Linguistic neutrosophic Hamacher aggregation operators and the application in evaluating land reclamation schemes for mines. PloS one 2018; 13(11): e0206178. doi: 10.1371/journal.pone.0206178 30399171

58. Muirhead RF. Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proceedings of the Edinburgh Mathematical Society 1902; 21: 144–162.

59. Wang J, Wei GW, Wei C, Wei Y. Dual hesitant q-Rung Orthopair fuzzy Muirhead mean operators in multiple attribute decision making. IEEE Access 2019; 7(1): 67139–67166.

60. Tang XY, Wei GW, Gao H. Models for multiple attribute decision making with interval-valued Pythagorean fuzzy Muirhead mean operators and their application to green suppliers selection. Informatica 2019; 30(1): 153–186.

61. Wang R, Wang J, Gao H, Wei GW. Methods for MADM with picture fuzzy Muirhead mean operators and their application for evaluating the financial investment risk. Symmetry 2019; 11(1): 6. doi: 10.3390/sym11010006

62. Yager RR. The power average operator. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 2001; 31(6): 724–731.

63. Liu PD, Chen SM, Wang P. Multiple-attribute group decision-making based on q-Rung Orthopair fuzzy power Maclaurin symmetric mean operators. IEEE Transactions on Systems, Man, and Cybernetics: Systems 2018; (99): 1–16. doi: 10.1109/TSMC.2018.2852948

64. Garg H, Nancy. (2018). Multi-criteria decision-making method based on prioritized muirhead mean aggregation operator under neutrosophic set environment. Symmetry, 10(7), 280. doi: 10.3390/sym10070280

65. Liu PD, Mahmood T, Khan Q. Group decision making based on power Heronian aggregation operators under linguistic neutrosophic environment. International Journal of Fuzzy Systems 2018; 20(3): 970–985.

66. Li L, Zhang RT, Wang J, Zhu XM, Xing YP. Pythagorean fuzzy power Muirhead mean operators with their application to multi-attribute decision making. Journal of Intelligent & Fuzzy Systems 2018; 35(2): 2035–2050.

67. Khan Q, Hassan N, Mahmood T. Neutrosophic cubic power Muirhead mean operators with uncertain data for multi-attribute decision-making. Symmetry 2018; 10(10): 444. doi: 10.3390/sym10100444

68. Luo SZ, Cheng PF, Wang JQ, Huang YJ, Selecting project delivery systems based on simplified neutrosophic linguistic preference relations, Symmetry 2017; 9(8): 151. doi: 10.3390/sym9080151

69. Jahan A, Ismail MY, Shuib S, Norfazidah D, Edwards KL. An aggregation technique for optimal decision-making in materials selection. Materials & Design 2011; 32(10): 4918–4924.

70. Smarandache F. Plithogenic Set, an extension of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets-revisited. Neutrosophic Sets and Systems 2018; 21: 153–166.

71. Smarandache F. Plithogeny, plithogenic set, logic, probability, and statistics. 1st ed. Brussels: Pons Publishing House; 2017.

72. Smarandache F. Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset, Similarly for Neutrosophic Over-/Under-/Off- Logic, Probability, and Statistics. 1st ed. Brussels: Pons Edition; 2016.

Článek vyšel v časopise


2019 Číslo 10