Set pair analysis is a successful theory to deal with the certainty and uncertainty in the system based on “identity”-“discrepancy”-“contrary” degree of the connection number. It is very important to construct a reasonable connection number for handling the uncertainty between the feature of set pair. Considering the semantics of linguistic terms, we define a new approach to propose a linguistic connection number(LCN) corresponding to linguistic intuitionistic fuzzy number based on the set pair analysis theory and numerical scale function for semantics of linguistic terms. Then we define a cosine distance measure between the new LCNs and develop the TOPSIS method to the proposed cosine distance measure. Furthermore, we give a numerical example of coal mine safety evaluation to illustrate the proposed method, and the sensitivity analysis of the ranking results is made based on different numerical scale functions. The feasibility and effectiveness of the proposed method are also verified by comparison with the existing methods.
ZadehL.A., Fuzzy sets[J], Information and Control8(3) (1965), 338–353.
2.
KingP.J. and MamdaniE.H., The application of fuzzy control systems to industrial processes[J], Automatica13(3) (1977), 235–242.
3.
WangH., XuZ. and PedryczW., An overview on the roles of fuzzy set techniques in big data processing: Trends, challenges and opportunities[J], Knowledge-Based Systems118 (2017), 15–30.
4.
GrabischM., The application of fuzzy integrals in multicriteria decision making[J], European Journal of Operational Research89(3) (1996), 445–456.
5.
DeS.K., BiswasR. and RoyA.R., An application of intuitionistic fuzzy sets in medical diagnosis[J], Fuzzy Sets and Systems117(2) (2001), 209–213.
6.
AtanassovK.T., Intuitionistic fuzzy sets[J], Fuzzy Sets and Systems20(1) (1986), 87–96.
7.
BustinceH. and BurilloP., Vague sets are intuitionistic fuzzy sets[J], Fuzzy Sets and Systems79(3) (1996), 403–405.
8.
DeschrijverG. and KerreE.E., On the relationship between some extensions of fuzzy set theory[J], Fuzzy Sets and Systems133(2) (2003), 227–235.
9.
GargH., An improved cosine similarity measure for intuitionistic fuzzy sets and their applications to decision-making process[J], Hacettepe Journal of Mathematics and Statistics47 (2018), 1585–1601.
10.
GargH., Distance and similarity measures for intuitionistic multiplicative preference relation and its applications[J],117 C, International Journal for Uncertainty Quantification7(2) (2017), 133.
11.
LiuD., ChenX. and PengD., Distance Measures for Hesitant Fuzzy Linguistic Sets and Their Applications in Multiple Criteria Decision Making[J], International Journal of Fuzzy Systems20(7) (2018), 1–11.
12.
TanA., WuW.Z., QianY., et al., Intuitionistic fuzzy rough set-based granular structures and attribute subset selection[J], IEEE Transactions on Fuzzy Systems27(3) (2019), 527–539.
13.
KhanM.S. and AbdullahS., Interval-valued Pythagorean fuzzy GRA method for multiple-attribute decision making with incomplete weight information[J], International Journal of Intelligent Systems33(8) (2018), 1689–1716.
14.
Sajjad Ali KhanM., AbdullahS., Yousaf AliM., HussainM. and FarooqM., Extension of TOPSIS method base on Choquet integral under interval-valued Pythagorean fuzzy environment[J], Journal of Intelligent and Fuzzy Systems34(1) (2018), 267–282.
15.
Sajjad Ali KhanM., AliA., AbdullahS., AminF. and HussainF., New extension of TOPSIS method based on Pythagorean hesitant fuzzy sets with incomplete weight information[J], Journal of Intelligent and Fuzzy Systems35(5) (2018), 5435–5448.
16.
KhanM.S., AbdullahS., AliA., SiddiquiN. and AminF., Pythagorean hesitant fuzzy sets and their application to group decision making with incomplete weight information[J], Journal of Intelligent and Fuzzy Systems33(6) (2017), 3971–3985.
17.
KhanM.S., AbdullahS., AliA., AminF. and HussainF., Pythagorean hesitant fuzzy Choquet integral aggregation operators and their application to multi-attribute decision-making[J], Soft Computing23(1) (2019), 251–267.
18.
KhanM.S., AbdullahS. and AliA., Multiattribute group decision-making based on Pythagorean fuzzy Einstein prioritized aggregation operators[J], International Journal of Intelligent Systems34(5) (2019), 1001–1033.
19.
ZebA., KhanM.S. and IbrarM., Approaches to multi-attribute decision making with risk preference under extended Pythagorean fuzzy environment[J], Journal of Intelligent and Fuzzy Systems36(2) (2019), 325–335.
20.
AggarwalM., HanmandluM., KeaneM.T., et al.Intuitionistic Fuzzy Logit Model of Discrete Choice[J], IEEE Transactions on Emerging Topics in Computational Intelligence3(1) (2019), 85–89.
21.
ZadehL.A., The concept of a linguistic variable and its application to approximate reasoning-I[J], Information Sciences8(3) (1975), 199–249.
22.
ZadehL.A., The concept of a linguistic variable and its application to approximate reasoning-II[J], Information Sciences8(4) (1975), 301–357.
23.
ZadehL.A., The concept of a linguistic variable and its application to approximate reasoning-III[J], Information Sciences9(1) (1975), 43–80.
24.
GargH. and KumarK., Linguistic interval-valued Atanassov intuitionistic fuzzy sets and their applications to group decision-making problems[J], IEEE Transactions on Fuzzy Systems (2019), 1–10, doi: 10.1109/TFUZZ.2019.2897961
25.
WuJ., LiX., ChiclanaF., et al., An attitudinal trust recommendation mechanism to balance consensus and harmony in group decision making[J], IEEE Transactions on Fuzzy Systems (2019), 1. doi: 10.1109/TFUZZ.2019.2895564
26.
WuJ., ChiclanaF. and LiaoH., Isomorphic multiplicative transitivity for intuitionistic and intervalvalued fuzzy preference relations and its application in deriving their priority vectors[J], IEEE Transactions on Fuzzy Systems26(1) (2016), 193–202.
27.
WuJ., SunQ., FujitaH., et al., An attitudinal consensus degree to control the feedback mechanism in group decision making with different adjustment cost[J], Knowledge-Based Systems164 (2019), 265–273.
28.
LiuY., LiangC., ChiclanaF., et al.A trust induced recommendation mechanism for reaching consensus in group decision making[J], Knowledge-Based Systems119 (2017), 221–231.
29.
WuJ., ChangJ., CaoQ., et al., A trust propagation and collaborative filtering based method for incomplete information in social network group decision making with type-2 linguistic trust[J], Computers and Industrial Engineering127 (2019), 853–864.
30.
HerreraF. and Herrera-ViedmaE., Linguistic decision analysis: steps for solving decision problems under linguistic information[J], Fuzzy Sets and Systems115(1) (2000), 67–82.
31.
XuZ., A method based on linguistic aggregation operators for group decision making with linguistic preference relations[J], Information Sciences166(1) (2004), 19–30.
32.
ChenZ., LiuP. and PeiZ., An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers[J], International Journal of Computational Intelligence Systems8(4) (2015), 747–760.
33.
ZhangH., PengH., WangJ., et al., An extended outranking approach for multi-criteria decisionmaking problems with linguistic intuitionistic fuzzy numbers[J], Applied Soft Computing59 (2017), 462–474.
34.
PengH., WangJ. and ChengP., A linguistic intuitionistic multi-criteria decision-making method based on the Frank Heronian mean operator and its application in evaluating coal mine safety[J], International Journal of Machine Learning and Cybernetics (2018), 1–16.
35.
DongY., XuY. and YuS., Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model[J], IEEE Transactions on Fuzzy Systems17(6) (2009), 1366–1378.
36.
DongY., ZhangG., HongW.C. and YuS., Linguistic computational model based on 2-tuples and intervals, IEEE Transactions on Fuzzy Systems21(6) (2013), 1006–1018.
37.
DongY., LiC.C. and HerreraF., Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its uses to deal with hesitant unbalanced linguistic information, Information Sciences[J]367 (2016), 259–278.
38.
DongY., LiC.C., XuY.F. and GuX., Consensus-based group decision making under multi-granular unbalanced 2-tuple linguistic preference relations, Group Decision and Negotiation[J]24 (2015), 217–242.
39.
LiC.C., DongY., HerreraF., Herrera-ViedmaE. and MartnezL., Personalized individual semantics in computing with words for supporting linguistic group decision making. An application on consensus reaching[J], Information Fusion33 (2017), 29–40.
40.
LiC.C., RodrguezR.M., MartnezL., DongY. and HerreraF., Personalized individual semantics based on consistency in hesitant linguistic group decision making with comparative linguistic expressions, Knowledge-Based Systems[J]145 (2018), 156–65.
41.
LiC.C., DongY. and HerreraF., A consensus model for large-scale linguistic group decision making with a feedback recommendation based on clustered personalized individual semantics and opposing consensus groups[J], IEEE Transactions on Fuzzy Systems27(2) (2018), 221–233.
42.
WuZ., XuJ., JiangX., et al., Two MAGDM models based on hesitant fuzzy linguistic term sets with possibility distributions: VIKOR and TOPSIS[J], Information Sciences 473 (2019), 101–120.
43.
LiuD., LiuY. and ChenX., Fermatean fuzzy linguistic set and its application in multicriteria decision making[J], International Journal of Intelligent Systems34(5) (2019), 878–894.
44.
ZhaoK.Q., Set pair and set pair analysis-a new concept and systematic analysis method[C], Proceedings of the National Conference on System Theory and Regional Planning5 (1989), 87–91.
45.
KumarK. and GargH., Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making[J], Applied Intelligence48(8) (2018), 2112–2119.
46.
GargH. and KumarK., An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making[J], Soft Computing22 (2018), 4959–4970.
47.
ZhaoK. and XuanA., Set Pair Theory-a new theory method of non-dfine and its applications[J], Systems Engineering14(1) (1996), 18–23.
48.
CaoY., ZhouH. and WangJ., An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis[J], International Journal of Machine Learning and Cybernetics9(4) (2018), 629–640.
49.
GargH. and KumarK., A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application[J], Scientia Iranica. Transaction E, Industrial Engineering25(4) (2018), 2373–2388.
50.
GargH. and KumarK., Some aggregation operators for linguistic intuitionistic fuzzy set and its application to group decision-making process using the set pair analysis[J], Arabian Journal for Science and Engineering43(6) (2018), 3213–3227.
51.
SaltonG. and McGillM.J., Introduction to modern information retrieval[M]. mcgraw-hill, 1983.
52.
WangJ., WuJ., WangJ., et al., Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems[J], Information Sciences288 (2014), 55–72.
53.
KahnemanD. and TverskyA., Prospect Theory: An analysis of decision under risk[J], Econometrica47(2) (1979), 263–291.
54.
BaoG.Y., LianX.L., HeM., et al., Improved two-tuple linguistic representation model based on new linguistic evaluation scale[J], Control and Decision25(5) (2010), 780–784.
55.
HwangC.L. and YoonK., Methods for multiple attribute decision making[J], Springer, Berlin, Heidelberg, (1981), 58–191.
56.
ChenZ.S., YangY., WangX.J., et al.Fostering Linguistic Decision-Making under Uncertainty: A Proportional Interval Type-2 Hesitant Fuzzy TOPSIS Approach Based on Hamacher Aggregation Operators and Andness Optimization Models[J], Information Sciences500 (2019), 229–258.
57.
XuZ., Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment[J], Information Sciences168(1-4) (2004), 171–184.
58.
XuZ., An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations[J], Decision Support Systems41(2) (2006), 488–499.
