Sports field is important material foundation which popularizes 〈〈National Fitness Program〉〉 and 〈〈the Olympics Glory Program〉〉 in our country. It is an importance carrier of the development of our country’s sports undertaking. In the meantime, the development scale and level of the sports field is one of importance sign of the national economies development level and social civilization degree. There exists difference in the society, economy, culture...etc. in our country, which causes the “out of line” of sports field construction and development in each region.And the “out of line” of the structure of regional sports field in our country is the key problem that restricts the development of the region sports and is also the key problem that restricts the development of our country’s sports undertaking. In this paper, we first introduce some operations on the intuitionistic fuzzy sets, such as Hamacher sum, Hamacher product, Hamacher exponentiation, etc., and further develop the intuitionistic fuzzy Hamacher correlated averaging (IFHCA) operator. The prominent characteristic of the operators is that they can not only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We have applied the IFHCA operators to multiple attribute decision making with intuitionistic fuzzy information. Finally, a practical example for evaluating the management performance of the sports sites is used to illustrate the developed procedures.
AtanassovK., Intuitionistic fuzzy sets, Fuzzy Sets and Systems20 (1986), 87–96.
2.
AtanassovK., More on intuitionistic fuzzy sets, Fuzzy Sets and Systems33 (1989), 37–46.
3.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–356.
4.
ChenT.Y., WangH.P. and LuY.Y., A multicriteria group decision-making approach based on Intuitionistic fuzzy sets: A comparative perspective, Expert Systems with Applications38 (2011), 7647–7658.
5.
BustinceH., Construction of intuitionistic fuzzy relations with predetermined properties, Fuzzy Sets and Systems109 (2000), 379–403.
6.
LiuH.W., Multi-criteria decision-making methods based on intuitionistic fuzzy sets, European Journal of Operational Research179(1) (2007), 220–233.
7.
GongZ.W., LiL.S., ForrestJ. and ZhaoY., The optimal priority models of the intuitionistic fuzzy preference relation and their application in selecting industries with higher meteorological sensitivity, Expert Systems with Applications38 (2011), 4394–4402.
8.
WeiG.W., Approaches to interval intuitionistic trapezoidal fuzzy multiple attribute decision making with incomplete weight information, International Journal of Fuzzy Systems17(3) (2015), 484–489.
9.
WeiG.W., WangJ.M. and ChenJ., Potential optimality and robust optimality in multiattribute decision analysis with incomplete information: A comparative study, Decision Support Systems55(3) (2013), 679–684.
10.
GuiwuWei, XiaofeiZhao, RuiLin and HongjunWang, Uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making, Applied Mathematical Modelling37 (2013), 5277–5285.
11.
WeiG.W. and ZhaoX.F., Induced hesitant interval-valued fuzzy einstein aggregation operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems24 (2013), 789–803.
12.
WeiG.W., Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making, Expert Systems with Applications38(9) (2011), 11671–11677.
13.
YeJ., Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment, European Journal of Operational Research205 (2010), 202–204.
14.
YeJ., Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of Intuitionistic fuzzy sets, Applied Mathematical Modelling34 (2010), 3864–3870.
15.
WeiG.W. and ZhaoX.F., Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making, Expert Systems with Applications39(2) (2012), 2026–2034.
16.
GrzegorzewskiP., Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric, Fuzzy Sets and Systems148 (2004), 319–328.
17.
HongD.H. and ChoiC.H., Multicriteria fuzzy problems based on vague set theory, Fuzzy Sets and Systems114 (2000), 103–113.
18.
YagerR., Some aspects of intuitionistic fuzzy sets, Fuzzy Optimization and Decision Making8 (2009), 67–90.
19.
YeJ., Expected value method for intuitionistic trapezoidal fuzzy multicriteria decision-making problems, Expert Systems with Applications38 (2011), 11730–11734.
20.
YeJ., Fuzzy cross entropy of Intuitionistic fuzzy sets and its optimal decision-making method based on the weights of alternatives, Expert Systems with Applications38 (2011), 6179–6183.
21.
XuZ.S., Intuitionistic preference relations and their application in group decision making, Information Science177(11) (2007), 2363–2379.
XuZ.S. and YagerR.R., Some geometric aggregation operators based on intuitionistic fuzzy sets, International Journal of General System35 (2006), 417–433.
24.
XuZ.S. and YagerR.R., Dynamic intuitionistic fuzzy multi-attribute decision making, International Journal of Approximate Reasoning48(1) (2008), 246–262.
25.
WeiG.W., Some geometric aggregation functions and their application to dynamic multiple attribute decision making in intuitionistic fuzzy setting, International Journal of Uncertainty, Fuzziness and Knowledge- Based Systems17(2) (2009), 179–196.
26.
WeiG.W., Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making, Applied Soft Computing10(2) (2010), 423–431.
27.
WeiG.W. and ZhaoX.F., Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making, Expert Systems with Applications39(2) (2012), 2026–2034.
28.
ChenS.M. and TanJ.M., Handling multicriteria fuzzy decision-making problems based on vague set theory, Fuzzy Sets and Systems67 (1994), 163–172.
29.
HongD.H. and ChoiC.H., Multicriteria fuzzy problems based on vague set theory, Fuzzy Sets and Systems114 (2000), 103–113.
30.
DeschrijverG., CornelisC. and KerreE.E., On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE Transactions on Fuzzy Systems12 (2004), 45–61.
31.
RoychowdhuryS. and WangB.H., On generalized Hamacher families of triangular operators, International Journal of Approximate Reasoning19 (1998), 419–439.
32.
DeschrijverG. and KerreE.E., A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms, Notes on Intuitionistic Fuzzy Sets8 (2002), 19–27.
33.
HamacharH., Uber logische verknunpfungenn unssharfer Aussagen undderen Zugenhorige Bewertungsfunktione, in: Trappl, Klir, Riccardi, (Eds.), Progress in Cybernatics and systems research, vol. 3, Hemisphere, Washington DC, 1978, pp 276–288.
34.
Ju-YingHuang, Intuitionistic fuzzy hamacher aggregation operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems27(1) (2014), 505–513.
35.
GrabischM., MurofushiT. and SugenoM., Fuzzy Measure and Integrals, Physica-Verlag, New York, 2000.
36.
Ling-GangRan and GuiwuWei, Uncertain prioritized operators and their application to multiple attribute group decision making, Technological and Economic Development of Economy21(1) (2015), 118–139.
37.
YeJ., Fuzzy cross entropy of interval-valued intuitionistic fuzzy sets and its optimal decision-making method based on the weights of alternatives, Expert Systems with Applications38 (2011), 6179–6183.
38.
LiuF. and YuanX.H., fuzzy number intuitionistic fuzzy set, Fuzzy Systems and Mathematics21(1) (2007), 88–91.
39.
LinRui, GuiwuWei, HongjunWang and XiaofeiZhao, Choquet integrals of weighted triangular fuzzy linguistic information and their applications to multiple attribute decision making, Journal of Business Economics and Management15(5) (2014), 795–809.
40.
WangX.F., Fuzzy number intuitionistic fuzzy geometric aggregation operators and their application to decision making, Control and Decision23(6) (2008), 607–612.
41.
RuiLin, XiaofeiZhao, HongjunWang and GuiwuWei, Hesitant fuzzy linguistic aggregation operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems27 (2014), 49–63.
42.
RuiLin, XiaofeiZhao* and GuiwuWei, Models for selecting an ERP system with hesitant fuzzy linguistic information, Journal of Intelligent and Fuzzy Systems26(5) (2014), 2155–2165.
XuyangLi and GuiwuWei, GRA method for multiple criteria group decision making with incomplete weight information under hesitant fuzzy setting, Journal of Intelligent and Fuzzy Systems27 (2014), 1095–1105.
45.
XuZ.S. and ChenJ., An overview of distance and similarity measures of intuitionistic fuzzy sets, International Journal of Uncertainty Fuzziness and Knowledge-Based Systems16 (2008), 529–555.
46.
Xian-PingJiang and Gui-WuWei, Some Bonferroni mean operators with 2-tuple linguistic information and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems27 (2014), 2153–2162.
47.
LiD.F., Extension of the LINMAP for multiattribute decision making under Atanassov’s intuitionistic fuzzy environment, Fuzzy Optimization and Decision Making7 (2008), 17–34.
48.
LiD.F., A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems, Computers & Mathematics with Applications60 (2010), 1557–1570.
49.
ChenT.Y. and LiC.H., Determining objective weights with intuitionistic fuzzy entropy measures: A comparative analysis, Information Sciences180 (2010), 4207–4222.
WangJ.Q., LiK.J. and ZhangH.Y., Interval-valued intuitionistic fuzzy multi-criteria decision-making approach based on prospect score function, Knowledge-Based Systems27 (2012), 119–125.
52.
YaoOuyang and WitoldPedrycz, A new model for intuitionistic fuzzy multi-attributes decision making, European Journal of Operational Research249(2) (2016), 677–682.
53.
Laura DeMiguel, HumbertoBustince, JavierFernández, EstebanInduráin, AnnaKolesárová and RadkoMesiar, Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making, Information Fusion27 (2016), 189–197.
54.
Shyi-MingChen, Shou-HsiungCheng and Chu-HanChiou, Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology, Information Fusion27 (2016), 215–227.
55.
MihaiGabroveanu, IonIancu and MirelCosulschi, An Atanassov’s intuitionistic fuzzy reasoning model, Journal of Intelligent and Fuzzy Systems30(1) (2016), 117–128.
