[1] K. Atanassov, Intuitionistic Fuzzy Sets, Theory and Applications, Physica-Verlag, Heidel-
berg, 1999.
[2] K. Atanassov and G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Sys-
tems, 31(3) (1989), 343 { 349.
[3] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87 { 96.
[4] O. Castillo, P. Melin, R. Tsvetkov and K. Atanassov, Short remark on interval type-2 fuzzy
sets and intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 20 (2) (2014), 1 { 5.
[5] S. M. Chen and L. W. Lee, Fuzzy multiple attributes group decision-making based on the
ranking values and the arithmetic operations of interval type - 2 fuzzy sets, Expert Systems
with Applications, 37 (1) (2010), 824 { 833.
[6] S. M. Chen, M. W. Yang, L. W. Lee and S. W. Yang, Fuzzy multiple attributes group decision-
making based on ranking interval type-2 fuzzy sets, Expert Systems with Applications, 39 (5)
(2012), 5295{5308.
[7] S. M. Chen, M. W. Yang, S. W. Yang, T. W. Sheu and C. J. Liau, Multicriteria fuzzy decision
making based on interval-valued intuitionistic fuzzy sets, Expert Systems with Applications,
39(15) (2012), 12085 { 12091.
[8] K. P. Chiao, Multiple criteria group decision making with triangular interval type-2 fuzzy
sets, 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011), (2011),
2575 - 2582.
[9] G. Deschrijver and E. Kerre, A generalization of operators on intuitionistic fuzzy sets using
triangular norms and conorms, Notes on Intuitionistic Fuzzy sets, 8(1) (2002), 19 {27.
[10] M. J. Frank, On the simultaneous associativity of F(x; y) and x + y F(x; y), Aequationes
Mathematicae, 19(1) (1979), 194 { 226.
[11] H. Garg, Generalized intuitionistic fuzzy interactive geometric interaction operators using
Einstein t-norm and t-conorm and their application to decision making, Computer and In-
dustrial Engineering, 101 (2016), 53 { 69.
[12] H. Garg, Some picture fuzzy aggregation operators and their applications to multicriteria
decision-making, Arabian Journal for Science and Engineering, 42(12) (2017), 5275 { 5290.
[13] H. Garg, A new improved score function of an interval-valued Pythagorean fuzzy set based
TOPSIS method, International Journal for Uncertainty Quantifi cation, 7 (2017), 463 - 474.
[14] H. Garg, Generalized intuitionistic fuzzy multiplicative interactive geometric operators and
their application to multiple criteria decision making, International Journal of Machine
Learning and Cybernetics, 7(6) (2016), 1075 { 1092.
[15] H. Garg, A new generalized improved score function of interval-valued intuitionistic fuzzy
sets and applications in expert systems, Applied Soft Computing, 38 (2016), 988 { 999.
[16] H. Garg, A new generalized Pythagorean fuzzy information aggregation using Einstein oper-
ations and its application to decision making, International Journal of Intelligent Systems,
31(9) (2016), 886 { 920.
[17] H. Garg, Some series of intuitionistic fuzzy interactive averaging aggregation operators,
SpringerPlus, doi: 10.1186/s40064-016-2591-9, 5(1) (2016), 999.
[18] H. Garg, Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-
norm and t-conorm for multicriteria decision-making process, International Journal of Intel-
ligent Systems, 32(6) (2017), 597 { 630.
[19] H. Garg, Novel intuitionistic fuzzy decision making method based on an improved operation
laws and its application, Engineering Applications of Artifi cial Intelligence, 60 (2017), 164 {
174.
[20] H. Garg, N. Agarwal and A. Choubey, Entropy based multi-criteria decision making method
under fuzzy environment and unknown attribute weights, Global Journal of Technology and
Optimization, 6(3) (2015), 13 { 20.
[21] D. K. Jana, Novel arithmetic operations on type-2 intuitionistic fuzzy and its applications to
transportation problem, Pacifi c Science Review A: Natural Science and Engineering, 18(3)
(2016), 178 { 189.
[22] K. Kumar and H. Garg, TOPSIS method based on the connection number of set pair anal-
ysis under interval-valued intuitionistic fuzzy set environment, Computational and Applied
Mathematics, 37(2) (2018), 1319 - 1329.
[23] L. W. Lee and S. M. Chen, Fuzzy multiple attributes group decision-making based on the
extension of TOPSIS method and interval type - 2 fuzzy sets, in: Proceedings of 2008 Inter-
national Conference on Machine Learning and Cybernetics, IEEE, (2008), 1-7.
[24] P. Liu, Some Hamacher aggregation operators based on the interval-valued intuitionistic
fuzzy numbers and their application to group decision making, IEEE Transactions on Fuzzy
Systems, 22(1) (2014), 83 { 97.
[25] J. M. Mendel, R. I. John and F. Liu, Interval type-2 fuzzy logic systems made simple, IEEE
Transactions on Fuzzy Systems, 14(6) (2006), 808 { 821.
[26] J. M. Mendel and G. C. Mouzouris, Type-2 fuzzy logic systems, IEEE Transactions on Fuzzy
Systems, 7 (1999), 643 { 658.
[27] J. M. Mendel and H. Wu, Type-2 fuzzistics for symmetric interval type-2 fuzzy sets: Part 1,
forward problems, IEEE Transactions on Fuzzy Systems, 14(6) (2006), 781{792.
[28] J. M. Mendel and H. Wu, Type-2 fuzzistics for symmetric interval type-2 fuzzy sets: Part 2,
inverse problems, IEEE Transactions on Fuzzy Systems, 15(2) (2007), 301{308.
[29] Nancy and H. Garg, Novel single-valued neutrosophic decision making operators under Frank
norm operations and its application, International Journal for Uncertainty Quantifi cation,
6(4) (2016), 361 { 375.
[30] J. Qin and X. Liu, Frank Aggregation Operators for Triangular Interval Type-2 Fuzzy Set
and Its Application in Multiple Attribute Group Decision Making, Journal of Applied Math-
ematics, Article ID 923213, doi:10.1155/2014/923213, (2014), 24 pages.
[31] J. Qin, X. Liu and W. Pedrycz, Frank aggregation operators and their application to hesitant
fuzzy multiple attribute decision making, Applied Soft Computing, 41 (2016), 428 { 452.
[32] S. Singh and H. Garg, Distance measures between type-2 intuitionistic fuzzy sets and their
application to multicriteria decision-making process, Applied Intelligence, 46(4) (2017), 788
{ 799.
[33] W.Wang and X. Liu, Intuitionistic Fuzzy information Aggregation using Einstein operations,
IEEE Transactions on Fuzzy Systems, 20(5) (2012), 923 { 938.
[34] W. Wang, X. Liu and Y. Qin, Multi-attribute group decision making models under interval
type-2 fuzzy environment, Knowledge-Based Systems, 30 (2012), 121{128.
[35] Y. Xu, H. Wang and J. M. Merigo, Intuitionistic fuzzy Einstein Choquet intergral operators
for multiple attribute decision making, Technological and Economic Development of Economy,
20(2) (2014), 227 { 253.
[36] Z. S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Transactions of Fuzzy Systems,
15(6) (2007), 1179 { 1187.
[37] Z. S. Xu and R. R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy
sets, International Journal of General Systems, 35(4) (2006), 417 { 433.
[38] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{353.
[39] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-
1, Information Science, 8 (1975), 199{249.
[40] T. Zhao and J. Xia, Type-2 intuitionistic fuzzy sets, Control Theory & Applications, 29(9)
(2012), 1215 { 1222.
)