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A NOVEL TRIANGULAR INTERVAL TYPE-2 INTUITIONISTIC FUZZY SETS AND THEIR AGGREGATION OPERATORS | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 5، دوره 15، شماره 5، آذر و دی 2018، صفحه 69-93 اصل مقاله (615.76 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2018.4159 | ||
نویسندگان | ||
Harish Garg ![]() | ||
School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University Patiala-147004, India | ||
چکیده | ||
The objective of this work is to present a triangular interval type-2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws. Furthermore, based on these operators, an approach to multi-criteria decision-making, in which assessments are in the form of TIT2 intuitionistic fuzzy numbers has been developed. A practical example to illustrate the decision-making process has been presented and compared their results with the existing operator results. | ||
کلیدواژهها | ||
Type-2 fuzzy set؛ Type-2 intuitionistic fuzzy sets؛ Triangular interval type-2 intuitionistic fuzzy sets؛ Multi criteria decision-making؛ Aggregation operators | ||
مراجع | ||
[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 Quantification, 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 Artificial 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, Pacific 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 Quantification, 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. | ||
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