The article provides a definition and properties of inclusion degree in type-two intuitionistic fuzzy sets and, on the basis of inclusion degree, gives the definition and attributes of type two intuitionistic fuzzy rough sets based on inclusion degree. At the same time, uncertainty measurement factors such as approximate accuracy, roughness, and importance are provided.
ZadehLA. The concept of a linguistic variable and its application to approximate reasoning. Inf Sci1975; 8(3): 199–249.
2.
WuDRMendelJM. Aggregation using the linguistic weighted average and interval type-2 fuzzy sets. IEEE Trans Fuzzy Syst2007; 15(6): 1145–1161.
3.
JohnRHagrasHCastilloO. Type-2 fuzzy logic and systems: dedicated to professor Jerry Mendel for his pioneering contribution. Berlin: Springer, 2018, pp. 25–47.
WuDRZhangHTHuangJ. A constrained representation theorem for well-shaped interval type-2 fuzzy sets, and the corresponding constrained uncertainty measures. IEEE Trans Fuzzy Syst2019; 27(6): 1237–1251.
6.
WuDRMendelJM. A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets. Inf Sci2009; 179(8): 1169–1192.
7.
WuDRMendelJM. A vector similarity measure for linguistic approximation: Interval type-2 and type-1fuzzy sets. Inf Sci2008; 178(2): 381–402.
8.
MendelJMJohnRIB. Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst2002; 10(2): 117–127.
9.
QinJD. A survey of type-2 fuzzy aggregation and application for multiple criteria decision making. J of Data Inf and Manag2019; 1(1/2): 17–32.
10.
ZhouSMChiclanaFJohnRI, et al.Type-2 OWA operators-aggregating type-2 fuzzy sets in soft decision making. In: 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence), Hong Kong, 01–06 June 2008, pp. 625–630.
11.
ZhouSMJohnRIChiclanaF, et al.On aggregating uncertain information by type-2 OWA operators for soft decision making. Int J Intell Syst2010; 25(6): 540–558.
12.
QinJD. Interval type-2 fuzzy Hamy mean operators and their application in multiple criteria decision making. Granul Comput2017; 2(4): 249–269.
13.
WangHHLiuPDLiuZM. Trapezoidal interval type-2 fuzzy Maclaurin symmetric mean operators and their applications to multiple attribute group decision making. Int J Uncertain Quantification2018; 8(4): 343–360.
14.
HavensTCAndersonDTKellerJM. A fuzzy Choquet integral with an interval type-2 fuzzy number-valued integrand. In: InternationalConference on Fuzzy Systems, Barcelona, 18–23 July 2010, pp. 1–8.
15.
WuYNXuCBHuangY, et al.Green supplier selection of electric vehicle charging based on Choquet integral and type-2 fuzzy uncertainty. Soft Comput2020; 24(5): 3781–3795.
16.
MelinPMartinezGE. Extension of the fuzzy sugeno integral based on generalized type-2 fuzzy logic. Berlin: Springer, 2020, pp. 29–36.
17.
TangGLChiclanaFLinXC, et al.Interval type-2 fuzzy multi-attribute decision-making approaches for evaluating the service quality of Chinese commercial banks. Knowl Base Syst2020; 193: 105–438.
18.
XuZQinJDLiuJ, et al.Sustainable supplier selection based on AHPSort II in interval type-2 fuzzy environment. Inf Sci2019; 483: 273–293.
ChenTY. A PROMETHEE-based outranking method for multiple criteria decision analysis with interval type-2 fuzzy sets. Soft Comput2014; 18(5): 923–940.
21.
UreñaRKouGWuJ, et al.Dealing with incomplete information in linguistic group decision making by means of interval type-2 fuzzy sets. Int J Intell Syst2019; 34(6): 1261–1280.
22.
HendianiSJiangLSSharifiE, et al.Multi-expert multi-criteria decision making based on the likelihoods of interval type-2 trapezoidal fuzzy preference relations. Int J Mach Learn Cybern2020; 11(12): 2719–2741.
23.
QinJDLiuXWPedryczW. A multiple attribute interval type-2 fuzzy group decision making and its application to supplier selection with extended LINMAP method. Soft Comput2017; 21(12): 3207–3226.
24.
SangXZLiuXW. An analytical solution to the TOPSISmodel with interval type-2 fuzzy sets. Soft Comput2016; 20(3): 1213–1230.
25.
ZengWYLiHX. Relationship between similarity measure and entropy of interval valued fuzzy sets. Fuzzy Set Syst2006; 157(11): 1477–1484.
26.
ZengWYGuoP. Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship. Inf Sci2008; 178(5): 1334–1342.
27.
HwangCMYangMSHungWL, et al.Similarity, inclusion and entropy measures between type-2 fuzzy sets based on the Sugeno integral. Math Comput Model2011; 53(9/10): 1788–1797.
28.
de MiguelLSantosHSesma-SaraM, et al.Type-2 fuzzy entropy sets. IEEE Trans Fuzzy Syst2017; 25(4): 993–1005.
WuDRMendelJM. Similarity measures for closed general type-2 fuzzy sets: Overview, comparisons, and a geometric approach. IEEE Trans Fuzzy Syst2019; 27(3): 515–526.
31.
McCullochJWagnerC. Measuring the directional or non-directional distance between type-1 and type-2 fuzzy sets with complex membership functions. IEEE Trans Fuzzy Syst2019; 27(7): 1506–1515.
32.
McCullochJWagnerC. On the choice of similarity measures for type-2 fuzzy sets. Inf Sci2020; 510: 135–154.
33.
ZhongLYaoLM. An ELECTRE I-based multi-criteria group decision making method with interval type-2 fuzzy numbers and its application to supplier selection. Appl Soft Comput2017; 57: 556–576.
34.
YangYYLiuXWLiuF. Trapezoidal interval type-2 fuzzy TOPSIS using alpha-cuts. Int J Fuzzy Syst2020; 22(1): 293–309.
35.
ChenSMHongJA. Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets and the TOPSIS method. IEEE Trans Syst Man Cybern Syst2014; 44(12): 1665–1673.
36.
WuTLiuXWLiuF. An interval type-2 fuzzy TOPSIS model for large scale group decision making problems with social network information. Inf Sci2018; 432: 392–410.
37.
AfsharMRShahhosseiniVSebtMH. An interval type-2 fuzzy MCDM model for work package subcontractor prequalification. Soft Comput2021; 25(1): 635–648.
38.
QinJDLiuXWPedryczW. An extended VIKOR method based on prospect theory for multiple attribute decision making under interval type-2 fuzzy environment. Knowl Base Syst2015; 86: 116–130.
39.
QinJDLiuXWPedryczW. An extended TODIM multi-criteria group decision making method for green supplier selection in interval type-2 fuzzy environment. Eur J Oper Res2017; 258(2): 626–638.
40.
WuQZhouLGChenY, et al.An integrated approach to green supplier selection based on the interval type-2 fuzzy best-worst and extended VIKOR methods. Inf Sci2019; 502: 394–417.
41.
LiuKLiuYWQinJD. An integrated ANP-VIKOR methodology for sustainable supplier selection with interval type-2 fuzzy sets. Granul Comput2018; 3(3): 193–208.
42.
TürkSDeveciMÖzcanE, et al.Interval type-2 fuzzy sets improved by simulated annealing for locating the electric charging stations. Inf Sci2021; 547: 641–666.
43.
ZhaoTXiaoJ. Type-2 intuitionistic fuzzy sets. Control Theory & Appl2012; 29(9): 1215–1222.
