This paper addresses an extension of the concept of topological spaces to that of hesitant fuzzy spaces. The topology is established using a conjunction and disjunction operator on hesitant fuzzy sets whose properties are discussed in the beginning. Some examples are discussed before introducing the concepts of interior and closure of a hesitant fuzzy set. The properties of these operators are verified to justify the definitions. The concepts of a hesitant fuzzy subspace topology and continuous mappings on hesitant fuzzy sets are studied. The concepts of connectedness and compactness of hesitant fuzzy topological spaces are studied and various results regarding them are proved.
Joseph A.Goguen, L-fuzzy sets, Journal of Mathematical Analysis and Applications18(1) (1967), 145–174.
3.
Jerry M.Mendel and R.I.Bob John, Type-2 fuzzy sets made simple, IEEE Transactions on Fuzzy Systems10(2) (2002), 117–127.
4.
LotfiAsker Zadeh, The concept of a linguistic variable and its application to approximate reasoningi, Information Sciences8(3) (1975), 199–249.
5.
Lotfi A.Zadeh, Fuzzy sets, Information and Control8(3) (1965), 338–353.
6.
Vincent.Torra, Hesitant fuzzy sets, International Journal of Intelligent Systems25 (2010), 529–539.
7.
Chin-LiangChang, Fuzzy topological spaces, Journal of Mathematical Analysis and Applications24(1) (1968), 182–190.
8.
ErdalEkici, More on θ-compact fuzzy topological spaces, Chaos, Solitons & Fractals27(5) (2006), 1157–1161.
9.
C.A.S.Silva and R.R.Landim, Fuzzy spaces topology change and bh thermodynamics.In Journal of Physics: Conference Series, volume 490, page 012012. IOP Publishing, 2014.
10.
MeimeiXia and ZeshuiXu, Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning52(3) (2011), 395–407.
11.
WenyingWu, YingLi, ZhiweiNi, FeifeiJin and XuhuiZhu, Probabilistic intervalvalued hesitant fuzzy information aggregation operators and their application to multi-attribute decision making, Algorithms11(8) (2018), 120.
12.
WenyuYu, ZhenZhang, QiuyanZhong and LeileiSun, Extended todim for multicriteria group decision making based on unbalanced hesitant fuzzy linguistic term sets, Computers & Industrial Engineering114 (2017), 316–328.
13.
ZeshuiXu and MeimeiXia, On distance and correlation measures of hesitant fuzzy information, International Journal of Intelligent Systems26(5) (2011), 410–425.
14.
Zhi-yongBai, Distance similarity measures for interval-valued hesitant fuzzy sets and their application in multicriteria decision making, Journal of Decision Systems22(3) (2013), 190–201.
15.
GuiwuWei, RuiLin and HongjunWang, Distance and similarity measures for hesitant interval-valued fuzzy sets, Journal of Intelligent & Fuzzy Systems27(1) 2014.
16.
DeqingLi, WenyiZeng and YibinZhao, Note on distance measure of hesitant fuzzy sets, Information Sciences321 (2015), 103–115.
17.
XiaoluZhang and ZeshuiXu, Novel distance and similarity measures on hesitant fuzzy sets with applications to clustering analysis, Journal of Intelligent & Fuzzy Systems28(5) (2015), 2279–2296.
18.
NaChen, ZeshuiXu and MeimeiXia, Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis, Applied Mathematical Modelling37(4) (2013), 2197–2211.
19.
BinZhu and ZeshuiXu, Regression methods for hesitant fuzzy preference relations, Technological and Economic Development of Economy19(sup1) (2013), S214-S227.
20.
ZhenZhang, XinyueKou and QingxingDong, Additive consistency analysis and improvement for hesitant fuzzy preference relations, Expert Systems With Applications98 (2018), 118–128.
21.
ZhenZhang, XinyueKou, WenyuYu and ChonghuiGuo, On priority weights and consistency for incomplete hesitant fuzzy preference relations, Knowledge-Based Systems143 (2018), 115–126.
22.
HuchangLiao, ZeshuiXu and MeimeiXia, Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making, International Journal of Information Technology & Decision Making13(01) (2014), 47–76.
23.
JianLi, Jian-qiangWang and Jun-huaHu, Consensus building for hesitant fuzzy preference relations with multiplicative consistency, Computers & Industrial Engineering128 (2019), 387–400.
24.
Cong-CongLi, Rosa M.Rodríguez, LuisMartínez, YuchengDong, and FranciscoHerrera, Consistency of hesitant fuzzy linguistic preference relations: An interval consistency index, Information Sciences432 (2018), 347–361.
25.
K.V.Babitha and SunilJacob John, Hesitant fuzzy soft sets, Journal of New Results in Science2(3) 2013.
26.
XindongPeng and YongYang, Interval-valued hesitant fuzzy soft sets and their application in decision making, Fundamenta Informaticae141(1) (2015), 71–93.
27.
XindongPeng and JingguoDai, Hesitant fuzzy soft decision making methods based on waspas, mabac and copras with combined weights, Journal of Intelligent & Fuzzy Systems33(2) (2017), 1313–1325.
28.
HarishGarg and RishuArora, Distance and similarity measures for dual hesitant fuzzy soft sets and their applications in multicriteria decision making problem, International Journal for Uncertainty Quantification7(3), 2017.
29.
RishuArora and HarishGarg, A robust correlation coefficient measure of dual hesitant fuzzy soft sets and their application in decision making, Engineering Applications of Artificial Intelligence72 (2018), 80–92.
30.
XindongPeng, JingguoDai and LinLiu, Interval-valued dual hesitant fuzzy information aggregation and its application in multiple attribute decision making, International Journal for Uncertainty Quantification8(4), 2018.
31.
JianLi and Jian-qiangWang, Multi-criteria decision-making with probabilistic hesitant fuzzy information based on expected multiplicative consistency, Neural Computing and Applications (2018), 1–19.
32.
XiaokangWang, JianqiangWang and HongyuZhang, Distance-based multicriteria group decision-making approach with probabilistic linguistic term sets, Expert Systems (2018), e12352.
33.
R.Lowen, Fuzzy topological spaces and fuzzy compactness, Journal of Mathematical Analysis and Applications56(3) (1976), 621–633.
34.
RobertLowen, Initial and final fuzzy topologies and the fuzzy tychonoff theorem, Journal of Mathematical Analysis and Applications58(1) (1977), 11–21.
35.
RobertLowen, A comparison of different compactness notions in fuzzy topological spaces, Journal of Mathematical Analysis and Applications64(2) (1978), 446–454.
36.
T.E.Gantner, R.C.Steinlage and R.H.Warren, Compactness in fuzzy topological spaces, Journal of Mathematical Analysis and Applications62(3) (1978), 547–562.
37.
WangGuojun, A new fuzzy compactness defined by fuzzy nets, Journal of Mathematical Analysis and Applications94(1) (1983), 1–23.
38.
D.Deepak and SunilJacob John, Hesitant fuzzy rough sets through hesitant fuzzy relations, Annals of Fuzzy Mathematics and Informatics8(1) (2014), 33–46.
39.
Ronald R.Yager, Pythagorean membership grades in multicriteria decision making, IEEE Transactions on Fuzzy Systems22(4) (2014) 958–965.
40.
BuiCông Cng, Picture fuzzy sets, Journal of Computer Science and Cybernetics30(4) (2014), 409.
41.
Ronald R.Yager, Generalized orthopair fuzzy sets, IEEE Transactions on Fuzzy Systems25(5) (2017), 1222–1230.
