Complex intuitionistic fuzzy sets (CIFSs) can represent problems in multicriteria decision-making that involve uncertainty and periodicity of semantics at the same time. CIFSs handle two-dimensional information that requires a long time and a huge number of calculations and processes. In this research, the complex intuitionistic shadowed set (CISHS) is defined as a novel threshold approximation method. CISHS is introduced to simplify processing and enhance the interpretation of outcomes obtained from CIFSs. The main idea of constructing CISHS is adding a complex non-membership function to the complex shadowed set (CSHS) range. Additionally, the basic operations, specifically complement, union, and intersection on CISHSs, are introduced. The properties of CISHSs are defined as null, absolute, and subset. Finally, an application to demonstrate the effectiveness of the proposed approach is employed by using an adaptive algorithm with CISHSs.
AbuhijlehE. A.Massa’dehM.SheimatA.AlkouriA. (2021). Complex fuzzy groups based on rosenfeld’s approach. WSEAS Transactions on Mathematics, 20(August), 368–377. https://doi.org/10.37394/23206.2021.20.38
2.
AkramM.ShahzadS.ButtA.KhaliqA. (2013). Intuitionistic fuzzy logic control for heater fans. Mathematics in Computer Science, 7(3), 367–378. https://doi.org/10.1007/s11786-013-0161-x
3.
Al-MasarwahA.AhmadA. G.MuhiuddinG.Al-KadiD. (2021). Generalized m-polar fuzzy positive implicative ideals of BCK-algebras. Journal of Mathematics, 2021. https://doi.org/10.1155/2021/6610009
4.
Al-SharoaD. (2023). (1, 2, 1, 2)-complex intuitionistic fuzzy subgroups and its algebraic structure. AIMS Math, 8(4), 8082–8116. https://doi.org/10.3934/math.2023409
AlsharoD.AbuteenE.AlkouriA. U. M. J. S.AlkhasawnehM.Al-ZubiF. M. A. (2024). Complex shadowed set theory and its application in decision-making problems. AIMS Math, 9(6), 16810–16825. https://doi.org/10.3934/math.2024815
GargH.RaniD. (2019). Some generalized complex intuitionistic fuzzy aggregation operators and their application to multicriteria decision-making process. Arabian Journal for Science and Engineering, 44(3), 2679–2698. https://doi.org/10.1007/s13369-018-3413-x
12.
HlaelN. (2024). Operations on Intuitionistic Shadowed Sets with an Application. M.S. thesis, Ajloun National Univ., Ajloun, Jordan.
13.
KozaeM.ShokryM.OmranM. (2020). Intuitionistic fuzzy set and its application in corona covid-19. Applied and Computational Mathematics, 9(5), 146. https://doi.org/10.11648/j.acm.20200905.11
14.
MaX.ZhanJ.KahanM.ZeeshanM.AnisS.AwanA. S. (2019). Complex fuzzy sets with applications in decision-making. Computational and Applied Mathematics, 38, 149–183. https://doi.org/10.22111/ijfs.2022.7093
15.
NarasimhanR. (1979). A fuzzy subset characterization of a site-selection problem Ram. 10(4), 618–628.
16.
PedryczW. (1998). Shadowed sets: Representing and processing fuzzy sets. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 28(1), 103–109.
RaniD.GargH. (2017). Distance measures between the complex intuitionistic fuzzy sets and its applications to the decision-making process. International Journal for Uncertainty Quantification, 7, 423–439.
19.
SobhiS.DickS. (2023). An investigation of complex fuzzy sets for large-scale learning. Fuzzy Sets and Systems, 471, 108660. https://doi.org/10.1016/j.fss.2023.108660
WójcikW.MezhiievskaI.Pavlov S. V.LewandowskiT.VlasenkoO. V.MaslovskyiV. VolosovychO.KobylianskaI.MoskovchukO. OvcharukV.LewandowskaA. (2023). Medical fuzzy-expert system for assessment of the degree of anatomical lesion of coronary arteries. International Journal of Environmental Research and Public Health, 20(2). https://doi.org/10.3390/ijerph20020979
22.
YangJ.YaoY. (2021). A three-way decision based construction of shadowed sets from atanassov intuitionistic fuzzy sets. Information Sciences, 577, 1–21. https://doi.org/10.1016/j.ins.2021.06.065
23.
YueX.ZhouJ.YaoY.MiaoD. (2020). Shadowed neighborhoods based on fuzzy rough transformation for three-way classification. IEEE Transactions on Fuzzy Systems, 28(5), 978–991. https://doi.org/10.1109/TFUZZ.2020.2979365
24.
ZadehL. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
25.
ZhangY.YaoJ. T. (2020). Game theoretic approach to shadowed sets: A three-way tradeoff perspective. Information Sciences, 507, 540–552. https://doi.org/10.1016/j.ins.2018.07.058
