In this manuscript, we introduce a multi-criteria decision-making (MCDM) method under T-spherical fuzzy set environment. Firstly, we propose a method to use the correlation coefficient and standard deviation (CCSD) method to determine the attribute weight under T-spherical fuzzy environment, when the attribute weight information is completely unknown or partially unknown. Secondly, we introduce a T-spherical fuzzy complex proportional assessment (COPRAS) method. Finally, a numerical example is given to illustrate the application of the T-spherical fuzzy COPRAS method, and some comparative analysis is carried out to verify the feasibility and effectiveness of the proposed method.
ZadehL.A., Fuzzy Sets[J], Information and Control8(3) (1965), 338–353.
2.
AtanassovK., Intuitionistic fuzzy sets[J], Fuzzy Sets and Systems20(1) (1986), 87–96.
3.
AtanassovK., More on intuitionistic fuzzy sets[J], Fuzzy Sets and Systems33(1) (1989), 37–46.
4.
YagerR.R., Pythagorean Fuzzy Subsets, Joint World Congress of the Internationa Fuzzy Systems Association (IFSA) / Annual Meeting of the North-American-Fuzzy-Information-Processing-Society (NAFIPS), Edmonton, CANADA, 2013.
HuangC., LinM.W. and XuZ.S., Pythagorean fuzzy MULTIMOORA method based on distance measure and score function: its application in multicriteria decision making process[J], Knowledge And Information Systems62(11) (2020), 4373–4406.
7.
CuongB. and KreinovichV., Picture fuzzy sets-a new concept for computational intelligence problems, in Proceedings of the 2013 Third World Congress on Information and Communication Technologies (WICT), Hanoi,Vietnam, 2013.
8.
CuongB. and HaiP.V., Some fuzzy logic operators for picture fuzzy sets, in: Seventh International Conference on Knowledge and Systems Engineering(KSE), Ho Chi Minh City, VIETNAM, 2015.
9.
MahmoodT., UllahK., KhanQ. and JanN., An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets[J], Neural Computing and Applications31(11) (2019), 7041–7053.
10.
GargH., MunirM., UllahK., MahmoodT. and JanN., Algorithm for T-Spherical Fuzzy Multi-Attribute Decision Making Based on Improved Interactive Aggregation Operators[J], Symmetry-Basel10(12) (2018), 670.
11.
UllahK., MahmoodT. and JanN., Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognition[J], Symmetry-Basel10(6) (2018), 193.
12.
ZengS.Z., GargH., MunirM. and Mahmood.T., A Multi-Attribute Decision Making Process with Immediate Probabilistic Interactive Averaging Aggregation Operators of T-Spherical Fuzzy Sets and Its Application in the Selection of Solar Cells[J], Energies12(23) (2019), 4436.
13.
WuM.Q., ChenT.Y. and FanJ.P., Divergence Measure of T-Spherical Fuzzy Sets and its Applications in Pattern Recognition[J], IEEE ACCESS8 (2020), 10208–10221.
14.
LiuP.D., KhanQ., MahmoodT. and HassanN., T-Spherical Fuzzy Power Muirhead Mean Operator Based on Novel Operational Laws and Their Application in Multi-Attribute Group Decision Making[J], IEEE Access7 (2019), 22613–22632.
15.
ZedamL., JanN., RakE., MahmoodT. and UllahK., An Approach Towards Decision-Making and Shortest Path Problems Based on T-Spherical Fuzzy Information[J], International Journal of Fuzzy Systems22(5) (2020), 1521–1534.
16.
UllahK., GargH., MahmoodT., JanN. and AliZ., Correlation coefficients for T-spherical fuzzy sets and their applications in clustering and multi-attribute decision making[J], Soft Computing24(3) (2020), 1647–1659.
17.
UllahK., MahmoodT. and GargH., Evaluation of the Performance of Search and Rescue Robots Using T-spherical Fuzzy Hamacher Aggregation Operators[J], Nternational Journal of Fuzzy Systems22(2) (2020), 570–582.
18.
WuM.Q., ChenT.Y. and FanJ.P., Similarity Measures of T-Spherical Fuzzy Sets Based on the Cosine Function and Their Applications in Pattern Recognition[J], IEEE Access8 (2020), 98181–98192.
19.
MunirM., KalsoomH., UllahK. and MahmoodT., T-Spherical Fuzzy Einstein Hybrid Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems[J], Symmetry-Basel12(3) (2020), 365.
20.
KhanQ., GwakJ., ShahzadM. and AlamM.K., A Novel Approached Based on T-Spherical Fuzzy Schweizer-Sklar Power Heronian Mean Operator for Evaluating Water Reuse Applications under Uncertainty[J], Sustainability13(13) (2021), 7108.
21.
MunirM., MahmoodT. and HussainA., Algorithm for T-spherical fuzzy MADM based on associated immediate probability interactive geometric aggregation operators[J], Artificial Intelligence Review54(8) (2021), 6033–6061.
22.
LiuP.D. and WangD.Y., An Extended Taxonomy Method Based on Normal T-Spherical Fuzzy Numbers for Multiple-Attribute Decision-Making[J], International Journal of Fuzzy Systems (2021). Doi: 10.1007/s40815-021-01109-7.
23.
MahmoodT., WarraichM.S., AliZ. and PamucarD., Generalized MULTIMOORA method and Dombi prioritized weighted aggregation operators based on T-spherical fuzzy sets and their applications[J], International Journal of Intelligent Systems36(9) (2021), 4659–4692.
24.
GargH., UllahK., MahmoodT., HassanN. and JanN., T-spherical fuzzy power aggregation operators and their applications in multi-attribute decision making[J], Journal of Ambient Intelligence and Humanized Computing12(10) (2021), 9067–9080.
25.
JuY.B., LiangY.Y., LuoC., DongP.W., GonzalezE.D.R.S. and WangA., T-spherical fuzzy TODIM method for multi-criteria group decision-making problem with incomplete weight information[J], Soft Computing25(4) (2020), 2981–3001.
26.
OpricovicS. and DucksteinL., Multiobjective optimisation in river basin development[J],:, Water Resources Research16(1), 14–20.
27.
YamazakiM., IshibeK., YamashitaS., MiyamotoI., KuriharaM. and ShindoH., An analysis of obstructive factors to welfare service using DEMATEL method[J], Reports of the Faculty of Engineering48 (1997), 25–30.
28.
ErtugrulI. and OztasT., The application of sewing machine selection with the multi-objective optimization on the basis of ratio analysis method (MOORA) in apparel sector[J], Tekstil ve Konfeksiyon25(1) (2015), 80–85.
29.
ZavadskasE.K., KaklauskasA., PeldschusF. and TurskisZ., Multi-attribute assessment of road design solutions by using the COPRAS method[J], Baltic Journal of Road and Bridge Engineering2(4) (2007), 195–203.
30.
ZavadskasE.K. and TurskisZ., A new additive ratio assessment (ARAS) method in multi-criteria decision-making[J], Technological and Economic Development of Economy16(2) (2010), 159–172.
31.
ZavadskasE.K., AntuchevicieneJ., SaparauskasJ. and TurskisZ., MCDM methods WASPAS and MULTIMOORA: Verification of robustness of methods when assessing alternative solutions[J], Economic Computation and Economic Cybernetics Studies and Research47(2) (2013), 5–20.
32.
GomesL.F.A.M. and RangelL.A.D., An application of the TODIM method to the multicriteria rental evaluation of residential properties[J], European Journal of Operational Research193(1) (2009), 204–211.
33.
Keshavarz GhorabaeeM., AmiriM., ZavadskasE.K., TurskisZ. and AntuchevicieneJ., Stochastic EDAS method for multi-criteria decision-making with normally distributed data[J], Journal of Intelligent & Fuzzy Systems33(3) (2017), 1627–1638.
34.
LaiY.J., LiuT.Y. and HwangC.L., TOPSIS for MODM[J], European Journal of Operational Research76(3) (1994), 486–500.
35.
LinM.W., WangH.B. and XuZ.S., TODIM-based multi-criteria decision-making method with hesitant fuzzy linguistic term sets[J], Artificial Intelligence Review53(5) (2020), 3647–3671.
36.
SimicV., LazarevicD. and DobrodolacM., Picture fuzzy WASPAS method for selecting last-mile delivery mode: a case study of Belgrade[J], European Transport Research Review13(1) (2021), 43.
37.
DemircanM.L. and AcarbayA., Evaluation of software development suppliers in banking sector using neutrosophic fuzzy EDAS[J], Journal of Intelligent & Fuzzy Systems42(1) (2022), 389–400.
38.
AlipourM., HafeziR., RaniP., HafeziM. and MardaniA., A new Pythagorean fuzzy-based decision-making method through entropy measure for fuel cell and hydrogen components supplier selection[J], Energy234 (2021), 121208.
39.
KrishankumarR., GargH., ArunK., SahaA., RavichandranK.S. and KarS., An integrated decision-making COPRAS approach to probabilistic hesitant fuzzy set information[J], Complex & Intelligent Systems7(5) (2021), 2281–2298.
40.
WeiG.W., WuJ., GuoY.F., WangJ. and WeiC., An extended COPRAS model for multiple attribute group decision making based on single-valued neutrosophic 2-tuple linguistic environment[J], Technological and Economic Development of Economy27(2) (2021), 353–368.
41.
DarkoA.P. and LiangD.C., An extended COPRAS method for multiattribute group decision making based on dual hesitant fuzzy Maclaurin symmetric mean[J], International Journal of Intelligent Systems35(6) (2020), 1021–1068.
42.
BuyukozkanG. and GocerF., A Novel Approach Integrating AHP and COPRAS Under Pythagorean Fuzzy Sets for Digital Supply Chain Partner Selection[J], IEEE Transactions on Engineering Management68(5) (2021), 1486–1503.
43.
YucenurG.N., CaylakS., GonulG. and PostalciogluM., An integrated solution with SWARA & COPRAS methods in renewable energy production: City selection for biogas facility[J], Renewable Energy145 (2020), 2587–2597.
44.
YuanY.Y., XuZ.S. and ZhangY.X., The DEMATEL-COPRAS hybrid method under probabilistic linguistic environment and its application in Third Party Logistics provider selection[J], Fuzzy Optimization and Decision Making (2021). Doi: 0.1007/s10700-021-09358-9.
45.
WangY.M. and LuoY., Integration of correlations with standard deviations for determining attribute weights in multiple attribute decision making[J], Mathematical and Computer Modelling51(1-2) (2010), 1–12.
46.
MirM.S.S., AfzaliradM. and GhorbanzadehM., A robust fuzzy hybrid MCDM ranking method for optimal selection of lithium extraction process from brine and seawater[J], Minerals Engineering169 (2021), 106957.
47.
DahooieJ.H., HajiaghaS.H.R., FarazmehrS., ZavadskasE.K. and AntuchevicieneJ., A novel dynamic credit risk evaluation method using data envelopment analysis with common weights and combination of multi-attribute decision-making methods[J], Computers & Operations Research129 (2021), 105223.
48.
LeH.S., PhamV.V. and PhamV.H., Picture inference system: a new fuzzy inference system on picture fuzzy set[J], Applied Intelligence46(3) (2017), 652–669.
49.
ZhangZ. and LiZ.L., Personalized Individual Semantics-Based Consistency Control and Consensus Reaching in Linguistic Group Decision Making[J], IEEE Transactions on Systems Man Cybernetics-Systems (2021). doi: 10.1109/TSMC.2021.3129510
50.
GaoY. and ZhangZ., Consensus reaching with non-cooperative behavior management for personalized individual semantics-based social network group decision making[J], Journal of the Operational Research Society (2021). doi: 10.1080/01605682.2021.1997654
51.
ZhangZ., LiZ.L. and GaoY., Consensus reaching for group decision making with multi-granular unbalanced linguistic information: A bounded confidence and minimum adjustment-based approach[J], Information Fusion74 (2021), 96–110.
52.
ParkC., AshrafS., RehmanN., AbdullahS. and AslamM., Evaluation of the product quality of the online shopping platform using t-spherical fuzzy preference relations[J], Journal of Intelligent & Fuzzy Systems41(6) (2021), 6245–6262.
