The basic idea underneath the generalized picture fuzzy soft set is very constructive in decision-making, since it considers, how to exploit an extra picture fuzzy input from the director to make up for any distortion in the information provided by the evaluation experts, which is defined by Khan et al. In this paper, we introduce a method to solve decision-making problems using adjustable weighted soft discernibility matrix in a generalized picture fuzzy soft set. We define the threshold functions like mid threshold, top-bottom-bottom threshold, bottom-bottom-bottom threshold, top-top-top threshold, med threshold functions and their level soft sets for generalized picture fuzzy soft sets. After, we propose two algorithms based on threshold functions, weighted soft discernibility matrix, and generalized picture fuzzy soft set. To show the supremacy of the given method we illustrate a descriptive example using weighted soft discernibility matrix in the generalized picture fuzzy soft set. Results indicate that the proposed method is more effective and generalized overall existing methods of the fuzzy soft set.
GorzalzanyM.B., A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets Syst21 (1987), 1–17.
6.
MolodtsovD., Soft set theory-first results, Comput Math Appl37 (1999), 19–31.
7.
MolodtsovD., The Theory of Soft Sets. URSS Publishers, Moscow;2004 (in Russian).
8.
PengX., Some novel decision-making algorithms for intuitionistic fuzzy soft set, Journal of Intelligent and Fuzzy Systems37(1) (2019), 1327–1341.
9.
ZouY. and XiaoZ., Data analysis approaches of soft sets under incomplete information, Knowledge-Based Syst21(8) (2008), 941–945.
10.
XiaoZ., GongK. and ZouY., A combined forecasting approach based on fuzzy soft sets, J Comput Math Appl228(1) (2009), 326–333.
11.
DingQ. and WangY.M., An Improved Aggregation Operators based Method for Multiple Attribute Group decision-making Using Interval-valued Trapezoidal Intuitionistic Fuzzy Sets, Journal of Intelligent and Fuzzy Systems37(1) (2019), 965–980.
12.
PengX. and GargH., Algorithms for interval-valued fuzzy soft sets in emergency decision-making based on WDBA and CODAS with new information measure, 119 (2018), 439–452.
13.
PengX. and YangY., Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision-making based on regret theory and prospect theory with combined weight, Applied Soft Computing54 (2017), 415–430.
14.
GargH. and AroraR., Bonferroni mean aggregation operators under intuitionistic fuzzy soft set environment and their applications to decision-making, Journal of the Operational Research Society69(11) (2018), 1711–1724.
15.
GargH. and AroraR., Novel scaled prioritized intuitionistic fuzzy soft interaction averaging aggregation operators and their application to multi criteria decision-making, Engineering Applications of Artificial Intelligence71 (2018), 100–112.
16.
AgarwalM., BiswasK.K. and HanmandluM., Generalized intuitionistic fuzzy soft sets with applications in decision-making, Appl Soft Comput13 (2013), 3552–3566.
17.
FengF., FujitaH., AliM.A. and YagerR., Another view on generalized intuitionistic fuzzy soft sets and related multi attribute decision-making methods, IEEE Trans Fuzzy Syst27 (2018), 474–488.
18.
KhalilA.M., LiS.G., GargH., LiH. and MaS., New Operations on Interval-Valued Picture Fuzzy Set, Interval-Valued Picture Fuzzy Soft Set and Their Applications, IEEE Access7 (2019), 51236–51253.
ZhangX.Y., WangX., YuS., WangJ. and WangT., Location selection of offshore wind power station by consensus decision framework using picture fuzzy modelling, Journal of Cleaner Production202 (2018), 980–992.
22.
WeiG. and GaoH., The Generalized Dice Similarity Measures for Picture Fuzzy Sets and Their Applications, INFORMATICA29(1) (2018), 107–124.
ZhangS., GaoH., WeiG., WeiY. and WeiC., Evaluation Based on Distance from Average Solution Method for Multiple Criteria Group decision-making under Picture 2-Tuple Linguistic Environment, Mathematics7(3) (2019), 243.
25.
WangL., ZhangH., WangJ. and LiL., Picture fuzzy normalized projection-based VIKOR method for the risk evaluation of construction project, Applied Soft Computing64 (2018), 216–226.
26.
WeiG., Picture Fuzzy Hamacher Aggregation Operators and their Application to Multiple Attribute decision-making, Fundamenta Informaticae157 (2018), 271–320.
27.
WeiG., Picture fuzzy aggregation operator and their application to multiple attribute decision-making, J Int Fuzzy Syst33 (2017), 713–724.
28.
WeiG.W., Picture fuzzy cross-entropy for multiple attribute decision-making problems, J Bus Econ Manag17 (2016), 491–502.
29.
GargH., Some picture fuzzy aggregation operators and their applications to multi criteria decision-making, Arab J Sci Eng42 (2017), 5275–5290.
30.
KhanM.J., KumamP., AshrafS. and KumamW., Generalized Picture Fuzzy Soft Sets and Their Application in Decision Support Systems, Symmetry11(3) (2019), 415; doi: 10.3390/sym11030415.
31.
GargH. and AroraR., Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decisionmaking, Applied Intelligence48(2) (2018), 343–335.
32.
KhanM.J., KumamP., LiuP., KumamW. and AshrafS., A Novel Approach to Generalized Intuitionistic Fuzzy Soft Sets and Its Application in Decision Support System, Mathematics7(8) (2019), 742; doi: 10.3390/math7080742.
33.
SelvachandranG., GargH. and QuekS.G., Vague Entropy Measure for Complex Vague Soft Sets, Entropy20(6) (2018), 403.
34.
HayatK., AliM.I., CaoB.Y., KaraaslanF. and YangX.P., Another View of Aggregation Operators on Group-Based Generalized Intuitionistic Fuzzy Soft Sets: Multi-Attribute decision-making Methods, Symmetry10(12) (2018),753; doi: 10.3390/sym10120753.
35.
HayatK., AliM.I., CarlosA.J., CaoB.Y. and KalimT., Best concept selection in design process: An application of generalized intuitionistic fuzzy soft sets, Journal of Intelligent and Fuzzy Systems35(5) (2018), 5707–5720.
36.
AshrafS., MahmoodT., AbdullahS. and KhanQ., Different approaches to multi-criteria group decision making problems for picture fuzzy environment, Bull Braz Math Soc New Ser (2018), 1–25: doi: 10.1007/s00574-018-0103-y
37.
AshrafS., AbdullahS. and QadirA., Novel concept of cubic picture fuzzy sets, J New Theory24 (2018), 59–72.
38.
ZengS., AsharfS., ArifM. and AbdullahS., Application of Exponential Jensen Picture Fuzzy Divergence Measure in Multi-Criteria Group decision-making, Mathematics7(2) (2019), doi: 10.3390/math7020191
39.
GargH. and AroraR., Maclaurin symmetric mean aggregation operators based on t-norm operations for the dual hesitant fuzzy soft set, Journal of Ambient Intelligence and Humanized Computing (2019), doi: 10.1007/s12652-019-01238-w.
40.
PengX., SelvachandranG., Pythagorean fuzzy set: State of the art and future directions, Artificial Intelligence Review, 3, (2019).
41.
SkowronA., RauszerC., The discernibility matrices and functions in information systems, R. Slowinski (Ed.), Intelligent Decision Support: Handbook of Applications and Advances of Rough Sets Theory, Kluwer Academic Publisher, Dordrecht, (1992), 331–362.
42.
CagmanN. and EnginogluS., Soft matrix theory and its decisionmaking, Comput Math Appl59 (2010), 3308–3314.
43.
FengQ. and ZhouY., Soft discernibility matrix and its applications in decision-making, Appl Soft Comput24 (2014), 749–756.
44.
FengF., JunY.B., LiuX. and LiL., An adjustable approach to fuzzy soft set based decision-making, J Comput Appl Math234(1) (2010), 10–20.
45.
JiangY., TangY. and ChenQ., An adjustable approach to intuitionistic fuzzy soft sets based decision-making, Applied Mathematical Modelling35 (2011), 824–836.
46.
YangY., LiangC., JiS. and LiuT., Adjustable soft discernibility matrix based on picture fuzzy soft sets and its application in decision-making, J Int Fuzzy Syst29 (2015), 1711–1722.
47.
KamaciH., Similarity measure for soft matrices and its applications, Journal of Intelligent and Fuzzy Systems36(4) (2019), 3061–3072.
48.
KamaciH., AtagunA.O. and ToktasE., Bijective Soft Matrix Theory and Multi-Bijective Linguistic Soft Decision System, Filomat32(11) (2018), 3799–3814.
49.
PetchimuthuS. and KamaciH., The row-products of inverse soft matrices in multicriteria decision-making, Journal of Intelligent and Fuzzy Systems36(6) (2019), 6425–6441.
50.
AliM.I., Another view on reduction of parameters in soft sets, Appl Soft Comput12 (2012), 1814–1821.
