The plan of this research is to establish an innovative multi-attribute group decision-making (MAGDM) based on a interval-valued bipolar fuzzy set (IVBFS) by unifying“ VIseKriterijumska Optimizacija I Kompromisno Rasenje (VIKOR)” method. The VIKOR method is regarded to be a helpful MAGDM technique, particularly in circumstances where an expert is unable to properly determine his decision at the outset of the design of the scheme. The theory of set pair analysis (SPA) is a state-of-the-art uncertainty theory consisting of three variables, including “identity degree”, “discrepancy degree” and “opposite degree” of connection numbers (CNs) and a combination of many current theories dealing with vagueness in the data. Inspired by this, we are therefore making an attempt in the current research to enhance the theory of information measurement by incorporating certain metrics using CNs. In this research paper, we present the linguistic VIKOR method in the context of the CNs based metrics obtained from the interval-valued bipolar fuzzy numbers (IVBFNs). First of all, we create CNs of IVBFNs and then CN-based metrics. Secondly, we develop linguistic VIKOR method using CNs based metrics to handle an MAGDM problem under IVBF type information. The predominance and advantages of proposed approach are also highlighted. Furthermore, we demonstrate the efficiency of the extended VIKOR method by solving a numerical example, sensitivity analysis and a detailed comparison with some existing approaches.
AbdullahS., AslamM. and UllahK., Bipolar fuzzy soft sets and its applications in decision making problem, J Intell Fuzzy Syst27(2) (2014), 729–742.
2.
AkramM. and ArshadM., A novel trapezoidal bipolar fuzzy TOPSIS method for group decision-making, Group Decision and Negotiation28(3) (2018), 565–584.
3.
AkramM. and SumaizaS.F., Decision-making with bipolar neutrosophic TOP-SIS and bipolar neutrosophic ELECTRE-I, Axioms7(2) (2018), 33.
4.
AlghamdiM.A., AlshehriN.O. and AkramM., Multi-criteria decision-making methods in bipo-lar fuzzy environment, Int J Fuzzy Syst20(6) (2018), 20–57.
5.
AshtianiM. and Abdollahi AzgomiM., Trust modeling based on a combination of fuzzy analytic hierarchy process and fuzzy VIKOR, Soft Computing20(1) (2016), 399–421.
BenferhatS., DuboisD., KaciS. and PradeH., Bipolar possibility theory in preference mod-eling: Representation, fusion and optimal solutions, Information Fusion7(1) (2006), 135–150.
9.
BeraT. and MahapatraN.K., On Neutrosophic Soft Metric Space, International Journal of Advances in Mathematics2018(1) (2018), 180–200.
10.
BlochI., Geometry of spatial bipolar fuzzy sets based on bipolar fuzzy numbers and mathematical morphology, International Workshop on Fuzzy Logic and Applications WILF 2009: Fuzzy Logic and Applications (2009), pp. 237–245.
11.
CaoY.X., ZhouH. and WangJ.Q., An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis, Int J Mach Learn Cybern9(4) (2018), 629–640.
12.
ChangC.L. and HsuC.H., Multi-criteria analysis via the VIKOR method for prioritizing land-use restraint strategies in the Tseng-Wen reservoir watershed, Journal of Environmental Management90 (2009), 3226–3230.
13.
DuboisD. and PradeH., An overview of the asymmetric bipolar representation of positive and negative information in possibility theory, Fuzzy Sets and Systems160(10) (2009), 1355–1366.
14.
DuttaP. and DoleyD., Medical diagnosis under uncertain environment through bipolar-valued fuzzy sets, Computer Vision and Machine Intelligence in Medical Image Analysis (2019), pp. 127–135, https://doi.org/10.1007/978-981-13-8798-2-13.
GaoH., WuJ., WeiC. and WeiG.W., MADM method with interval-valued bipolar uncertain linguistic information for evaluating the computer network security, IEEE Access99 (2019), 1–1, DOI: 10.1109/Access.2019.2946381
17.
GargH. and AroraR., Dual hesitant fuzzy soft aggregation operators and their application in decision making, Cognit Comput10(5) (2018), 769–789.
18.
GargH. and KumarK., Group decision making approach based on possibility degree measures and the linguistic intuitionistic fuzzy aggregation operators using Einstein norm operations, J Mult Valued Log Soft Comput31(1/2) (2018), 175–209.
19.
GargH. and KumarK., Distance measures for connection number sets based on set pair analysis and its applications to decision making process, Appl Intell48(10) (2018), 3346–3359.
20.
GargH. and KumarK., An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making, Soft Comput22(15) (2018), 4959–4974.
21.
GargH. and KumarK., Some aggregation operators for linguistic intuitionistic fuzzy set and its application to group decision-making process using the set pair analysis, Arab J Sci Eng43(6) (2018), 3213–3227.
22.
GargH. and KumarK., A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory, Artif Intell Revi (2018). https://doi.org/10.1007/s10462-018-9668-5.
23.
GulZ., Some bipolar fuzzy aggregations operators and their applications inmulti-criteria group decisionmaking, M.Phil Thesis (2015)
24.
HanY., LuZ., DuZ., LuoZ. and ChenS., A YinYang bipolar fuzzy cognitive TOPSIS method to bipolar disorder diagnosis, Computer Methods and Programs in Biomedicine158 (2018), 1–10.
25.
HwangC.L. and YoonK., Methods for multiple attribute decision-making. In: G. Fandel, Trockel W(eds), Multiple attribute decision making. Springer, Berlin (1981), 58–191.
26.
JanaC., PalM. and WangJ.Q., Bipolar fuzzy Dombi aggregation operators and its application in multiple-attribute decision-making process, Journal of Ambient Intelligence and Humanized Computing10(9) (2019), 3533–3549.
27.
JanaC., PalM. and WangJ.Q., Bipolar fuzzy Dombi prioritized aggregation opera-tors and its application in multiple-attribute decision-making process, Soft Computing (2019). https://doi.org/10.1007/s00500-019-04130-z
28.
JanaC., PalM. and WangJ.Q., A robust aggregation operators for multi-criteria decision making method with bipolar fuzzy soft environment, Iranian Journal of Fuzzy Systems (2019). DOI: 10.22111/ijfs.2019.4575
29.
JiangY.L., XuC.F., YaoY. and ZhaoK.Q., Systems information in set pair analysis and its applications, In: Proceedings of 2004 international conference on machine learning and cybernetics3 (2004), pp. 1717–1722.
30.
JuY. and WangA., Extension of VIKOR method for multi-criteria group decision making problem with linguistic information, Applied Mathematical Modelling: Simulation and Com-putation for Engineering and Environmental Systems37(5) (2013), pp. 3112–3125.
31.
KayaT. and KahrarnanC., Fuzzy multiple criteria forestry decision making based on an integrated VIKOR and AHP approach, Expert Systems with Applications38(6) (2011), 7326–7333.
32.
LiuH.-C., LiuL., LiuN. and MaoL.-X., Risk evaluation in failure mode and effects analysis with extended VIKOR method under fuzzy environment, Expert Systems with Applications39(17) (2012), 12926–12934.
33.
LuM. and BusemeyerJ.R., Do traditional chinese theories of Yi Jing Yin-Yang and Chinese medicine go beyond western concepts of mind and matter, Mind Matter12(1) (2014), 37–59.
34.
LuoX. and WangX., Extended VIKOR method for intuitionistic fuzzy multi-attribute decision-making based on a new distance measure, Mathematical Problems in Engineering2017 (2017), 16. ID:4072486
35.
MahmoodT., AbdullahS., BilalM. and RashidS., Multiple criteria decision making based on bipolar valued fuzzy set, Ann Fuzzy Math Inf11(6) (2016), 1003–1009.
36.
OpricovicS., Multi-criteria optimization of civil engineering systems, Faculty of Pennsylvania, Belgrade 1998.
37.
PramanikS., DalapatiS., AlamS. and RoyT.K., VIKOR based MAGDM strategy under bipolar neutrosophic set environment, Neutrosophic Sets and Systems19 (2018), 57–69.
38.
PatrascuV., Cardinality and entropy for bifuzzy sets. International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems IPMU 2010. Theory and Methods (2010), pp. 656–665.
39.
PatrascuV., Similarity, Cardinality and entropy for bipolar fuzzy set in the framework of penta-valued representation. (2015), DOI:10.13140/RG.2.1.4727.0566:Source arXiv
40.
RiazM. and TehrimS.T., Cubic bipolar fuzzy ordered weighted geometric aggregation operators and their application using internal and external cubic bipolar fuzzy data, Computational and Applied Mathematics38(2) (2019), 1–25. doi.org/10.1007/s40314-019-0843-3
41.
RiazM. and TehrimS.T., Multi-attribute group decision making based cubic bipolar fuzzy information using averaging aggregation operators, Journal of Intelligent and Fuzzy Systems37(2) (2019), 2473–2494. DOI: 10.3233/JIFS-182751
42.
RiazM. and HashmiM.R., MCGDM for agribusiness in the environment of various cubic m-polarfuzzy averaging aggregation operators, Journal of Intelligent and Fuzzy Systems (2019). DOI:10.3233/JIFS-182809
43.
RiazM. and TehrimS.T., Bipolar Fuzzy Soft Mappings with Application to Bipolar Disorders, International Journal of Biomathematics, (2019) Doi.org/10.1142/S1793524519500803
44.
SarwarM., AkramM. and ZafarF., Decision making approach based on competition graphs and extended TOPSIS method under bipolar fuzzy environment, Mathematical and Computational Applications23(4) (2018), 68.
45.
SayadiM.K., HeydariaM. and ShahanaghiaK., Extension of VIKOR method for decision making problem with interval numbers, Applied Mathematical Modelling33 (2009), 2257–2262.
46.
ShemshadiA., ShiraziH., ToreihiM. and TorakhM.J., A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting, Expert System with Applications38(10) (2011), 12160–12167.
47.
TsueiH. J., TsaiW.H., PanF.T. and TzengG.H., Improving search engine optimization (SEO) by using hybrid modified MCDM models, Artificial Intelligence Review, (2018). https://doi.org/10.1007/s10462-018-9644-0.
48.
WangJ.Q. and GongL., Interval probability stochastic multi-criteria decision-making ap-proach based on set pair analysis, Control Decis24 (2009), 1877–1880.
49.
WeiG., Pythagorean fuzzy interaction aggregation operators and their application to multiple attribute decision-making, J Intell Fuzzy Syst33 (2017), 2119–2132.
50.
WeiG. and WeiY., Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications, Int J Intell Syst33 (2018), 634–652.
51.
YoonK.P. and KimW.K., The behavioral TOPSIS, Expert Syst Appl89 (2017), 266–272.
ZhanJ. and XuW., Two types of coverings based multi-granulation rough fuzzy sets and applications to decision making, Artificial Intelligence Review, (2018). https://doi.org/10.1007/s10462-019-09729-0.
54.
ZhanJ. and AlcantudJ.C.R., A novel type of soft rough covering and its application to multi-criteria group decision-making, Artificial Intelligence Review, (2018). https://doi.org/10.1007/s10462-018-9617-3.
55.
ZhangW.R., Bipolar fuzzy sets and relations: a computational frame work for cognitive modeling and multi-agent decision analysis. In: Proceedings of IEEE conference, (1994), pp. 305–309.
56.
ZhangW.R., Bipolar fuzzy sets. In: Proceedings of FUZZY IEEE, (1998), pp. 835–840.
57.
ZhangW.R. and ZhangL., Bipolar logic and bipolar fuzzy logic, Inf Sci165(34) (2004), 265–287.
58.
ZhangW.R., PandurangiK.A., PeaceK.E., ZhangY. and ZhaoZ., Mental squares: a generic bipolar support vector machine for psychiatric disorder classification, diagnostic analysis and neurobiological data mining, Int J Data Min Bio-inform5(5) (2011), 532–572.
bibitemzhngW.R. Zhang, H.J. Zhang, Y. Shi and S.S. Chen, Bipolar linear algebra and YinYang N element cellular networks for equilibrium-based bio-system simulation and regulation, J Biol Syst17(4) (2009), 547–576.
59.
ZhangW.R., Bipolar quantum logic gates and quantum cellular combinatorics a logical extension to quantum entanglement, J Quantum Inf Sci3(2) (2013), 93–105.
60.
ZhaoK., Set pair and set pair analysis: a new concept and systematic analysis method. In: Proceedings of the national conference on system theory and regional planning, (1989), pp. 87–91.
